Research ArticleCustomized Transportation Equity Participation andCooperation Performance within Logistics Supply Chains

Xudong Lin1 Lijun Ma1 and Zunxin Zheng23

1 College of Management Shenzhen University Shenzhen 518060 China2 College of Economics Shenzhen University Shenzhen 518060 China3 Shenzhen Key Laboratory of Urban Planning and Decision Making Shenzhen Graduate School Harbin Institute of TechnologyShenzhen 518055 China

Correspondence should be addressed to Zunxin Zheng zxzhengszueducn

Received 6 August 2014 Accepted 8 September 2014

Academic Editor Tsan-Ming Choi

Copyright copy 2015 Xudong Lin et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Customized transportation has received growing concerns by researchers and practitioners in recent years Despite the fact thatone consignor often holds partial ownership of its carrier within a supply chain the existing interpretations behind them remainrelatively unexplored Based on the game models we find that a simple take-or-pay contract is not likely to solve the low-efficient customized production problem and equity participation mechanism plus simple contract may improve the cooperationperformance of customized transportation In the case of the owner-managed carrier only when purchasing at par can it beensured to obtain the socially optimal customization investment but when purchasing at premium or discount the optimal partialownership selected by consignor cannotmotivate the carrier tomake themost efficient customization investmentWith the optimalsolutions we also provide a theoretic foundation for calculating the optimal partial ownership and for interpretingwhy the interfirmshare-holding ratios of the member-firms within the familial-type logistic supply chains are much larger than the ratios within thepublic-type logistic supply chains Finally our results show that the familial-type logistic supply chains may choose more efficientcustomized production level than public-type logistic supply chains

1 Introduction

Customized production is a production strategy focused onthe broad provision of personalized products and servicesmostly through modularized productservice design flexi-ble processes and integration between supply chain mem-bers Recent years have witnessed growing concerns aboutcustomized transportation services within logistic supplychains The customization relationships among two or moremember-firms form a complex network in which there existsquite thorough and formal cooperation pointed out by Choi[1] Strategic cooperation usually occurs in the shape ofsubcontracts or manufacturing and marketing interfaces sothat cooperative arrangement for technical sharing technicaltransfer and customization service has become one of themost important cooperation ways in the last two decades [2]

According to Richardson [3] since two parties mustnot only take promised responsibilities for their future

cooperation behaviors but also should be provided withequivalent guarantee then long-term contracts or equityparticipation schemes become the quite formal cooperationways Many of the interfirm research and development(RampD) cooperation in theUnited States among small biotech-nology firms and established pharmaceutical companies arecemented by equity participation [4]

In China it is well documented that many manufacturers(consignor) hold minority equity ownership in their trans-portation service suppliers (carrier) and thereafter thesetransportation service providers make substantial invest-ments such as refrigerating equipment for retaining fresh-ness or integrated ERP systems used as tracking parcelthat Choi et al suggested in [5] and provide customizedtransportation service for their downstream consignor [5 6]just as the similar cases of Japanese auto industry describedby Aoki et al [7 8] In fact these features have been suggestedas some keys to the success of Chinese logistic industry For

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 792792 9 pageshttpdxdoiorg1011552015792792

2 Mathematical Problems in Engineering

the above mentioned cooperation transactions why is equityparticipation adopted rather than long-term contract Thatis exactly the paradox in transaction efficiency from differentcooperative arrangements that we want to investigate

In reality due to the complexity and uncertainty of futureaffairs and tradersrsquo bound rationality it is impossible orimplausible to list all the related details of contract whentaking transaction cost into consideration Since incompletecontracts cannot resolve the ldquohold-uprdquo problem of oppor-tunists and discounts its value [9] under the backgroundsof opportunism [10] assets specificity [11] incomplete con-tracts and futurersquos uncertainty [12] various organizationalinterventions such as vertical integration exchange hostagesshifting property rights and designing an authority relation-ship are proposed to solve the ldquohold-uprdquo problem which canprevent two parties from breaking a contract

Cooperative transaction among member-firms withinlogistic supply chain may lose efficiency because of expost opportunistic behavior caused by specific investmentresulting likely from customized production or outsideoptions Williamson [13] Klein et al [14] believe that specificinvestment does not likely acquire the optimal efficiencywith the anticipation of ex post opportunistic behaviors andvertical integration instead of spotmarket can avoid or reduceopportunistic behaviors caused by assets specificity The finalchoice is made based on the comparison of transaction costsof two types of cooperative mechanisms

However integration (internal transaction) is not alwaysmore outperformed than market transaction which meansthat it would lead to inefficiencywhen all productive activitiesare arranged in one integrated organization Why cannotmarket relationship among independent entities be replacedfully by integration Williamsonrsquos replacement model pro-vides the following reasons for avoiding integration Thatis if firms manufacture inputting products by themselveseconomies of scale and economies of scope may not beachieved Otherwise when the degree of assets specificity islow governance cost of internal organizations will be largerthan that of market organizations [13] When analyzing thedisadvantage of governance cost of internal organizationsrelated interpretations of loss of control rights and malfunc-tion of selective optimal intervention are convincing

Based on the criticism and inheritance of existent theo-ries Milgrom and Roberts [15] propose that the cost of polit-ical activities within one organization is also an importantobstacle for concentration of control rights which interpretsthat internal transaction within integration organizations isnot always better than market transaction among entitiesin view of nonmarket transaction costs The limitations ofintegration organizations indicate that a single mode ofintegration among parent firm and its member-firms is notoptimal and the concurrence of various bonding relation-ships within supply chains is a feasible choice of decision-makers when constructing an up-down stream relationship

With growing cooperation transactions within sup-ply chains share-holding arrangement (partial ownership)becomes one of the most important cooperative schemesHowever there are few theoretical explanations aiming atequity participation phenomena especially within logistic

supply chain [2 16] Conventional wisdom is that partialownership by reducing opportunism helps to promotethe bond between upstream firms and downstream firmsthrough inspiring greater specific investment and customizedproduction level [9ndash12] So without contractual remediesequity participation may perhaps play a role instead How-ever under symmetric information equity participation bythe downstream firm in an upstream supplier has no effect onthe payoffs when two parties bargain to allocate the benefitsof specific investment [11] In view of this it remains unclearhow partial ownership promotes the bond

In the related models Bolton and Whinston [17] andRajan and Zingales [18] discuss how to make optimal own-ership allocation in details However they only make someanalyses about efficiency loss within integration organizationbut do not measure enhanced efficiency resulting fromcooperation mechanism of partial ownership Different fromtheir works this paper focuses on demonstrating what rolespartial ownership plays in customized production used tomotivate investors and simultaneously probing into why thecomplete ownership is not possible to be optimal

Dasgupta and Tao [19] provide some theoretical interpre-tations for partial ownership phenomena based on the mod-els about selective investment decisionmade by the upstreamfirms They consider two types of investment in whichspecific investment levels differ Given potential income ofinvestment to be random when the downstream firm holdspartial ownership of the upstream firm the upstream firmwould choose more efficient types of investment than thesimple contract

Compared with innovative mechanism design theory ofownership suggested by Aghion and Tirole [20] Dasguptarsquostheoretical interpretation on partial ownership is more pro-found as they not only agree on the viewpoint that the relativebargaining power of the trade parties will affect the efficiencyof ownership allocation but also install the bargaining powerparameter into the models and obtain the relevance betweenthe related parameters and the magnitude of partial owner-ship When the downstream firm takes equity participationratio into account the optimal partial ownership is not onlyof the credible commitment that can boost the upstream firmto choose a high specific investment level but also of themechanism arrangement in order tomaximize the benefits ofthe downstream firmThe equity participation ratio decisionmust tradeoff these two mechanisms which means that thedownstream firm maximizing its own benefits does not haveto choose equity participation ratio that can motivate theupstream firm to make the complete specific investment

Hence viewing customization level as a variable chosenby the upstream firmmay meet the realistic condition withinlogistic supply chains better In this paper the potentialincome of customization investment is assumed to increasewith customized production level which accords with ratio-nal principle and is our logic starting point of research

In addition the existence of partial ownership mayaffect customization decision and the success probability ofobtaining outside opportunity income slightly On the onehand partial ownership could lower the diligence expen-diture of the upstream firmrsquos entrepreneurs On the other

Mathematical Problems in Engineering 3

hand it has the supervisory effects on them imposed by thedownstream firm which was neglected by Dasgupta and Tao[19] but is taken into account in our paper Then in factpartial ownership wonrsquot change the diligence expenditure ofdecision-makers evidently Once investment and customizedproduction are made both the investment income and theoutside option income are supposed to be realizable This iswhy we incorporate customization level partial ownershipand outside opportunity into the same analytical frameworkwhich become a key point that distinguishes our researchfrom other customization literatures

In addition to analyzing the case of the owner-managedupstream firms our model also involves the case of public-firms managed by professional managers Obviously thedecision-makers of these two kinds of firms have so manydifferences between their customization decision behaviorsthat we should probe into them separately From this angle ofview we can demonstrate why the familial-type logistic sup-ply chains may choose more efficient customized productionlevel than public-type logistic supply chains

The remaining portion of this paper is organized asfollows Section 2 outlines the basic model and analyzesthe limitations of the simple contract Section 3 probes intothe problem of equity participation of the owner-managedcarrier Section 4 discusses the first-best partial ownership ofthe publicly traded carrier Section 5 analyses the effects of theoptimal ownership strategy on the efficiency of customizedtransportation Finally conclusion is made in Section 6

2 The Customized Transportation Models

21 Model Settings Assuming that the member-firms withinthe logistic supply chain are respectively one carrier andone consignor in a transportation trade the two parties canmake the specific investment for customized transportationbilaterally or unilaterally Without loss of generality weassume that the carrier can make the unilateral specificinvestment and customized transportation for consignorwhich can increase the goodsrsquo value of the consignor Forexample if the carrier invests in refrigerating equipment orant-vibration appliance for consignorrsquos goods in the great riskof decoy or brittleness then this customized transportationwould increase the goodsrsquo value and consignor would make alarger profit

The carrier can either be owner-managed firms or public-firms run by professional managers Here we call the own-ers of owner-managed firms as entrepreneur and call thedecision-maker of the publicly traded firm as the managerWe assume that the consignor is run by professional man-agers in the interest of the stockholders To bementioned theowner-managed consignorwill not affect our analysesUnlessspecially pointed out carrier is seen as an owner-managedone in our analyses In addition all players are assumed to berisk-neutral

For simplicity of the analyses and the generalization ofmodels three stages of game are considered that is 119905 = 0 1 2At 119905 = 0 the consignor offers to buy a fraction 119903 isin [0 1] ofthe transportation carrier at price 119875(119903) and the entrepreneurcan accept or reject the offer

At 119905 = 1 the entrepreneur chooses the customizationlevel parameter 119886 based on the potential value 119881(119886) andthe cost function 119862(119886) of customized transportation where119886 isin [0 1] Larger 119886 means the higher customized trans-portation level for carrier In order to grasp the nature ofcustomization investment behavior we assume the value oftransportation service 119881(119886) and its investment in customizedtransportation for example 119862(119886) are convexly increasing in119886 For simplifying analyses and without loss of generalitywe adopt the following function shape 119881(119886) = 119890

119886

119892 and119862(119886) = 120573119886

2 where 119892 represents the general transportationservice value without customized investment (in the case of119886 = 0) and 120573 is a constant expressing the needed investmentin the case of complete customization service In additionwe also suppose that the net revenue function of customizedproduction [119881(119860) minus 119862(119860)] is concave which ensures thatthere exists the optimal 119886 in our analyses That is forall119886 isin [0 1]

and 119903 isin [0 1] and inequalities 119890119886

119892 gt 2120573119886 and 119890119886

119892 lt 2120573 holdAt 119905 = 2 119881(119886) and 119862(119886) are realized 119881(119886) and 119862(119886)

are common knowledge but they cannot be verified so thecontract cannot be consigned on it

Then we consider that at 119905 = 0 the carrier and theconsignor sign a simple take-or-pay contract and (119875

119879 119875119873

) isthe payoff portfolio the consignor will pay to the carrier intwo cases when trade in the contract occurs or not At 119905 = 2the carriermakes renegotiationwith the consignor bilaterallyIf the renegotiation between them fails carrier will trade withother consignor and the potential value of the customizationwill be reduced to 119892(1 minus 119886)

If the relative bargaining power of the consignor isassumed to be 120582 then that of the upstream carrier is (1 minus

120582) where 120582 isin [0 1] We incorporate the analyses ofsurplus allocation in the cases of trade or nontrade into theframework of the Nash bargaining solutions By backwarddeductivemethod since (119875

119879 119875119873

) can be renegotiated at 119905 = 2it means (119875

119879 119875119873

) should obey the constraints of the Nashbargaining solutions

Under what condition could simple contract (119875119879 119875119873

)

acquire the optimal incentive outcome And why can equityparticipation arrangement enhancemore efficient customiza-tion level These paradoxes are what we are interested in

22 Simple Contract and Customization Level Choice Givensimple contract (119875

119879 119875119873

) and the equity participation ratior of consignor the payoff matrix of two trading partiesis expressed as in two cases when the negotiation eithertriumphs (denoted by T) or fails (denoted byN) as following

Carrier Consignor119879 (1 minus 119903) [119875

119879minus 119862 (119886)] 119881 (119886) minus 119875

119879+ 119903 [119875

119879minus 119862 (119886)]

119873 (1 minus 119903) [119875119873

+ 119892 (1 minus 119886) minus 119862 (119886)] 119903 [119875119873

+ 119892 (1 minus 119886) minus 119862 (119886)] minus 119875119873

(1)

In the game model of the repeated bargains the Nashbargaining solutions require that contract (119875

119879 119875119873

) satisfies

max (1 minus 119903) [119875119879

minus 119862 (119886)]

minus (1 minus 119903) [119875119873

+ 119892 (1 minus 119886) minus 119862 (119886)]1minus120582

4 Mathematical Problems in Engineering

lowast 119881 (119886) minus 119875119879

+ 119903 [119875119879

minus 119862 (119886)]

minus 119903 [119875119873

+ 119892 (1 minus 119886) minus 119862 (119886)] + 119875119873

120582

(2)

The first order condition of 119875119879demands

(1 minus 120582) (1 minus 119903)

(1 minus 119903) [119875119879

minus 119875119873

minus 119892 (1 minus 119886)]

+120582 (119903 minus 1)

119881 (119886) minus 119875119879

+ 119903 [119875119879

minus 119875119873

minus 119892 (1 minus 119886)] + 119875119873

= 0

(3)

Then

119875119879

=[119890119886

minus 119903 (1 minus 119886) + (1 minus 119886 minus 119890119886

) 120582] 119892

1 minus 119903+ 119875119873

(4)

Using payoff matrix we know that when transactionoccurs the revenues of carrier and consignor are (1 minus 119903)[119875

119879minus

119862(119886)] and (119881(119886) minus 119875119879

+ 119903[119875119879

minus 119862(119886)]) respectively expressedby 119878119879(119903 119875119873

) and 119861119879(119903 119875119873

) So we have

119878119879

(119903 119875119873

) = [119890119886

minus 119903 (1 minus 119886) + (1 minus 119886 minus 119890119886

) 120582] 119892

+ (1 minus 119903) [119875119873

minus 1205731198862

]

119861119879

(119903 119875119873

) = [119890119886

120582 + (1 minus 119886) (119903 minus 120582)] 119892

minus (1 minus 119903) 119875119873

minus 1199031205731198862

(5)

The socially optimal customization level choice mustsatisfy

max119886

[119881 (119886) minus 119862 (119886)] (6)

The first order condition demands119890119886

119886=

2120573

119892 (7)

That is the first-best customization level parameter 119886fb =

arg[119890119886

119886 = 2120573119892] But if 119903 = 0 can (119875119879 119875119873

) make sure thatthe entrepreneur chooses 119886fb

For simplicity of the analyses let 119875119873

= 0 and then itdemands that the manager chooses 119886

lowast to maximize carrierrsquosrevenue as follows

119886lowast

= argmax119886

119878119879

(119903 119875119873

) (8)

Then we have

119886lowast

= argmax [119890119886

119886=

120582 minus 119903

(1 minus 120582) 119886+

2 (1 minus 119903) 120573

(1 minus 120582) 119892] (9)

When 119903 = 0 above equation can be changed into

119886lowast

= argmax [119890119886

119886=

120582

(1 minus 120582) 119886+

2120573

(1 minus 120582) 119892] (10)

Apparently from 120582 isin [0 1] we can deduce

120582

(1 minus 120582) 119886+

2120573

(1 minus 120582) 119892ge

2120573

119892 (11)

The function [119881(119886) minus 119862(119886)] is concave so119886lowast

le 119886fb (12)It means when the entrepreneur of the upstream carrier

has the whole bargaining power (120582 = 0) simple contract(119875119879 119875119873

) can induce the entrepreneur to choose the optimalcustomization level It is not difficult to understand thatwhen the entrepreneur with an overwhelming bargainingpower can obtain all of investment surplus he or she willmake the choice of the fist-best customization level It isconsistent with the interpretation of Choi et al [19ndash22] thatthe incomplete contract can also lead to efficient outcomesunder some special conditions

But when 120582 gt 0 (119875119879 119875119873

) contract cannot ensure thatthe entrepreneur would make the efficient customizationinvestment Then how many ration of equity participationcan result in efficient outcomes

If 119886lowast

= 119886fb then 1198811015840

(119886lowast

) = 1198621015840

(119886lowast

) This means120573119897

119892=

120582 minus 119903

(1 minus 120582) 119886+

2 (1 minus 119903) 120573

(1 minus 120582) 119892 (13)

Obviously only when 119903 = 120582 may (14) hold Since 119875119879

=

119881(119886fb) then (119875119879 119875119873

) = (119881(119886fb) 0)Integrating the above analyses we can conclude the

following

Proposition 1 (i) Only when the entrepreneur of carrieroccupies all of bargaining power (eg 120582 = 1) can simplecontract (119881(119886

119891119887) 0) result in the socially optimal customization

level chosen by carrier (ii) but if 0 lt 120582 lt 1 theefficient customization investment outcome can be obtainedonly through equity participation 119903 = 120582 plus simple contract(119881(119886119891119887

) 0)

Proposition 1 does not mean the consignor 119889 must makethe decision of equity participation 119903 = 120582 at 119905 = 0 becauseas a rational entity maximizing its benefit the consignorwould not only consider the customization efficiency of theupstream carrier but alsomake benefit-cost analyses of equityparticipation Hence the optimal equity participation rationeed not satisfy the condition under which the managerwould choose the socially optimal customization level Innext section we will discuss the problem about optimalequity participation ratio

3 Equity Participation by Consignor inOwner-Managed Carrier

This section aims at obtaining the comparative static outcomeaffecting the equity participation ratio factors so we willinstall the cost items related to the equity participation inorder to obtain the internal angle solution about the optimalpartial ownership

31 Optimal Equity Participation Ratio Given 119903 theentrepreneur will choose 119886

lowast to maximize the customizationinvestment revenue that is

119886lowast

= argmax119886

119878119879

(119903) (14)

Mathematical Problems in Engineering 5

Given 119886 chosen by carrier at 119905 = 1 the managerof consignor would at 119905 = 0 decide on optimal equityparticipation ratio 119903 to maximize its total net income Aswe all know under the mechanism of partial ownershipthe consignor can get a lot of benefits from customizedtransportation but must pay for obtaining partial ownershipof carrierThe reason why complete vertical integration is notalways the optimal choice lies in the fact that the integrationcost is likely to exceed the added-value benefits of customizedtransportation

Assuming that other outside income of the upstreamcarrier is 120587

0 we express 119875(119903) that the consignor pays for

obtaining an equity ratio 119903 of the carrier in the followingequation

119875 (119903) = (1 + 120579) [(119878119879

(119900) + 1205870) minus (119878

119879(119903) + (1 minus 119903) 120587

0)] (15)

In this equation (119878119879(119900)+120587

0) term represents total income

of entrepreneur when 119903 = 0 and (119878119879(119903) + (1 minus 119903)120587

0) is the

correspondent revenue that entrepreneur earns when equityparticipation ratio is 119903 The surplus between these two termscan be regarded as the real value of the equity fraction 119903

of the upstream carrier Let 120579 denote the average premium(discount) price coefficient at which the consignor acquires afraction 119903 of the carrier where 120579 gt 0 represents purchasingat premium 120579 = 0 represents purchasing at par and 120579 lt 0

represents purchasing at discount In order to accord with theactual scenarios of equity fight we install 120579-coefficient intothe formula to calculate 119875(119903)

Let 120587119889denote net income of the downstream consignor

then120587119889

= 119861119879

(119903) + 1199031205870

minus 119875 (119903) (16)

Substituting 119861119879(119903) and 119875(119903) into above equation we get

120587119889

= 119890119886

119892 minus 1205731198862

+ 120579119878119879

(119903) minus 1205791205870119903 minus (1 + 120579) 119878

119879(0) (17)

Anticipating that the entrepreneur chooses 119886lowast based on

equity participation ratio 119903 that is 119886lowast

= 119886lowast

(119903) the managerof the downstream consignor will try to acquire optimalequity ratio 119903

lowast for maximizing 120587119889 that is

119903lowast

= argmax119903

120587119889 (18)

The first order condition demands120597119886lowast

120597119903[1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)]

+ 120579 [119862 (119886lowast

) minus 119892 (1 minus 119886lowast

)] minus 1205791205870

= 0

(19)

Without loss of generality suppose 1205731198862

fb minus 119892(1 minus 119886fb) le 0we will discuss the results in the cases of different 120579-values

32 The Effects of 120579 on 119886lowast and 119903

lowast

(1) 120579 gt 0 which means purchasing at premiumBy (9) we know

1205972

119878119879

(119903)

120597(119886lowast)2

lt 0 (20)

Moreover 1205972119878119879(119903)120597119886

lowast

120597119903 = 2120573 gt 0

Thus 120597119886lowast

120597119903= (minus1205972

119878119879(119903)120597119886

lowast

120597119903)(1205972

119878119879(119903)120597(119886

lowast

)2

) gt

0Since 119881

1015840

(119886lowast

) minus 1198621015840

(119886lowast

) lt 0 when 120579 is sufficientlysmaller we have

120597120587119889

120597119903|119903=0

gt 0

120597120587119889

120597119903|119903=120582

= 120579 [119862 (119886fb) minus (1 minus 119886fb) 119892 minus 1205870] lt 0

(21)

Thus the optimal partial ownership 119903lowast

isin (0 120582) andwe can get 119886

lowast

gt 119886fbIf 120579 is sufficiently larger forall119903 isin [0 1] 120597120587

119889120597119903 lt 0 then

119903lowast

= 0

(2) 120579 = 0 which means purchasing at parObviously for (19) to hold it requires

1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

) = 0 (22)

Then 119903lowast = 120582 and 119886lowast

= 119886fb(3) 120579 lt 0 which means purchasing at discount

Evidently when the value of the upstream fabric supplieris underestimated the consignor will buy as much equity aspossible to maximize its total net income Although over-incentive effects of equitymay lead to customized productionlevel exceeding the social optimality and the increase ofthe equity investment revenue renders the manager of theconsignor to purchase the share of 119903

lowast greatly exceedingsocial optimal level that is 119903

lowast

gt 120582 Besides when theshare-holding ratio of the downstream consignor exceeds theentrepreneurrsquos the customization level of carrier should equalthe social optimal one So we have

119886lowast

= 119886fb if 119903lowast

ge1

2

lt 119886fb if 119903lowast

lt1

2

(23)

If 120579 is sufficiently negative then 119903lowast

= 1 and 119886lowast

= 119886fbNotably we regard 120579 as a constant in this paper which doesnot affect our analyses about the optimal equity participationratio

But what we must pay attention to is that with 119903

vibrating average discount (or premium) price parameter 120579

may also be changeable The exact magnitude of the optimalcustomization level 119886 and partial ownership 119903 will depend on120579-value

The three-dimension chart (see Figure 1) shows thatwhen 120579 drops from 04 to minus04 120587

119889(119886 119903) the equilibrium

path demonstrates an increasing trend and the optimalcustomization level 119886 is increasing in 119903 With equity purchaseshifting from discount price to premium price the drop ofoptimal equity participation ratiowill result in the customiza-tion transportation level and the net income of consignordecreasing simultaneously

6 Mathematical Problems in Engineering

0 01 02 03 04 05 06 07 08 09 1

001020304050607minus02minus01

00102030405

ar

120579 = minus04120579 = minus02120579 = 0

120579 = 02120579 = 04

120587d

Figure 1 The relationship chart among 120587119889 119886 and 119903 given 120582 = 05

120573 = 2 and 119892 = 2

Concluding the above analyses we get the following

Proposition 2 (i) If 120579 is a sufficiently small positive value119862(119886119891119887

)minus119892(1minus119886119891119887

) le 0 the consignor holds the optimal partialequity of the carrier 119903

lowast

isin (0 120582) and the customization levelwhich the entrepreneur chooses is below social optimal levelthat is 119886

lowast

lt 119886119891119887 If 120579 is sufficiently larger choosing 119903

lowast

= 0 willbe beneficial for the consignor

(ii) In the case when purchasing at par (120579 = 0) 119903lowast

= 120582

and 119886lowast

= 119886119891119887

hold and the efficient customization level can beobtained

(iii) In the case when purchasing at discount 119903lowast

gt 120582 and119886lowast

gt 119886119891119887

hold and optimal partial ownership can motivate theentrepreneur to choose the socially optimal customization type

Proposition 2 demonstrates that only when purchasing atpar can optimal equity participation mechanism make surethat themost efficient outcome is obtainedWhen purchasingat premium or discount price the distortion effects of wealthtransfer will make the customization outcome brought upby optimal partial ownership deviate from social optimalinvestment type

According to Proposition 2 we can interpret why theaverage equity ratios Chinese consignors hold of carriersrsquoequity ownership exceed the corresponding value of Amer-ican firms under the condition of the same technologyparameters In China majority equity ownership of the firmsis under the control of individual investors or institutioninvestors the exchange ratio of the stock is very low and theexchange of stock is often solved by private negotiation [22]Generally in this case 119875(119903) will not deviate seriously from itsreal value and 120579 is likely to be bigger than zero slightly Butin the United States whose capital markets are very matureequity ownership of firms is widely dispersed the publicshareholders hold the majority equities the ownership 119903 isobtained by exchange in the stock market and the bids ofmany trade entities lead to 120579-value exceeding zero greatly[23ndash25] Therefore when other technical parameters arenot changed the mechanism that the greater 120579-value wouldlead to the smaller 119903

lowast will result in the interfirm equityparticipation ratio in China to be obviously higher than thatof the same industry in the United States

4 Equity Participation by the Consignor inthe Public-Type Carrier

In this section we will expand our analyses of the opti-mal partial ownership to the public carrier operated byprofessional managers When the carrier is not owner-managed but is a public-firm the analyses of last sectiondo not apply completely in that professional managers inthe interest of the stockholders will not be affected directlyby the dispersive equities when considering investmentincome Even so our analyses belowdemonstrates that partialownership still affects the customization choice of managersand a conclusion similar to the last section will be obtained

For simplicity of analyses besides the assumption that themanager of carrier is risk neutral we also assume that thereexists nomanagerrsquosmoral hazard about reward compensatingmechanism and endeavor choice problem Assume thatrewards of manager are a minority part of the whole profit ofcarrier which ensures that manager makes decisions in theinterest of the stockholders Based on these assumptions wecan attain the bargaining outcome below

Lemma 3 Given r and 120582 let 119875119873

= 0 then the consignor pays

119879

=(1 minus 120582) 119890

119886

119892 + (120582 minus 119903) 119892 (1 minus 119886)

1 minus 119903

(24)

to the public-type carrier

And the incomes obtained by the two trade parties arerespectively

119878119879

(119903) =(1 minus 120582) 119890

119886

119892 + (120582 minus 119903) 119892 (1 minus 119886)

1 minus 119903minus 1205731198862

119861119879

(119903) = 120582119892119890119886

minus (120582 minus 119903) 119892 (1 minus 119886) minus 1199031205731198862

(25)

From the payoff matrix of two trade parties we canobtain

119879= 119875119879 that is no matter what type the carrier

belongs to the payoffs of the consignor are the same Thereexist differences between two types of carrierrsquo trade incomefunction But for the consignor the function formof the tradeincome remains unchanged

Observing that the manager of the carrier will choosethe customization level 119886

lowast to maximize its utility given themanagerrsquos risk neutrality we know

119886lowast

= arg[120597119878119879

(119903)

120597119886= 0] (26)

Given 119903 the manager would choose 119886lowast

(119903) to maximizethe earnings of the carrier then decision-makers of consignorcan decide on equity participation ratio to maximize its netincome

119889 Here we adopt the form below to describe

119889

119889

= 119861119879

(119903) + 1199031205870

minus (119903) (27)

where (119903) denotes the price at which the consignor buys afraction 119903 of equity of the carrier Assuming that the faction119903 of equity is purchased through tender offers the real value

Mathematical Problems in Engineering 7

120575(119903) of the carrier based on the partial ownership 119903 can beexpressed as

120575 (119903) = 119878119879

(119903) + 1205870 (28)

(119903) can be denoted as follows

(119903) = (1 + 120579) 119903120575 (119903) (29)

Therefore the total net income of the consignor can bedescribed as

119889

= 119861119879

(119903) + 1199031205870

minus 119903 (1 + 120579) [119878119879

(119903) + 1205870] (30)

The optimal partial ownership 119903lowast must satisfy the first-

order condition

120597119889

120597119903 | 119903 = 119903lowast

= 0 (31)

We further have

(120597119886lowast

120597119903) [1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)] minus 120579119878119879

(119903) minus 1205791205870

minus(1 + 120579119903) (1 minus 119886) 119892

(1 minus 119903)2

= 0

(32)

Obviously when 120579 gt 0 and is sufficiently small 119903lowast

isin

(0 120582) Similar to the conclusions of the last section the valuesof 119886lowast and 119903

lowast will be adjusted to correspond to positive ornegative 120579-value In this paper we will only analyze the caseof 120579 gt 0

By (32) we get

1205972

119889

120597119903120597120582= [

120597119886lowast

120597119903] [11988110158401015840

(119886lowast

) minus 11986210158401015840

(119886lowast

)] [120597119886lowast

120597120582] minus

1 + 120573119903

(1 minus 119903)2

lowast [minus (1 minus 119886lowast

) 119881 (119886lowast

) minus (1 minus 120582) 119881 (119886lowast

) (120597119886lowast

120597120582)

+ (1 minus 119886) (1 minus 120582) 119881 (119886lowast

) (120597119886lowast

120597120582)]

+ [1205972

119886lowast

120597119903120597120582] [1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)] +120573 (1 minus 119886

lowast

) 119881 (119886lowast

)

1 minus 119903

(33)

By 120597119878119879(119903)(120597119886 | 119886 = 119886

lowast

) = 0 we know

120597119886lowast

120597119903gt 0

120597119886lowast

120597120582lt 0

1205972

119886lowast

120597119903120597120582lt 0 (34)

Then in (33) all the right-hand terms exceed zero thus

1205972

120587119889

120597119903120597120582gt 0 (35)

Since Sign(120597119903lowast

120597120582) = Sign(1205972

119889120597119903120597120582) we can get

120597119903lowast

120597120582gt 0

120597119903lowast

1205971205870

lt 0 (36)

0 01 02 03 04 05 06 07 08 090

010203040506070809

1

r

a

120582 = 02120582 = 05120582 = 08

Figure 2 The relationship chart between 119886 and 119903 given 120573 = 2 119892 =

12

Given the values of 120582 120573 and 119892 we can find out therelationship between 119886 and 119903 through numerical simulationin Figure 2

Our numerical result shows that parameters 119886 and 119903 areincreasing function of 120582 and 119886 increases nonlinearly in r

From the above analyses we can conclude the following

Proposition 4 Assuming that the carrier is a public-firmmanaged by the manager in the interest of the share-holderswhen purchasing at premium price the optimal equity partic-ipation ratio 119903

lowast by the consignor increases in 120582 but decreasesin 1205870

5 Discussions about Customized ProductionEfficiency and Policy Implications

The theory of optimal ownership structure extracts thedistillate of two stream academic ideas the financial structuretheory and the managerial motivation theory which havebeen agreed on in economic literature [19] For exampleJensen andMeckling [26] pointed out that agent costs causedby dilution of ownership are derived from the fact thatthe incentive of inside controllers cannot keep track withthat of the ownerrsquos On the other hand many academicpapers demonstrate that an outside artificial person whoholds a major part of ownership has a positive effect onthe firmrsquos value [10 17 26ndash28] These papers emphasizedthe supervising function of the outside artificial personsrsquoshare-holders to the firmrsquos managers Compared with theseexisting articles we provide a theoretical interpretation whyoutside artificial persons hold partial ownership under thecircumstance of vertical transaction relationship Our resultis if the downstream firm holds partial ownership of theupstream firm it may function as a bonding mechanismwhich improves the performance of twoparties Itmeans thatcompared with 119903 = 0 the mechanism of partial ownershipimproves the efficiency of customization service

However can the optimal partial ownership result insocial optimal customized transportation level

As we know no matter what type the carrier is eitherowner-managed one or a public-firm managed by managers119903lowast

= 120582 or 119903lowast

= 05 is the necessary condition bringing in

8 Mathematical Problems in Engineering

social optimal customization level If the carrier is an owner-managed one only when the purchasing of partial ownershipat par price occursmay choosing 119903

lowast

= 120582 be a rational decisionfor the consignor aiming at maximizing its total net incomeBut purchasing at premium price is dominant in reality ifcalculated under general case of 120582 = 05 the optimal partialownership 119903

lowast is less than 120582 not large enough to motivatethe decision-maker of the carrier to choose the most efficientcustomized production level The marginal return obtainedby the consignor through enlarging equity participation ratiowill be offset by marginal costs of purchasing the equityownership and premium price distorting effects lead to theefficiency loss of the carrierrsquos customization investment (119903

lowast

lt

05)On the opposite when purchasing at discount overmoti-

vation leads to 119903lowast

gt 120582 and the customization efficiency lossmay still occur Therefore we hold that the effect of wealthtransfer in the purchase of equity ownership is the mainreason that leads to efficiency loss of customized productionwhich shows our theory about partial ownership differentfrom the entrepreneur endeavor choice interpretation byDasgupta and Tao but similar to the conclusion of Aghionand Tirolersquos that partial ownership arrangement can motivatespecial investment but cannot solve the investorsrsquo underin-vestment problem totally

However when the carrier is public-managed even ifthere exist 120579 = 0 and the optimal partial ownership 119903

lowast

lt

120582 social optimal customization level cannot be obtainedbecause the benefit of the consignor does not keep consistentwith the trade partiesrsquo common benefit When 120579 gt 0119903lowast will become smaller and the higher loss degree of thecustomization investment efficiency will occur Obviouslyunder the second-order condition constraint that we can getthe optimal solution satisfying (32) the larger the averagepremium price parameter is the smaller 119903

lowast is the lowercustomized production efficiency becomes and the greatersocial welfare loss will be which holds true in the caseof owner-managed carrier As for the case of 120579 lt 0 itaccords with the aforementioned analyses that is the over-motivation of equity ownership may lead to customizedproduction efficiency loss

In China the state-owned equity reform in logisticindustry just began with unclear ownership partition andmany social functions assumed by firms are not peeled offThe high premium-price acquisitions may make carriers tochoose 119903

lowast

= 0 which leads to the undermotivation of thecustomization investment of consignors and the social opti-mal customized transportation cannot be realizedThereforein the developing process of logistic supply chains in Chinait is necessary that the logistic firms should become theentities that can be self-managed self-constricted and self-motivated and the burden of the social functions will lead tothe loss of the transportation efficiency which are all what wemust pay attention to

In addition when all technical parameters keep constantcomparing optimal partial ownership in the cases of twodifferent types of carrier we can discover that in theorythe ratio of optimal equity participation by the consignor inthe owner-managed carrier should exceed the ratio in the

public-managed firm that is 119903lowast

gt 119903lowast It provides a theoretic

foundation for us to interpret that the interfirmmutual share-holding ratios of the member-firms within the familial-typelogistic supply chains aremuch larger than those ratioswithinthe public-type logistic supply chains At the same time italso means that the customized production efficiency of theformer is higher than that of the latter Although there is roomfor improvement we still firmly believe that the success ofChinese logistic industry should be mainly attributed to theadvantage of owner-managed efficiency

To be mentioned the mechanism of partial ownershipundoubtedly improves the cooperative efficiency of twotrade parties Although social welfare level this arrangementprovides is not optimal the cooperative mechanism helpsto enhance Pareto improvement of the return of two tradeparties compared with simple contract system

6 Conclusions

The phenomena that one consignor holds equity ownershipof one carrier within logistic supply chain are often observedDespite its importance the existing interpretations for inter-firm partial ownership scheme remain relatively unexploredIn this paper a theoretical explanation for equity partici-pation arrangement existing between member-firms withinlogistic supply chain is provided under the background ofcustomized production

Based on the models in which we view the parame-ter for customization level as the selective variable of thecarrier we figure out that the simple contract cannot solvethe low-efficient customized production problem Equityparticipation mechanism together with simple contract canimprove the efficiency of customized transportation Thepartial ownership mechanism supported by customized pro-duction plays a role as a bond in keeping the relationaltransactions among member-firms but not a role as theefficiency-enhancing mechanism resulting from outside arti-ficial personsrsquo supervision in some literature about equityownership structure

What is more on the basis of keeping the logic deductiveconsistency we obtain the outcome of the optimal partialownership affected by the relative bargaining power 120582 ofthe consignor and the other outside income 120587

0of the

carrier under two cases of owner-managed firm type andpublic-firm type respectively and showwhy the familial-typelogistic supply chains may choose more efficient customizedproduction level than public-type logistic supply chains

To be mentioned our theory provides few cases inwhich we can verify the interfirm equity participation ratioAlthough many important conclusions we obtain seem to beconsistent with some evidences there is a need for furtherstudy such as analyzing bilateral cross-shareholding case andconsidering the relationship between bargaining power andequity participation ratio through extending our models

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Mathematical Problems in Engineering 9

Acknowledgments

We acknowledge financial support from the National NatureScience Foundation of China (Grant nos 71001073 71371127and 71471118) the National Soft Science Research Plan(Grant no 2013GXS4D138) the Humanities and SocialSciences Foundation of Ministry of Education of China(Grant nos 13YJA630050 and 14YJC630096) DevelopmentProgram for Distinguished Young Teachers in Higher Edu-cation of Guangdong Province (Grant no Yq2013140 andYq2013147) and the Open Foundation of Shenzhen KeyLaboratory of Urban Planning and Decision Making (Grantno UPDMHITSZ2014B07) We would like to thank theanonymous referees for their valuable suggestions

References

[1] T M Choi Fashion Supply Chain Management Industry andBusiness Analysis IGI Global Hershey Pa USA 2011

[2] S Guercini and A Runfola ldquoRelational paths in business net-work dynamics evidence from the fashion industryrdquo IndustrialMarketing Management vol 41 no 5 pp 807ndash815 2012

[3] G B Richardson ldquoThe organization of industryrdquo EconomicJournal vol 82 pp 883ndash896 1972

[4] G P Pisano ldquoUsing equity participation to support exchangeevidence from the biotechnology industryrdquo Journal of LawEconomics and Organization vol 5 no 1 pp 109ndash126 1989

[5] TMChoi P S Chow and SC Liu ldquoImplementation of fashionERP systems in China case study of a fashion brand reviewand future challengesrdquo International Journal of ProductionEconomics vol 146 no 1 pp 70ndash81 2013

[6] X D Lin ldquoSpecial investment optimal partial ownership andincentive efficiencyrdquo in Proceedings of the 4th International Con-ference on Wireless Communications Networking and MobileComputing (WiCOM rsquo08) pp 1ndash4 Dalian China October 2008

[7] M Aoki Information Incentives and Bargaining in the JapaneseEconomy Cambridge University Press Cambridge UK 1988

[8] J H Dyer andWGOuchi ldquoJapanese-style partnerships givingcompanies a competitive edgerdquo Sloan Management Review vol14 pp 51ndash63 1993

[9] Y-K Che and D B Hausch ldquoCooperative investments and thevalue of contractingrdquo The American Economic Review vol 89no 1 pp 125ndash147 1999

[10] O E Williamson ldquoCredible commitments using hostages tosupport exchangerdquo American Economic Review vol 73 no 2pp 519ndash540 1983

[11] O Hart and JMoore ldquoIncomplete contracts and renegotiationrdquoEconometrica vol 56 no 4 pp 755ndash785 1988

[12] S Grossman and O Hart ldquoThe costs and benefits of ownershipa theory of vertical and lateral integrationrdquo Journal of PoliticalEconomy vol 94 no 2 pp 691ndash719 1989

[13] O E Williamson The Economic Institutions of CapitalismFirms Markets Relational Contracting Macmillan PrincetonNJ USA 1985

[14] B Klein R Crawford and A Alchian ldquoVertical integrationappropriable rents and the competitive contracting processrdquoThe Journal of Law and Economics vol 21 no 1 pp 297ndash3261978

[15] P Milgrom and J Roberts Economics Organization andManagement Prentice Hall Englewood Cliffs NJ USA 1992

[16] M R Scheffer ldquoTrends in textile markets and their implicationsfor textile products and processesrdquo in The Global Textile andClothing Industry pp 8ndash28 2012

[17] P Bolton and M D Whinston ldquoIncomplete contracts verticalintegration and supply assurancerdquoReview of Economics Studiesvol 60 no 1 pp 121ndash148 1993

[18] R G Rajan and L Zingales ldquoPower in a theory of the firmrdquoQuarterly Journal of Economics vol 113 no 1 pp 387ndash432 1998

[19] S Dasgupta and Z Tao ldquoBargaining bonding and partialownershiprdquo International Economic Review vol 41 no 3 pp609ndash635 2000

[20] P Aghion and J Tirole ldquoThe management of innovationrdquoQuarterly Journal of Economics vol 109 no 3 pp 1185ndash12091994

[21] T Y Chung ldquoIncomplete contracts specific investments andrisk sharingrdquo Review of Economic Studies vol 58 pp 1031ndash10421991

[22] Y Yu T-M Choi C-L Hui and T-K Ho ldquoA new andefficient intelligent collaboration scheme for fashion designrdquoIEEE Transactions on Systems Man and Cybernetics A Systemsand Humans vol 41 no 3 pp 463ndash475 2011

[23] T-M Choi C-L Hui N Liu S-F Ng and Y Yu ldquoFast fashionsales forecasting with limited data and timerdquo Decision SupportSystems vol 59 no 1 pp 84ndash92 2014

[24] W K Wong and S Y S Leung ldquoGenetic optimization of fabricutilization in apparel manufacturingrdquo International Journal ofProduction Economics vol 114 no 1 pp 376ndash387 2008

[25] B Asanuma ldquoManufacturer-supplier relationships in Japan andthe concept of relation-specific skillrdquo Journal of The Japaneseand International Economies vol 3 no 1 pp 1ndash30 1989

[26] M C Jensen and W H Meckling ldquoTheory of the firmmanagerial behavior agency costs and ownership structurerdquoJournal of Financial Economics vol 3 no 4 pp 305ndash360 1976

[27] T-M Choi C-L Hui S-F Ng and Y Yu ldquoColor trendforecasting of fashionable products with very few historicaldatardquo IEEE Transactions on Systems Man and Cybernetics PartC Applications and Reviews vol 42 no 6 pp 1003ndash1010 2012

[28] P Aghion and P Bohton ldquoAn incomplete contracts approach tofinancial contractingrdquo Review of Economic Studies vol 59 no3 pp 473ndash494 1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

the above mentioned cooperation transactions why is equityparticipation adopted rather than long-term contract Thatis exactly the paradox in transaction efficiency from differentcooperative arrangements that we want to investigate

In reality due to the complexity and uncertainty of futureaffairs and tradersrsquo bound rationality it is impossible orimplausible to list all the related details of contract whentaking transaction cost into consideration Since incompletecontracts cannot resolve the ldquohold-uprdquo problem of oppor-tunists and discounts its value [9] under the backgroundsof opportunism [10] assets specificity [11] incomplete con-tracts and futurersquos uncertainty [12] various organizationalinterventions such as vertical integration exchange hostagesshifting property rights and designing an authority relation-ship are proposed to solve the ldquohold-uprdquo problem which canprevent two parties from breaking a contract

Cooperative transaction among member-firms withinlogistic supply chain may lose efficiency because of expost opportunistic behavior caused by specific investmentresulting likely from customized production or outsideoptions Williamson [13] Klein et al [14] believe that specificinvestment does not likely acquire the optimal efficiencywith the anticipation of ex post opportunistic behaviors andvertical integration instead of spotmarket can avoid or reduceopportunistic behaviors caused by assets specificity The finalchoice is made based on the comparison of transaction costsof two types of cooperative mechanisms

However integration (internal transaction) is not alwaysmore outperformed than market transaction which meansthat it would lead to inefficiencywhen all productive activitiesare arranged in one integrated organization Why cannotmarket relationship among independent entities be replacedfully by integration Williamsonrsquos replacement model pro-vides the following reasons for avoiding integration Thatis if firms manufacture inputting products by themselveseconomies of scale and economies of scope may not beachieved Otherwise when the degree of assets specificity islow governance cost of internal organizations will be largerthan that of market organizations [13] When analyzing thedisadvantage of governance cost of internal organizationsrelated interpretations of loss of control rights and malfunc-tion of selective optimal intervention are convincing

Based on the criticism and inheritance of existent theo-ries Milgrom and Roberts [15] propose that the cost of polit-ical activities within one organization is also an importantobstacle for concentration of control rights which interpretsthat internal transaction within integration organizations isnot always better than market transaction among entitiesin view of nonmarket transaction costs The limitations ofintegration organizations indicate that a single mode ofintegration among parent firm and its member-firms is notoptimal and the concurrence of various bonding relation-ships within supply chains is a feasible choice of decision-makers when constructing an up-down stream relationship

With growing cooperation transactions within sup-ply chains share-holding arrangement (partial ownership)becomes one of the most important cooperative schemesHowever there are few theoretical explanations aiming atequity participation phenomena especially within logistic

supply chain [2 16] Conventional wisdom is that partialownership by reducing opportunism helps to promotethe bond between upstream firms and downstream firmsthrough inspiring greater specific investment and customizedproduction level [9ndash12] So without contractual remediesequity participation may perhaps play a role instead How-ever under symmetric information equity participation bythe downstream firm in an upstream supplier has no effect onthe payoffs when two parties bargain to allocate the benefitsof specific investment [11] In view of this it remains unclearhow partial ownership promotes the bond

In the related models Bolton and Whinston [17] andRajan and Zingales [18] discuss how to make optimal own-ership allocation in details However they only make someanalyses about efficiency loss within integration organizationbut do not measure enhanced efficiency resulting fromcooperation mechanism of partial ownership Different fromtheir works this paper focuses on demonstrating what rolespartial ownership plays in customized production used tomotivate investors and simultaneously probing into why thecomplete ownership is not possible to be optimal

Dasgupta and Tao [19] provide some theoretical interpre-tations for partial ownership phenomena based on the mod-els about selective investment decisionmade by the upstreamfirms They consider two types of investment in whichspecific investment levels differ Given potential income ofinvestment to be random when the downstream firm holdspartial ownership of the upstream firm the upstream firmwould choose more efficient types of investment than thesimple contract

Compared with innovative mechanism design theory ofownership suggested by Aghion and Tirole [20] Dasguptarsquostheoretical interpretation on partial ownership is more pro-found as they not only agree on the viewpoint that the relativebargaining power of the trade parties will affect the efficiencyof ownership allocation but also install the bargaining powerparameter into the models and obtain the relevance betweenthe related parameters and the magnitude of partial owner-ship When the downstream firm takes equity participationratio into account the optimal partial ownership is not onlyof the credible commitment that can boost the upstream firmto choose a high specific investment level but also of themechanism arrangement in order tomaximize the benefits ofthe downstream firmThe equity participation ratio decisionmust tradeoff these two mechanisms which means that thedownstream firm maximizing its own benefits does not haveto choose equity participation ratio that can motivate theupstream firm to make the complete specific investment

Hence viewing customization level as a variable chosenby the upstream firmmay meet the realistic condition withinlogistic supply chains better In this paper the potentialincome of customization investment is assumed to increasewith customized production level which accords with ratio-nal principle and is our logic starting point of research

In addition the existence of partial ownership mayaffect customization decision and the success probability ofobtaining outside opportunity income slightly On the onehand partial ownership could lower the diligence expen-diture of the upstream firmrsquos entrepreneurs On the other

Mathematical Problems in Engineering 3

hand it has the supervisory effects on them imposed by thedownstream firm which was neglected by Dasgupta and Tao[19] but is taken into account in our paper Then in factpartial ownership wonrsquot change the diligence expenditure ofdecision-makers evidently Once investment and customizedproduction are made both the investment income and theoutside option income are supposed to be realizable This iswhy we incorporate customization level partial ownershipand outside opportunity into the same analytical frameworkwhich become a key point that distinguishes our researchfrom other customization literatures

In addition to analyzing the case of the owner-managedupstream firms our model also involves the case of public-firms managed by professional managers Obviously thedecision-makers of these two kinds of firms have so manydifferences between their customization decision behaviorsthat we should probe into them separately From this angle ofview we can demonstrate why the familial-type logistic sup-ply chains may choose more efficient customized productionlevel than public-type logistic supply chains

The remaining portion of this paper is organized asfollows Section 2 outlines the basic model and analyzesthe limitations of the simple contract Section 3 probes intothe problem of equity participation of the owner-managedcarrier Section 4 discusses the first-best partial ownership ofthe publicly traded carrier Section 5 analyses the effects of theoptimal ownership strategy on the efficiency of customizedtransportation Finally conclusion is made in Section 6

2 The Customized Transportation Models

21 Model Settings Assuming that the member-firms withinthe logistic supply chain are respectively one carrier andone consignor in a transportation trade the two parties canmake the specific investment for customized transportationbilaterally or unilaterally Without loss of generality weassume that the carrier can make the unilateral specificinvestment and customized transportation for consignorwhich can increase the goodsrsquo value of the consignor Forexample if the carrier invests in refrigerating equipment orant-vibration appliance for consignorrsquos goods in the great riskof decoy or brittleness then this customized transportationwould increase the goodsrsquo value and consignor would make alarger profit

The carrier can either be owner-managed firms or public-firms run by professional managers Here we call the own-ers of owner-managed firms as entrepreneur and call thedecision-maker of the publicly traded firm as the managerWe assume that the consignor is run by professional man-agers in the interest of the stockholders To bementioned theowner-managed consignorwill not affect our analysesUnlessspecially pointed out carrier is seen as an owner-managedone in our analyses In addition all players are assumed to berisk-neutral

For simplicity of the analyses and the generalization ofmodels three stages of game are considered that is 119905 = 0 1 2At 119905 = 0 the consignor offers to buy a fraction 119903 isin [0 1] ofthe transportation carrier at price 119875(119903) and the entrepreneurcan accept or reject the offer

At 119905 = 1 the entrepreneur chooses the customizationlevel parameter 119886 based on the potential value 119881(119886) andthe cost function 119862(119886) of customized transportation where119886 isin [0 1] Larger 119886 means the higher customized trans-portation level for carrier In order to grasp the nature ofcustomization investment behavior we assume the value oftransportation service 119881(119886) and its investment in customizedtransportation for example 119862(119886) are convexly increasing in119886 For simplifying analyses and without loss of generalitywe adopt the following function shape 119881(119886) = 119890

119886

119892 and119862(119886) = 120573119886

2 where 119892 represents the general transportationservice value without customized investment (in the case of119886 = 0) and 120573 is a constant expressing the needed investmentin the case of complete customization service In additionwe also suppose that the net revenue function of customizedproduction [119881(119860) minus 119862(119860)] is concave which ensures thatthere exists the optimal 119886 in our analyses That is forall119886 isin [0 1]

and 119903 isin [0 1] and inequalities 119890119886

119892 gt 2120573119886 and 119890119886

119892 lt 2120573 holdAt 119905 = 2 119881(119886) and 119862(119886) are realized 119881(119886) and 119862(119886)

are common knowledge but they cannot be verified so thecontract cannot be consigned on it

Then we consider that at 119905 = 0 the carrier and theconsignor sign a simple take-or-pay contract and (119875

119879 119875119873

) isthe payoff portfolio the consignor will pay to the carrier intwo cases when trade in the contract occurs or not At 119905 = 2the carriermakes renegotiationwith the consignor bilaterallyIf the renegotiation between them fails carrier will trade withother consignor and the potential value of the customizationwill be reduced to 119892(1 minus 119886)

If the relative bargaining power of the consignor isassumed to be 120582 then that of the upstream carrier is (1 minus

120582) where 120582 isin [0 1] We incorporate the analyses ofsurplus allocation in the cases of trade or nontrade into theframework of the Nash bargaining solutions By backwarddeductivemethod since (119875

119879 119875119873

) can be renegotiated at 119905 = 2it means (119875

119879 119875119873

) should obey the constraints of the Nashbargaining solutions

Under what condition could simple contract (119875119879 119875119873

)

acquire the optimal incentive outcome And why can equityparticipation arrangement enhancemore efficient customiza-tion level These paradoxes are what we are interested in

22 Simple Contract and Customization Level Choice Givensimple contract (119875

119879 119875119873

) and the equity participation ratior of consignor the payoff matrix of two trading partiesis expressed as in two cases when the negotiation eithertriumphs (denoted by T) or fails (denoted byN) as following

Carrier Consignor119879 (1 minus 119903) [119875

119879minus 119862 (119886)] 119881 (119886) minus 119875

119879+ 119903 [119875

119879minus 119862 (119886)]

119873 (1 minus 119903) [119875119873

+ 119892 (1 minus 119886) minus 119862 (119886)] 119903 [119875119873

+ 119892 (1 minus 119886) minus 119862 (119886)] minus 119875119873

(1)

In the game model of the repeated bargains the Nashbargaining solutions require that contract (119875

119879 119875119873

) satisfies

max (1 minus 119903) [119875119879

minus 119862 (119886)]

minus (1 minus 119903) [119875119873

+ 119892 (1 minus 119886) minus 119862 (119886)]1minus120582

4 Mathematical Problems in Engineering

lowast 119881 (119886) minus 119875119879

+ 119903 [119875119879

minus 119862 (119886)]

minus 119903 [119875119873

+ 119892 (1 minus 119886) minus 119862 (119886)] + 119875119873

120582

(2)

The first order condition of 119875119879demands

(1 minus 120582) (1 minus 119903)

(1 minus 119903) [119875119879

minus 119875119873

minus 119892 (1 minus 119886)]

+120582 (119903 minus 1)

119881 (119886) minus 119875119879

+ 119903 [119875119879

minus 119875119873

minus 119892 (1 minus 119886)] + 119875119873

= 0

(3)

Then

119875119879

=[119890119886

minus 119903 (1 minus 119886) + (1 minus 119886 minus 119890119886

) 120582] 119892

1 minus 119903+ 119875119873

(4)

Using payoff matrix we know that when transactionoccurs the revenues of carrier and consignor are (1 minus 119903)[119875

119879minus

119862(119886)] and (119881(119886) minus 119875119879

+ 119903[119875119879

minus 119862(119886)]) respectively expressedby 119878119879(119903 119875119873

) and 119861119879(119903 119875119873

) So we have

119878119879

(119903 119875119873

) = [119890119886

minus 119903 (1 minus 119886) + (1 minus 119886 minus 119890119886

) 120582] 119892

+ (1 minus 119903) [119875119873

minus 1205731198862

]

119861119879

(119903 119875119873

) = [119890119886

120582 + (1 minus 119886) (119903 minus 120582)] 119892

minus (1 minus 119903) 119875119873

minus 1199031205731198862

(5)

The socially optimal customization level choice mustsatisfy

max119886

[119881 (119886) minus 119862 (119886)] (6)

The first order condition demands119890119886

119886=

2120573

119892 (7)

That is the first-best customization level parameter 119886fb =

arg[119890119886

119886 = 2120573119892] But if 119903 = 0 can (119875119879 119875119873

) make sure thatthe entrepreneur chooses 119886fb

For simplicity of the analyses let 119875119873

= 0 and then itdemands that the manager chooses 119886

lowast to maximize carrierrsquosrevenue as follows

119886lowast

= argmax119886

119878119879

(119903 119875119873

) (8)

Then we have

119886lowast

= argmax [119890119886

119886=

120582 minus 119903

(1 minus 120582) 119886+

2 (1 minus 119903) 120573

(1 minus 120582) 119892] (9)

When 119903 = 0 above equation can be changed into

119886lowast

= argmax [119890119886

119886=

120582

(1 minus 120582) 119886+

2120573

(1 minus 120582) 119892] (10)

Apparently from 120582 isin [0 1] we can deduce

120582

(1 minus 120582) 119886+

2120573

(1 minus 120582) 119892ge

2120573

119892 (11)

The function [119881(119886) minus 119862(119886)] is concave so119886lowast

le 119886fb (12)It means when the entrepreneur of the upstream carrier

has the whole bargaining power (120582 = 0) simple contract(119875119879 119875119873

) can induce the entrepreneur to choose the optimalcustomization level It is not difficult to understand thatwhen the entrepreneur with an overwhelming bargainingpower can obtain all of investment surplus he or she willmake the choice of the fist-best customization level It isconsistent with the interpretation of Choi et al [19ndash22] thatthe incomplete contract can also lead to efficient outcomesunder some special conditions

But when 120582 gt 0 (119875119879 119875119873

) contract cannot ensure thatthe entrepreneur would make the efficient customizationinvestment Then how many ration of equity participationcan result in efficient outcomes

If 119886lowast

= 119886fb then 1198811015840

(119886lowast

) = 1198621015840

(119886lowast

) This means120573119897

119892=

120582 minus 119903

(1 minus 120582) 119886+

2 (1 minus 119903) 120573

(1 minus 120582) 119892 (13)

Obviously only when 119903 = 120582 may (14) hold Since 119875119879

=

119881(119886fb) then (119875119879 119875119873

) = (119881(119886fb) 0)Integrating the above analyses we can conclude the

following

Proposition 1 (i) Only when the entrepreneur of carrieroccupies all of bargaining power (eg 120582 = 1) can simplecontract (119881(119886

119891119887) 0) result in the socially optimal customization

level chosen by carrier (ii) but if 0 lt 120582 lt 1 theefficient customization investment outcome can be obtainedonly through equity participation 119903 = 120582 plus simple contract(119881(119886119891119887

) 0)

Proposition 1 does not mean the consignor 119889 must makethe decision of equity participation 119903 = 120582 at 119905 = 0 becauseas a rational entity maximizing its benefit the consignorwould not only consider the customization efficiency of theupstream carrier but alsomake benefit-cost analyses of equityparticipation Hence the optimal equity participation rationeed not satisfy the condition under which the managerwould choose the socially optimal customization level Innext section we will discuss the problem about optimalequity participation ratio

3 Equity Participation by Consignor inOwner-Managed Carrier

This section aims at obtaining the comparative static outcomeaffecting the equity participation ratio factors so we willinstall the cost items related to the equity participation inorder to obtain the internal angle solution about the optimalpartial ownership

31 Optimal Equity Participation Ratio Given 119903 theentrepreneur will choose 119886

lowast to maximize the customizationinvestment revenue that is

119886lowast

= argmax119886

119878119879

(119903) (14)

Mathematical Problems in Engineering 5

Given 119886 chosen by carrier at 119905 = 1 the managerof consignor would at 119905 = 0 decide on optimal equityparticipation ratio 119903 to maximize its total net income Aswe all know under the mechanism of partial ownershipthe consignor can get a lot of benefits from customizedtransportation but must pay for obtaining partial ownershipof carrierThe reason why complete vertical integration is notalways the optimal choice lies in the fact that the integrationcost is likely to exceed the added-value benefits of customizedtransportation

Assuming that other outside income of the upstreamcarrier is 120587

0 we express 119875(119903) that the consignor pays for

obtaining an equity ratio 119903 of the carrier in the followingequation

119875 (119903) = (1 + 120579) [(119878119879

(119900) + 1205870) minus (119878

119879(119903) + (1 minus 119903) 120587

0)] (15)

In this equation (119878119879(119900)+120587

0) term represents total income

of entrepreneur when 119903 = 0 and (119878119879(119903) + (1 minus 119903)120587

0) is the

correspondent revenue that entrepreneur earns when equityparticipation ratio is 119903 The surplus between these two termscan be regarded as the real value of the equity fraction 119903

of the upstream carrier Let 120579 denote the average premium(discount) price coefficient at which the consignor acquires afraction 119903 of the carrier where 120579 gt 0 represents purchasingat premium 120579 = 0 represents purchasing at par and 120579 lt 0

represents purchasing at discount In order to accord with theactual scenarios of equity fight we install 120579-coefficient intothe formula to calculate 119875(119903)

Let 120587119889denote net income of the downstream consignor

then120587119889

= 119861119879

(119903) + 1199031205870

minus 119875 (119903) (16)

Substituting 119861119879(119903) and 119875(119903) into above equation we get

120587119889

= 119890119886

119892 minus 1205731198862

+ 120579119878119879

(119903) minus 1205791205870119903 minus (1 + 120579) 119878

119879(0) (17)

Anticipating that the entrepreneur chooses 119886lowast based on

equity participation ratio 119903 that is 119886lowast

= 119886lowast

(119903) the managerof the downstream consignor will try to acquire optimalequity ratio 119903

lowast for maximizing 120587119889 that is

119903lowast

= argmax119903

120587119889 (18)

The first order condition demands120597119886lowast

120597119903[1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)]

+ 120579 [119862 (119886lowast

) minus 119892 (1 minus 119886lowast

)] minus 1205791205870

= 0

(19)

Without loss of generality suppose 1205731198862

fb minus 119892(1 minus 119886fb) le 0we will discuss the results in the cases of different 120579-values

32 The Effects of 120579 on 119886lowast and 119903

lowast

(1) 120579 gt 0 which means purchasing at premiumBy (9) we know

1205972

119878119879

(119903)

120597(119886lowast)2

lt 0 (20)

Moreover 1205972119878119879(119903)120597119886

lowast

120597119903 = 2120573 gt 0

Thus 120597119886lowast

120597119903= (minus1205972

119878119879(119903)120597119886

lowast

120597119903)(1205972

119878119879(119903)120597(119886

lowast

)2

) gt

0Since 119881

1015840

(119886lowast

) minus 1198621015840

(119886lowast

) lt 0 when 120579 is sufficientlysmaller we have

120597120587119889

120597119903|119903=0

gt 0

120597120587119889

120597119903|119903=120582

= 120579 [119862 (119886fb) minus (1 minus 119886fb) 119892 minus 1205870] lt 0

(21)

Thus the optimal partial ownership 119903lowast

isin (0 120582) andwe can get 119886

lowast

gt 119886fbIf 120579 is sufficiently larger forall119903 isin [0 1] 120597120587

119889120597119903 lt 0 then

119903lowast

= 0

(2) 120579 = 0 which means purchasing at parObviously for (19) to hold it requires

1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

) = 0 (22)

Then 119903lowast = 120582 and 119886lowast

= 119886fb(3) 120579 lt 0 which means purchasing at discount

Evidently when the value of the upstream fabric supplieris underestimated the consignor will buy as much equity aspossible to maximize its total net income Although over-incentive effects of equitymay lead to customized productionlevel exceeding the social optimality and the increase ofthe equity investment revenue renders the manager of theconsignor to purchase the share of 119903

lowast greatly exceedingsocial optimal level that is 119903

lowast

gt 120582 Besides when theshare-holding ratio of the downstream consignor exceeds theentrepreneurrsquos the customization level of carrier should equalthe social optimal one So we have

119886lowast

= 119886fb if 119903lowast

ge1

2

lt 119886fb if 119903lowast

lt1

2

(23)

If 120579 is sufficiently negative then 119903lowast

= 1 and 119886lowast

= 119886fbNotably we regard 120579 as a constant in this paper which doesnot affect our analyses about the optimal equity participationratio

But what we must pay attention to is that with 119903

vibrating average discount (or premium) price parameter 120579

may also be changeable The exact magnitude of the optimalcustomization level 119886 and partial ownership 119903 will depend on120579-value

The three-dimension chart (see Figure 1) shows thatwhen 120579 drops from 04 to minus04 120587

119889(119886 119903) the equilibrium

path demonstrates an increasing trend and the optimalcustomization level 119886 is increasing in 119903 With equity purchaseshifting from discount price to premium price the drop ofoptimal equity participation ratiowill result in the customiza-tion transportation level and the net income of consignordecreasing simultaneously

6 Mathematical Problems in Engineering

0 01 02 03 04 05 06 07 08 09 1

001020304050607minus02minus01

00102030405

ar

120579 = minus04120579 = minus02120579 = 0

120579 = 02120579 = 04

120587d

Figure 1 The relationship chart among 120587119889 119886 and 119903 given 120582 = 05

120573 = 2 and 119892 = 2

Concluding the above analyses we get the following

Proposition 2 (i) If 120579 is a sufficiently small positive value119862(119886119891119887

)minus119892(1minus119886119891119887

) le 0 the consignor holds the optimal partialequity of the carrier 119903

lowast

isin (0 120582) and the customization levelwhich the entrepreneur chooses is below social optimal levelthat is 119886

lowast

lt 119886119891119887 If 120579 is sufficiently larger choosing 119903

lowast

= 0 willbe beneficial for the consignor

(ii) In the case when purchasing at par (120579 = 0) 119903lowast

= 120582

and 119886lowast

= 119886119891119887

hold and the efficient customization level can beobtained

(iii) In the case when purchasing at discount 119903lowast

gt 120582 and119886lowast

gt 119886119891119887

hold and optimal partial ownership can motivate theentrepreneur to choose the socially optimal customization type

Proposition 2 demonstrates that only when purchasing atpar can optimal equity participation mechanism make surethat themost efficient outcome is obtainedWhen purchasingat premium or discount price the distortion effects of wealthtransfer will make the customization outcome brought upby optimal partial ownership deviate from social optimalinvestment type

According to Proposition 2 we can interpret why theaverage equity ratios Chinese consignors hold of carriersrsquoequity ownership exceed the corresponding value of Amer-ican firms under the condition of the same technologyparameters In China majority equity ownership of the firmsis under the control of individual investors or institutioninvestors the exchange ratio of the stock is very low and theexchange of stock is often solved by private negotiation [22]Generally in this case 119875(119903) will not deviate seriously from itsreal value and 120579 is likely to be bigger than zero slightly Butin the United States whose capital markets are very matureequity ownership of firms is widely dispersed the publicshareholders hold the majority equities the ownership 119903 isobtained by exchange in the stock market and the bids ofmany trade entities lead to 120579-value exceeding zero greatly[23ndash25] Therefore when other technical parameters arenot changed the mechanism that the greater 120579-value wouldlead to the smaller 119903

lowast will result in the interfirm equityparticipation ratio in China to be obviously higher than thatof the same industry in the United States

4 Equity Participation by the Consignor inthe Public-Type Carrier

In this section we will expand our analyses of the opti-mal partial ownership to the public carrier operated byprofessional managers When the carrier is not owner-managed but is a public-firm the analyses of last sectiondo not apply completely in that professional managers inthe interest of the stockholders will not be affected directlyby the dispersive equities when considering investmentincome Even so our analyses belowdemonstrates that partialownership still affects the customization choice of managersand a conclusion similar to the last section will be obtained

For simplicity of analyses besides the assumption that themanager of carrier is risk neutral we also assume that thereexists nomanagerrsquosmoral hazard about reward compensatingmechanism and endeavor choice problem Assume thatrewards of manager are a minority part of the whole profit ofcarrier which ensures that manager makes decisions in theinterest of the stockholders Based on these assumptions wecan attain the bargaining outcome below

Lemma 3 Given r and 120582 let 119875119873

= 0 then the consignor pays

119879

=(1 minus 120582) 119890

119886

119892 + (120582 minus 119903) 119892 (1 minus 119886)

1 minus 119903

(24)

to the public-type carrier

And the incomes obtained by the two trade parties arerespectively

119878119879

(119903) =(1 minus 120582) 119890

119886

119892 + (120582 minus 119903) 119892 (1 minus 119886)

1 minus 119903minus 1205731198862

119861119879

(119903) = 120582119892119890119886

minus (120582 minus 119903) 119892 (1 minus 119886) minus 1199031205731198862

(25)

From the payoff matrix of two trade parties we canobtain

119879= 119875119879 that is no matter what type the carrier

belongs to the payoffs of the consignor are the same Thereexist differences between two types of carrierrsquo trade incomefunction But for the consignor the function formof the tradeincome remains unchanged

Observing that the manager of the carrier will choosethe customization level 119886

lowast to maximize its utility given themanagerrsquos risk neutrality we know

119886lowast

= arg[120597119878119879

(119903)

120597119886= 0] (26)

Given 119903 the manager would choose 119886lowast

(119903) to maximizethe earnings of the carrier then decision-makers of consignorcan decide on equity participation ratio to maximize its netincome

119889 Here we adopt the form below to describe

119889

119889

= 119861119879

(119903) + 1199031205870

minus (119903) (27)

where (119903) denotes the price at which the consignor buys afraction 119903 of equity of the carrier Assuming that the faction119903 of equity is purchased through tender offers the real value

Mathematical Problems in Engineering 7

120575(119903) of the carrier based on the partial ownership 119903 can beexpressed as

120575 (119903) = 119878119879

(119903) + 1205870 (28)

(119903) can be denoted as follows

(119903) = (1 + 120579) 119903120575 (119903) (29)

Therefore the total net income of the consignor can bedescribed as

119889

= 119861119879

(119903) + 1199031205870

minus 119903 (1 + 120579) [119878119879

(119903) + 1205870] (30)

The optimal partial ownership 119903lowast must satisfy the first-

order condition

120597119889

120597119903 | 119903 = 119903lowast

= 0 (31)

We further have

(120597119886lowast

120597119903) [1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)] minus 120579119878119879

(119903) minus 1205791205870

minus(1 + 120579119903) (1 minus 119886) 119892

(1 minus 119903)2

= 0

(32)

Obviously when 120579 gt 0 and is sufficiently small 119903lowast

isin

(0 120582) Similar to the conclusions of the last section the valuesof 119886lowast and 119903

lowast will be adjusted to correspond to positive ornegative 120579-value In this paper we will only analyze the caseof 120579 gt 0

By (32) we get

1205972

119889

120597119903120597120582= [

120597119886lowast

120597119903] [11988110158401015840

(119886lowast

) minus 11986210158401015840

(119886lowast

)] [120597119886lowast

120597120582] minus

1 + 120573119903

(1 minus 119903)2

lowast [minus (1 minus 119886lowast

) 119881 (119886lowast

) minus (1 minus 120582) 119881 (119886lowast

) (120597119886lowast

120597120582)

+ (1 minus 119886) (1 minus 120582) 119881 (119886lowast

) (120597119886lowast

120597120582)]

+ [1205972

119886lowast

120597119903120597120582] [1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)] +120573 (1 minus 119886

lowast

) 119881 (119886lowast

)

1 minus 119903

(33)

By 120597119878119879(119903)(120597119886 | 119886 = 119886

lowast

) = 0 we know

120597119886lowast

120597119903gt 0

120597119886lowast

120597120582lt 0

1205972

119886lowast

120597119903120597120582lt 0 (34)

Then in (33) all the right-hand terms exceed zero thus

1205972

120587119889

120597119903120597120582gt 0 (35)

Since Sign(120597119903lowast

120597120582) = Sign(1205972

119889120597119903120597120582) we can get

120597119903lowast

120597120582gt 0

120597119903lowast

1205971205870

lt 0 (36)

0 01 02 03 04 05 06 07 08 090

010203040506070809

1

r

a

120582 = 02120582 = 05120582 = 08

Figure 2 The relationship chart between 119886 and 119903 given 120573 = 2 119892 =

12

Given the values of 120582 120573 and 119892 we can find out therelationship between 119886 and 119903 through numerical simulationin Figure 2

Our numerical result shows that parameters 119886 and 119903 areincreasing function of 120582 and 119886 increases nonlinearly in r

From the above analyses we can conclude the following

Proposition 4 Assuming that the carrier is a public-firmmanaged by the manager in the interest of the share-holderswhen purchasing at premium price the optimal equity partic-ipation ratio 119903

lowast by the consignor increases in 120582 but decreasesin 1205870

5 Discussions about Customized ProductionEfficiency and Policy Implications

The theory of optimal ownership structure extracts thedistillate of two stream academic ideas the financial structuretheory and the managerial motivation theory which havebeen agreed on in economic literature [19] For exampleJensen andMeckling [26] pointed out that agent costs causedby dilution of ownership are derived from the fact thatthe incentive of inside controllers cannot keep track withthat of the ownerrsquos On the other hand many academicpapers demonstrate that an outside artificial person whoholds a major part of ownership has a positive effect onthe firmrsquos value [10 17 26ndash28] These papers emphasizedthe supervising function of the outside artificial personsrsquoshare-holders to the firmrsquos managers Compared with theseexisting articles we provide a theoretical interpretation whyoutside artificial persons hold partial ownership under thecircumstance of vertical transaction relationship Our resultis if the downstream firm holds partial ownership of theupstream firm it may function as a bonding mechanismwhich improves the performance of twoparties Itmeans thatcompared with 119903 = 0 the mechanism of partial ownershipimproves the efficiency of customization service

However can the optimal partial ownership result insocial optimal customized transportation level

As we know no matter what type the carrier is eitherowner-managed one or a public-firm managed by managers119903lowast

= 120582 or 119903lowast

= 05 is the necessary condition bringing in

8 Mathematical Problems in Engineering

social optimal customization level If the carrier is an owner-managed one only when the purchasing of partial ownershipat par price occursmay choosing 119903

lowast

= 120582 be a rational decisionfor the consignor aiming at maximizing its total net incomeBut purchasing at premium price is dominant in reality ifcalculated under general case of 120582 = 05 the optimal partialownership 119903

lowast is less than 120582 not large enough to motivatethe decision-maker of the carrier to choose the most efficientcustomized production level The marginal return obtainedby the consignor through enlarging equity participation ratiowill be offset by marginal costs of purchasing the equityownership and premium price distorting effects lead to theefficiency loss of the carrierrsquos customization investment (119903

lowast

lt

05)On the opposite when purchasing at discount overmoti-

vation leads to 119903lowast

gt 120582 and the customization efficiency lossmay still occur Therefore we hold that the effect of wealthtransfer in the purchase of equity ownership is the mainreason that leads to efficiency loss of customized productionwhich shows our theory about partial ownership differentfrom the entrepreneur endeavor choice interpretation byDasgupta and Tao but similar to the conclusion of Aghionand Tirolersquos that partial ownership arrangement can motivatespecial investment but cannot solve the investorsrsquo underin-vestment problem totally

However when the carrier is public-managed even ifthere exist 120579 = 0 and the optimal partial ownership 119903

lowast

lt

120582 social optimal customization level cannot be obtainedbecause the benefit of the consignor does not keep consistentwith the trade partiesrsquo common benefit When 120579 gt 0119903lowast will become smaller and the higher loss degree of thecustomization investment efficiency will occur Obviouslyunder the second-order condition constraint that we can getthe optimal solution satisfying (32) the larger the averagepremium price parameter is the smaller 119903

lowast is the lowercustomized production efficiency becomes and the greatersocial welfare loss will be which holds true in the caseof owner-managed carrier As for the case of 120579 lt 0 itaccords with the aforementioned analyses that is the over-motivation of equity ownership may lead to customizedproduction efficiency loss

In China the state-owned equity reform in logisticindustry just began with unclear ownership partition andmany social functions assumed by firms are not peeled offThe high premium-price acquisitions may make carriers tochoose 119903

lowast

= 0 which leads to the undermotivation of thecustomization investment of consignors and the social opti-mal customized transportation cannot be realizedThereforein the developing process of logistic supply chains in Chinait is necessary that the logistic firms should become theentities that can be self-managed self-constricted and self-motivated and the burden of the social functions will lead tothe loss of the transportation efficiency which are all what wemust pay attention to

In addition when all technical parameters keep constantcomparing optimal partial ownership in the cases of twodifferent types of carrier we can discover that in theorythe ratio of optimal equity participation by the consignor inthe owner-managed carrier should exceed the ratio in the

public-managed firm that is 119903lowast

gt 119903lowast It provides a theoretic

foundation for us to interpret that the interfirmmutual share-holding ratios of the member-firms within the familial-typelogistic supply chains aremuch larger than those ratioswithinthe public-type logistic supply chains At the same time italso means that the customized production efficiency of theformer is higher than that of the latter Although there is roomfor improvement we still firmly believe that the success ofChinese logistic industry should be mainly attributed to theadvantage of owner-managed efficiency

To be mentioned the mechanism of partial ownershipundoubtedly improves the cooperative efficiency of twotrade parties Although social welfare level this arrangementprovides is not optimal the cooperative mechanism helpsto enhance Pareto improvement of the return of two tradeparties compared with simple contract system

6 Conclusions

The phenomena that one consignor holds equity ownershipof one carrier within logistic supply chain are often observedDespite its importance the existing interpretations for inter-firm partial ownership scheme remain relatively unexploredIn this paper a theoretical explanation for equity partici-pation arrangement existing between member-firms withinlogistic supply chain is provided under the background ofcustomized production

Based on the models in which we view the parame-ter for customization level as the selective variable of thecarrier we figure out that the simple contract cannot solvethe low-efficient customized production problem Equityparticipation mechanism together with simple contract canimprove the efficiency of customized transportation Thepartial ownership mechanism supported by customized pro-duction plays a role as a bond in keeping the relationaltransactions among member-firms but not a role as theefficiency-enhancing mechanism resulting from outside arti-ficial personsrsquo supervision in some literature about equityownership structure

What is more on the basis of keeping the logic deductiveconsistency we obtain the outcome of the optimal partialownership affected by the relative bargaining power 120582 ofthe consignor and the other outside income 120587

0of the

carrier under two cases of owner-managed firm type andpublic-firm type respectively and showwhy the familial-typelogistic supply chains may choose more efficient customizedproduction level than public-type logistic supply chains

To be mentioned our theory provides few cases inwhich we can verify the interfirm equity participation ratioAlthough many important conclusions we obtain seem to beconsistent with some evidences there is a need for furtherstudy such as analyzing bilateral cross-shareholding case andconsidering the relationship between bargaining power andequity participation ratio through extending our models

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Mathematical Problems in Engineering 9

Acknowledgments

We acknowledge financial support from the National NatureScience Foundation of China (Grant nos 71001073 71371127and 71471118) the National Soft Science Research Plan(Grant no 2013GXS4D138) the Humanities and SocialSciences Foundation of Ministry of Education of China(Grant nos 13YJA630050 and 14YJC630096) DevelopmentProgram for Distinguished Young Teachers in Higher Edu-cation of Guangdong Province (Grant no Yq2013140 andYq2013147) and the Open Foundation of Shenzhen KeyLaboratory of Urban Planning and Decision Making (Grantno UPDMHITSZ2014B07) We would like to thank theanonymous referees for their valuable suggestions

References

[1] T M Choi Fashion Supply Chain Management Industry andBusiness Analysis IGI Global Hershey Pa USA 2011

[2] S Guercini and A Runfola ldquoRelational paths in business net-work dynamics evidence from the fashion industryrdquo IndustrialMarketing Management vol 41 no 5 pp 807ndash815 2012

[3] G B Richardson ldquoThe organization of industryrdquo EconomicJournal vol 82 pp 883ndash896 1972

[4] G P Pisano ldquoUsing equity participation to support exchangeevidence from the biotechnology industryrdquo Journal of LawEconomics and Organization vol 5 no 1 pp 109ndash126 1989

[5] TMChoi P S Chow and SC Liu ldquoImplementation of fashionERP systems in China case study of a fashion brand reviewand future challengesrdquo International Journal of ProductionEconomics vol 146 no 1 pp 70ndash81 2013

[6] X D Lin ldquoSpecial investment optimal partial ownership andincentive efficiencyrdquo in Proceedings of the 4th International Con-ference on Wireless Communications Networking and MobileComputing (WiCOM rsquo08) pp 1ndash4 Dalian China October 2008

[7] M Aoki Information Incentives and Bargaining in the JapaneseEconomy Cambridge University Press Cambridge UK 1988

[8] J H Dyer andWGOuchi ldquoJapanese-style partnerships givingcompanies a competitive edgerdquo Sloan Management Review vol14 pp 51ndash63 1993

[9] Y-K Che and D B Hausch ldquoCooperative investments and thevalue of contractingrdquo The American Economic Review vol 89no 1 pp 125ndash147 1999

[10] O E Williamson ldquoCredible commitments using hostages tosupport exchangerdquo American Economic Review vol 73 no 2pp 519ndash540 1983

[11] O Hart and JMoore ldquoIncomplete contracts and renegotiationrdquoEconometrica vol 56 no 4 pp 755ndash785 1988

[12] S Grossman and O Hart ldquoThe costs and benefits of ownershipa theory of vertical and lateral integrationrdquo Journal of PoliticalEconomy vol 94 no 2 pp 691ndash719 1989

[13] O E Williamson The Economic Institutions of CapitalismFirms Markets Relational Contracting Macmillan PrincetonNJ USA 1985

[14] B Klein R Crawford and A Alchian ldquoVertical integrationappropriable rents and the competitive contracting processrdquoThe Journal of Law and Economics vol 21 no 1 pp 297ndash3261978

[15] P Milgrom and J Roberts Economics Organization andManagement Prentice Hall Englewood Cliffs NJ USA 1992

[16] M R Scheffer ldquoTrends in textile markets and their implicationsfor textile products and processesrdquo in The Global Textile andClothing Industry pp 8ndash28 2012

[17] P Bolton and M D Whinston ldquoIncomplete contracts verticalintegration and supply assurancerdquoReview of Economics Studiesvol 60 no 1 pp 121ndash148 1993

[18] R G Rajan and L Zingales ldquoPower in a theory of the firmrdquoQuarterly Journal of Economics vol 113 no 1 pp 387ndash432 1998

[19] S Dasgupta and Z Tao ldquoBargaining bonding and partialownershiprdquo International Economic Review vol 41 no 3 pp609ndash635 2000

[20] P Aghion and J Tirole ldquoThe management of innovationrdquoQuarterly Journal of Economics vol 109 no 3 pp 1185ndash12091994

[21] T Y Chung ldquoIncomplete contracts specific investments andrisk sharingrdquo Review of Economic Studies vol 58 pp 1031ndash10421991

[22] Y Yu T-M Choi C-L Hui and T-K Ho ldquoA new andefficient intelligent collaboration scheme for fashion designrdquoIEEE Transactions on Systems Man and Cybernetics A Systemsand Humans vol 41 no 3 pp 463ndash475 2011

[23] T-M Choi C-L Hui N Liu S-F Ng and Y Yu ldquoFast fashionsales forecasting with limited data and timerdquo Decision SupportSystems vol 59 no 1 pp 84ndash92 2014

[24] W K Wong and S Y S Leung ldquoGenetic optimization of fabricutilization in apparel manufacturingrdquo International Journal ofProduction Economics vol 114 no 1 pp 376ndash387 2008

[25] B Asanuma ldquoManufacturer-supplier relationships in Japan andthe concept of relation-specific skillrdquo Journal of The Japaneseand International Economies vol 3 no 1 pp 1ndash30 1989

[26] M C Jensen and W H Meckling ldquoTheory of the firmmanagerial behavior agency costs and ownership structurerdquoJournal of Financial Economics vol 3 no 4 pp 305ndash360 1976

[27] T-M Choi C-L Hui S-F Ng and Y Yu ldquoColor trendforecasting of fashionable products with very few historicaldatardquo IEEE Transactions on Systems Man and Cybernetics PartC Applications and Reviews vol 42 no 6 pp 1003ndash1010 2012

[28] P Aghion and P Bohton ldquoAn incomplete contracts approach tofinancial contractingrdquo Review of Economic Studies vol 59 no3 pp 473ndash494 1992

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Mathematical Problems in Engineering 3

hand it has the supervisory effects on them imposed by thedownstream firm which was neglected by Dasgupta and Tao[19] but is taken into account in our paper Then in factpartial ownership wonrsquot change the diligence expenditure ofdecision-makers evidently Once investment and customizedproduction are made both the investment income and theoutside option income are supposed to be realizable This iswhy we incorporate customization level partial ownershipand outside opportunity into the same analytical frameworkwhich become a key point that distinguishes our researchfrom other customization literatures

In addition to analyzing the case of the owner-managedupstream firms our model also involves the case of public-firms managed by professional managers Obviously thedecision-makers of these two kinds of firms have so manydifferences between their customization decision behaviorsthat we should probe into them separately From this angle ofview we can demonstrate why the familial-type logistic sup-ply chains may choose more efficient customized productionlevel than public-type logistic supply chains

The remaining portion of this paper is organized asfollows Section 2 outlines the basic model and analyzesthe limitations of the simple contract Section 3 probes intothe problem of equity participation of the owner-managedcarrier Section 4 discusses the first-best partial ownership ofthe publicly traded carrier Section 5 analyses the effects of theoptimal ownership strategy on the efficiency of customizedtransportation Finally conclusion is made in Section 6

2 The Customized Transportation Models

21 Model Settings Assuming that the member-firms withinthe logistic supply chain are respectively one carrier andone consignor in a transportation trade the two parties canmake the specific investment for customized transportationbilaterally or unilaterally Without loss of generality weassume that the carrier can make the unilateral specificinvestment and customized transportation for consignorwhich can increase the goodsrsquo value of the consignor Forexample if the carrier invests in refrigerating equipment orant-vibration appliance for consignorrsquos goods in the great riskof decoy or brittleness then this customized transportationwould increase the goodsrsquo value and consignor would make alarger profit

The carrier can either be owner-managed firms or public-firms run by professional managers Here we call the own-ers of owner-managed firms as entrepreneur and call thedecision-maker of the publicly traded firm as the managerWe assume that the consignor is run by professional man-agers in the interest of the stockholders To bementioned theowner-managed consignorwill not affect our analysesUnlessspecially pointed out carrier is seen as an owner-managedone in our analyses In addition all players are assumed to berisk-neutral

For simplicity of the analyses and the generalization ofmodels three stages of game are considered that is 119905 = 0 1 2At 119905 = 0 the consignor offers to buy a fraction 119903 isin [0 1] ofthe transportation carrier at price 119875(119903) and the entrepreneurcan accept or reject the offer

At 119905 = 1 the entrepreneur chooses the customizationlevel parameter 119886 based on the potential value 119881(119886) andthe cost function 119862(119886) of customized transportation where119886 isin [0 1] Larger 119886 means the higher customized trans-portation level for carrier In order to grasp the nature ofcustomization investment behavior we assume the value oftransportation service 119881(119886) and its investment in customizedtransportation for example 119862(119886) are convexly increasing in119886 For simplifying analyses and without loss of generalitywe adopt the following function shape 119881(119886) = 119890

119886

119892 and119862(119886) = 120573119886

2 where 119892 represents the general transportationservice value without customized investment (in the case of119886 = 0) and 120573 is a constant expressing the needed investmentin the case of complete customization service In additionwe also suppose that the net revenue function of customizedproduction [119881(119860) minus 119862(119860)] is concave which ensures thatthere exists the optimal 119886 in our analyses That is forall119886 isin [0 1]

and 119903 isin [0 1] and inequalities 119890119886

119892 gt 2120573119886 and 119890119886

119892 lt 2120573 holdAt 119905 = 2 119881(119886) and 119862(119886) are realized 119881(119886) and 119862(119886)

are common knowledge but they cannot be verified so thecontract cannot be consigned on it

Then we consider that at 119905 = 0 the carrier and theconsignor sign a simple take-or-pay contract and (119875

119879 119875119873

) isthe payoff portfolio the consignor will pay to the carrier intwo cases when trade in the contract occurs or not At 119905 = 2the carriermakes renegotiationwith the consignor bilaterallyIf the renegotiation between them fails carrier will trade withother consignor and the potential value of the customizationwill be reduced to 119892(1 minus 119886)

If the relative bargaining power of the consignor isassumed to be 120582 then that of the upstream carrier is (1 minus

120582) where 120582 isin [0 1] We incorporate the analyses ofsurplus allocation in the cases of trade or nontrade into theframework of the Nash bargaining solutions By backwarddeductivemethod since (119875

119879 119875119873

) can be renegotiated at 119905 = 2it means (119875

119879 119875119873

) should obey the constraints of the Nashbargaining solutions

Under what condition could simple contract (119875119879 119875119873

)

acquire the optimal incentive outcome And why can equityparticipation arrangement enhancemore efficient customiza-tion level These paradoxes are what we are interested in

22 Simple Contract and Customization Level Choice Givensimple contract (119875

119879 119875119873

) and the equity participation ratior of consignor the payoff matrix of two trading partiesis expressed as in two cases when the negotiation eithertriumphs (denoted by T) or fails (denoted byN) as following

Carrier Consignor119879 (1 minus 119903) [119875

119879minus 119862 (119886)] 119881 (119886) minus 119875

119879+ 119903 [119875

119879minus 119862 (119886)]

119873 (1 minus 119903) [119875119873

+ 119892 (1 minus 119886) minus 119862 (119886)] 119903 [119875119873

+ 119892 (1 minus 119886) minus 119862 (119886)] minus 119875119873

(1)

In the game model of the repeated bargains the Nashbargaining solutions require that contract (119875

119879 119875119873

) satisfies

max (1 minus 119903) [119875119879

minus 119862 (119886)]

minus (1 minus 119903) [119875119873

+ 119892 (1 minus 119886) minus 119862 (119886)]1minus120582

4 Mathematical Problems in Engineering

lowast 119881 (119886) minus 119875119879

+ 119903 [119875119879

minus 119862 (119886)]

minus 119903 [119875119873

+ 119892 (1 minus 119886) minus 119862 (119886)] + 119875119873

120582

(2)

The first order condition of 119875119879demands

(1 minus 120582) (1 minus 119903)

(1 minus 119903) [119875119879

minus 119875119873

minus 119892 (1 minus 119886)]

+120582 (119903 minus 1)

119881 (119886) minus 119875119879

+ 119903 [119875119879

minus 119875119873

minus 119892 (1 minus 119886)] + 119875119873

= 0

(3)

Then

119875119879

=[119890119886

minus 119903 (1 minus 119886) + (1 minus 119886 minus 119890119886

) 120582] 119892

1 minus 119903+ 119875119873

(4)

Using payoff matrix we know that when transactionoccurs the revenues of carrier and consignor are (1 minus 119903)[119875

119879minus

119862(119886)] and (119881(119886) minus 119875119879

+ 119903[119875119879

minus 119862(119886)]) respectively expressedby 119878119879(119903 119875119873

) and 119861119879(119903 119875119873

) So we have

119878119879

(119903 119875119873

) = [119890119886

minus 119903 (1 minus 119886) + (1 minus 119886 minus 119890119886

) 120582] 119892

+ (1 minus 119903) [119875119873

minus 1205731198862

]

119861119879

(119903 119875119873

) = [119890119886

120582 + (1 minus 119886) (119903 minus 120582)] 119892

minus (1 minus 119903) 119875119873

minus 1199031205731198862

(5)

The socially optimal customization level choice mustsatisfy

max119886

[119881 (119886) minus 119862 (119886)] (6)

The first order condition demands119890119886

119886=

2120573

119892 (7)

That is the first-best customization level parameter 119886fb =

arg[119890119886

119886 = 2120573119892] But if 119903 = 0 can (119875119879 119875119873

) make sure thatthe entrepreneur chooses 119886fb

For simplicity of the analyses let 119875119873

= 0 and then itdemands that the manager chooses 119886

lowast to maximize carrierrsquosrevenue as follows

119886lowast

= argmax119886

119878119879

(119903 119875119873

) (8)

Then we have

119886lowast

= argmax [119890119886

119886=

120582 minus 119903

(1 minus 120582) 119886+

2 (1 minus 119903) 120573

(1 minus 120582) 119892] (9)

When 119903 = 0 above equation can be changed into

119886lowast

= argmax [119890119886

119886=

120582

(1 minus 120582) 119886+

2120573

(1 minus 120582) 119892] (10)

Apparently from 120582 isin [0 1] we can deduce

120582

(1 minus 120582) 119886+

2120573

(1 minus 120582) 119892ge

2120573

119892 (11)

The function [119881(119886) minus 119862(119886)] is concave so119886lowast

le 119886fb (12)It means when the entrepreneur of the upstream carrier

has the whole bargaining power (120582 = 0) simple contract(119875119879 119875119873

) can induce the entrepreneur to choose the optimalcustomization level It is not difficult to understand thatwhen the entrepreneur with an overwhelming bargainingpower can obtain all of investment surplus he or she willmake the choice of the fist-best customization level It isconsistent with the interpretation of Choi et al [19ndash22] thatthe incomplete contract can also lead to efficient outcomesunder some special conditions

But when 120582 gt 0 (119875119879 119875119873

) contract cannot ensure thatthe entrepreneur would make the efficient customizationinvestment Then how many ration of equity participationcan result in efficient outcomes

If 119886lowast

= 119886fb then 1198811015840

(119886lowast

) = 1198621015840

(119886lowast

) This means120573119897

119892=

120582 minus 119903

(1 minus 120582) 119886+

2 (1 minus 119903) 120573

(1 minus 120582) 119892 (13)

Obviously only when 119903 = 120582 may (14) hold Since 119875119879

=

119881(119886fb) then (119875119879 119875119873

) = (119881(119886fb) 0)Integrating the above analyses we can conclude the

following

Proposition 1 (i) Only when the entrepreneur of carrieroccupies all of bargaining power (eg 120582 = 1) can simplecontract (119881(119886

119891119887) 0) result in the socially optimal customization

level chosen by carrier (ii) but if 0 lt 120582 lt 1 theefficient customization investment outcome can be obtainedonly through equity participation 119903 = 120582 plus simple contract(119881(119886119891119887

) 0)

Proposition 1 does not mean the consignor 119889 must makethe decision of equity participation 119903 = 120582 at 119905 = 0 becauseas a rational entity maximizing its benefit the consignorwould not only consider the customization efficiency of theupstream carrier but alsomake benefit-cost analyses of equityparticipation Hence the optimal equity participation rationeed not satisfy the condition under which the managerwould choose the socially optimal customization level Innext section we will discuss the problem about optimalequity participation ratio

3 Equity Participation by Consignor inOwner-Managed Carrier

This section aims at obtaining the comparative static outcomeaffecting the equity participation ratio factors so we willinstall the cost items related to the equity participation inorder to obtain the internal angle solution about the optimalpartial ownership

31 Optimal Equity Participation Ratio Given 119903 theentrepreneur will choose 119886

lowast to maximize the customizationinvestment revenue that is

119886lowast

= argmax119886

119878119879

(119903) (14)

Mathematical Problems in Engineering 5

Given 119886 chosen by carrier at 119905 = 1 the managerof consignor would at 119905 = 0 decide on optimal equityparticipation ratio 119903 to maximize its total net income Aswe all know under the mechanism of partial ownershipthe consignor can get a lot of benefits from customizedtransportation but must pay for obtaining partial ownershipof carrierThe reason why complete vertical integration is notalways the optimal choice lies in the fact that the integrationcost is likely to exceed the added-value benefits of customizedtransportation

Assuming that other outside income of the upstreamcarrier is 120587

0 we express 119875(119903) that the consignor pays for

obtaining an equity ratio 119903 of the carrier in the followingequation

119875 (119903) = (1 + 120579) [(119878119879

(119900) + 1205870) minus (119878

119879(119903) + (1 minus 119903) 120587

0)] (15)

In this equation (119878119879(119900)+120587

0) term represents total income

of entrepreneur when 119903 = 0 and (119878119879(119903) + (1 minus 119903)120587

0) is the

correspondent revenue that entrepreneur earns when equityparticipation ratio is 119903 The surplus between these two termscan be regarded as the real value of the equity fraction 119903

of the upstream carrier Let 120579 denote the average premium(discount) price coefficient at which the consignor acquires afraction 119903 of the carrier where 120579 gt 0 represents purchasingat premium 120579 = 0 represents purchasing at par and 120579 lt 0

represents purchasing at discount In order to accord with theactual scenarios of equity fight we install 120579-coefficient intothe formula to calculate 119875(119903)

Let 120587119889denote net income of the downstream consignor

then120587119889

= 119861119879

(119903) + 1199031205870

minus 119875 (119903) (16)

Substituting 119861119879(119903) and 119875(119903) into above equation we get

120587119889

= 119890119886

119892 minus 1205731198862

+ 120579119878119879

(119903) minus 1205791205870119903 minus (1 + 120579) 119878

119879(0) (17)

Anticipating that the entrepreneur chooses 119886lowast based on

equity participation ratio 119903 that is 119886lowast

= 119886lowast

(119903) the managerof the downstream consignor will try to acquire optimalequity ratio 119903

lowast for maximizing 120587119889 that is

119903lowast

= argmax119903

120587119889 (18)

The first order condition demands120597119886lowast

120597119903[1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)]

+ 120579 [119862 (119886lowast

) minus 119892 (1 minus 119886lowast

)] minus 1205791205870

= 0

(19)

Without loss of generality suppose 1205731198862

fb minus 119892(1 minus 119886fb) le 0we will discuss the results in the cases of different 120579-values

32 The Effects of 120579 on 119886lowast and 119903

lowast

(1) 120579 gt 0 which means purchasing at premiumBy (9) we know

1205972

119878119879

(119903)

120597(119886lowast)2

lt 0 (20)

Moreover 1205972119878119879(119903)120597119886

lowast

120597119903 = 2120573 gt 0

Thus 120597119886lowast

120597119903= (minus1205972

119878119879(119903)120597119886

lowast

120597119903)(1205972

119878119879(119903)120597(119886

lowast

)2

) gt

0Since 119881

1015840

(119886lowast

) minus 1198621015840

(119886lowast

) lt 0 when 120579 is sufficientlysmaller we have

120597120587119889

120597119903|119903=0

gt 0

120597120587119889

120597119903|119903=120582

= 120579 [119862 (119886fb) minus (1 minus 119886fb) 119892 minus 1205870] lt 0

(21)

Thus the optimal partial ownership 119903lowast

isin (0 120582) andwe can get 119886

lowast

gt 119886fbIf 120579 is sufficiently larger forall119903 isin [0 1] 120597120587

119889120597119903 lt 0 then

119903lowast

= 0

(2) 120579 = 0 which means purchasing at parObviously for (19) to hold it requires

1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

) = 0 (22)

Then 119903lowast = 120582 and 119886lowast

= 119886fb(3) 120579 lt 0 which means purchasing at discount

Evidently when the value of the upstream fabric supplieris underestimated the consignor will buy as much equity aspossible to maximize its total net income Although over-incentive effects of equitymay lead to customized productionlevel exceeding the social optimality and the increase ofthe equity investment revenue renders the manager of theconsignor to purchase the share of 119903

lowast greatly exceedingsocial optimal level that is 119903

lowast

gt 120582 Besides when theshare-holding ratio of the downstream consignor exceeds theentrepreneurrsquos the customization level of carrier should equalthe social optimal one So we have

119886lowast

= 119886fb if 119903lowast

ge1

2

lt 119886fb if 119903lowast

lt1

2

(23)

If 120579 is sufficiently negative then 119903lowast

= 1 and 119886lowast

= 119886fbNotably we regard 120579 as a constant in this paper which doesnot affect our analyses about the optimal equity participationratio

But what we must pay attention to is that with 119903

vibrating average discount (or premium) price parameter 120579

may also be changeable The exact magnitude of the optimalcustomization level 119886 and partial ownership 119903 will depend on120579-value

The three-dimension chart (see Figure 1) shows thatwhen 120579 drops from 04 to minus04 120587

119889(119886 119903) the equilibrium

path demonstrates an increasing trend and the optimalcustomization level 119886 is increasing in 119903 With equity purchaseshifting from discount price to premium price the drop ofoptimal equity participation ratiowill result in the customiza-tion transportation level and the net income of consignordecreasing simultaneously

6 Mathematical Problems in Engineering

0 01 02 03 04 05 06 07 08 09 1

001020304050607minus02minus01

00102030405

ar

120579 = minus04120579 = minus02120579 = 0

120579 = 02120579 = 04

120587d

Figure 1 The relationship chart among 120587119889 119886 and 119903 given 120582 = 05

120573 = 2 and 119892 = 2

Concluding the above analyses we get the following

Proposition 2 (i) If 120579 is a sufficiently small positive value119862(119886119891119887

)minus119892(1minus119886119891119887

) le 0 the consignor holds the optimal partialequity of the carrier 119903

lowast

isin (0 120582) and the customization levelwhich the entrepreneur chooses is below social optimal levelthat is 119886

lowast

lt 119886119891119887 If 120579 is sufficiently larger choosing 119903

lowast

= 0 willbe beneficial for the consignor

(ii) In the case when purchasing at par (120579 = 0) 119903lowast

= 120582

and 119886lowast

= 119886119891119887

hold and the efficient customization level can beobtained

(iii) In the case when purchasing at discount 119903lowast

gt 120582 and119886lowast

gt 119886119891119887

hold and optimal partial ownership can motivate theentrepreneur to choose the socially optimal customization type

Proposition 2 demonstrates that only when purchasing atpar can optimal equity participation mechanism make surethat themost efficient outcome is obtainedWhen purchasingat premium or discount price the distortion effects of wealthtransfer will make the customization outcome brought upby optimal partial ownership deviate from social optimalinvestment type

According to Proposition 2 we can interpret why theaverage equity ratios Chinese consignors hold of carriersrsquoequity ownership exceed the corresponding value of Amer-ican firms under the condition of the same technologyparameters In China majority equity ownership of the firmsis under the control of individual investors or institutioninvestors the exchange ratio of the stock is very low and theexchange of stock is often solved by private negotiation [22]Generally in this case 119875(119903) will not deviate seriously from itsreal value and 120579 is likely to be bigger than zero slightly Butin the United States whose capital markets are very matureequity ownership of firms is widely dispersed the publicshareholders hold the majority equities the ownership 119903 isobtained by exchange in the stock market and the bids ofmany trade entities lead to 120579-value exceeding zero greatly[23ndash25] Therefore when other technical parameters arenot changed the mechanism that the greater 120579-value wouldlead to the smaller 119903

lowast will result in the interfirm equityparticipation ratio in China to be obviously higher than thatof the same industry in the United States

4 Equity Participation by the Consignor inthe Public-Type Carrier

In this section we will expand our analyses of the opti-mal partial ownership to the public carrier operated byprofessional managers When the carrier is not owner-managed but is a public-firm the analyses of last sectiondo not apply completely in that professional managers inthe interest of the stockholders will not be affected directlyby the dispersive equities when considering investmentincome Even so our analyses belowdemonstrates that partialownership still affects the customization choice of managersand a conclusion similar to the last section will be obtained

For simplicity of analyses besides the assumption that themanager of carrier is risk neutral we also assume that thereexists nomanagerrsquosmoral hazard about reward compensatingmechanism and endeavor choice problem Assume thatrewards of manager are a minority part of the whole profit ofcarrier which ensures that manager makes decisions in theinterest of the stockholders Based on these assumptions wecan attain the bargaining outcome below

Lemma 3 Given r and 120582 let 119875119873

= 0 then the consignor pays

119879

=(1 minus 120582) 119890

119886

119892 + (120582 minus 119903) 119892 (1 minus 119886)

1 minus 119903

(24)

to the public-type carrier

And the incomes obtained by the two trade parties arerespectively

119878119879

(119903) =(1 minus 120582) 119890

119886

119892 + (120582 minus 119903) 119892 (1 minus 119886)

1 minus 119903minus 1205731198862

119861119879

(119903) = 120582119892119890119886

minus (120582 minus 119903) 119892 (1 minus 119886) minus 1199031205731198862

(25)

From the payoff matrix of two trade parties we canobtain

119879= 119875119879 that is no matter what type the carrier

belongs to the payoffs of the consignor are the same Thereexist differences between two types of carrierrsquo trade incomefunction But for the consignor the function formof the tradeincome remains unchanged

Observing that the manager of the carrier will choosethe customization level 119886

lowast to maximize its utility given themanagerrsquos risk neutrality we know

119886lowast

= arg[120597119878119879

(119903)

120597119886= 0] (26)

Given 119903 the manager would choose 119886lowast

(119903) to maximizethe earnings of the carrier then decision-makers of consignorcan decide on equity participation ratio to maximize its netincome

119889 Here we adopt the form below to describe

119889

119889

= 119861119879

(119903) + 1199031205870

minus (119903) (27)

where (119903) denotes the price at which the consignor buys afraction 119903 of equity of the carrier Assuming that the faction119903 of equity is purchased through tender offers the real value

Mathematical Problems in Engineering 7

120575(119903) of the carrier based on the partial ownership 119903 can beexpressed as

120575 (119903) = 119878119879

(119903) + 1205870 (28)

(119903) can be denoted as follows

(119903) = (1 + 120579) 119903120575 (119903) (29)

Therefore the total net income of the consignor can bedescribed as

119889

= 119861119879

(119903) + 1199031205870

minus 119903 (1 + 120579) [119878119879

(119903) + 1205870] (30)

The optimal partial ownership 119903lowast must satisfy the first-

order condition

120597119889

120597119903 | 119903 = 119903lowast

= 0 (31)

We further have

(120597119886lowast

120597119903) [1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)] minus 120579119878119879

(119903) minus 1205791205870

minus(1 + 120579119903) (1 minus 119886) 119892

(1 minus 119903)2

= 0

(32)

Obviously when 120579 gt 0 and is sufficiently small 119903lowast

isin

(0 120582) Similar to the conclusions of the last section the valuesof 119886lowast and 119903

lowast will be adjusted to correspond to positive ornegative 120579-value In this paper we will only analyze the caseof 120579 gt 0

By (32) we get

1205972

119889

120597119903120597120582= [

120597119886lowast

120597119903] [11988110158401015840

(119886lowast

) minus 11986210158401015840

(119886lowast

)] [120597119886lowast

120597120582] minus

1 + 120573119903

(1 minus 119903)2

lowast [minus (1 minus 119886lowast

) 119881 (119886lowast

) minus (1 minus 120582) 119881 (119886lowast

) (120597119886lowast

120597120582)

+ (1 minus 119886) (1 minus 120582) 119881 (119886lowast

) (120597119886lowast

120597120582)]

+ [1205972

119886lowast

120597119903120597120582] [1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)] +120573 (1 minus 119886

lowast

) 119881 (119886lowast

)

1 minus 119903

(33)

By 120597119878119879(119903)(120597119886 | 119886 = 119886

lowast

) = 0 we know

120597119886lowast

120597119903gt 0

120597119886lowast

120597120582lt 0

1205972

119886lowast

120597119903120597120582lt 0 (34)

Then in (33) all the right-hand terms exceed zero thus

1205972

120587119889

120597119903120597120582gt 0 (35)

Since Sign(120597119903lowast

120597120582) = Sign(1205972

119889120597119903120597120582) we can get

120597119903lowast

120597120582gt 0

120597119903lowast

1205971205870

lt 0 (36)

0 01 02 03 04 05 06 07 08 090

010203040506070809

1

r

a

120582 = 02120582 = 05120582 = 08

Figure 2 The relationship chart between 119886 and 119903 given 120573 = 2 119892 =

12

Given the values of 120582 120573 and 119892 we can find out therelationship between 119886 and 119903 through numerical simulationin Figure 2

Our numerical result shows that parameters 119886 and 119903 areincreasing function of 120582 and 119886 increases nonlinearly in r

From the above analyses we can conclude the following

Proposition 4 Assuming that the carrier is a public-firmmanaged by the manager in the interest of the share-holderswhen purchasing at premium price the optimal equity partic-ipation ratio 119903

lowast by the consignor increases in 120582 but decreasesin 1205870

5 Discussions about Customized ProductionEfficiency and Policy Implications

The theory of optimal ownership structure extracts thedistillate of two stream academic ideas the financial structuretheory and the managerial motivation theory which havebeen agreed on in economic literature [19] For exampleJensen andMeckling [26] pointed out that agent costs causedby dilution of ownership are derived from the fact thatthe incentive of inside controllers cannot keep track withthat of the ownerrsquos On the other hand many academicpapers demonstrate that an outside artificial person whoholds a major part of ownership has a positive effect onthe firmrsquos value [10 17 26ndash28] These papers emphasizedthe supervising function of the outside artificial personsrsquoshare-holders to the firmrsquos managers Compared with theseexisting articles we provide a theoretical interpretation whyoutside artificial persons hold partial ownership under thecircumstance of vertical transaction relationship Our resultis if the downstream firm holds partial ownership of theupstream firm it may function as a bonding mechanismwhich improves the performance of twoparties Itmeans thatcompared with 119903 = 0 the mechanism of partial ownershipimproves the efficiency of customization service

However can the optimal partial ownership result insocial optimal customized transportation level

As we know no matter what type the carrier is eitherowner-managed one or a public-firm managed by managers119903lowast

= 120582 or 119903lowast

= 05 is the necessary condition bringing in

8 Mathematical Problems in Engineering

social optimal customization level If the carrier is an owner-managed one only when the purchasing of partial ownershipat par price occursmay choosing 119903

lowast

= 120582 be a rational decisionfor the consignor aiming at maximizing its total net incomeBut purchasing at premium price is dominant in reality ifcalculated under general case of 120582 = 05 the optimal partialownership 119903

lowast is less than 120582 not large enough to motivatethe decision-maker of the carrier to choose the most efficientcustomized production level The marginal return obtainedby the consignor through enlarging equity participation ratiowill be offset by marginal costs of purchasing the equityownership and premium price distorting effects lead to theefficiency loss of the carrierrsquos customization investment (119903

lowast

lt

05)On the opposite when purchasing at discount overmoti-

vation leads to 119903lowast

gt 120582 and the customization efficiency lossmay still occur Therefore we hold that the effect of wealthtransfer in the purchase of equity ownership is the mainreason that leads to efficiency loss of customized productionwhich shows our theory about partial ownership differentfrom the entrepreneur endeavor choice interpretation byDasgupta and Tao but similar to the conclusion of Aghionand Tirolersquos that partial ownership arrangement can motivatespecial investment but cannot solve the investorsrsquo underin-vestment problem totally

However when the carrier is public-managed even ifthere exist 120579 = 0 and the optimal partial ownership 119903

lowast

lt

120582 social optimal customization level cannot be obtainedbecause the benefit of the consignor does not keep consistentwith the trade partiesrsquo common benefit When 120579 gt 0119903lowast will become smaller and the higher loss degree of thecustomization investment efficiency will occur Obviouslyunder the second-order condition constraint that we can getthe optimal solution satisfying (32) the larger the averagepremium price parameter is the smaller 119903

lowast is the lowercustomized production efficiency becomes and the greatersocial welfare loss will be which holds true in the caseof owner-managed carrier As for the case of 120579 lt 0 itaccords with the aforementioned analyses that is the over-motivation of equity ownership may lead to customizedproduction efficiency loss

In China the state-owned equity reform in logisticindustry just began with unclear ownership partition andmany social functions assumed by firms are not peeled offThe high premium-price acquisitions may make carriers tochoose 119903

lowast

= 0 which leads to the undermotivation of thecustomization investment of consignors and the social opti-mal customized transportation cannot be realizedThereforein the developing process of logistic supply chains in Chinait is necessary that the logistic firms should become theentities that can be self-managed self-constricted and self-motivated and the burden of the social functions will lead tothe loss of the transportation efficiency which are all what wemust pay attention to

In addition when all technical parameters keep constantcomparing optimal partial ownership in the cases of twodifferent types of carrier we can discover that in theorythe ratio of optimal equity participation by the consignor inthe owner-managed carrier should exceed the ratio in the

public-managed firm that is 119903lowast

gt 119903lowast It provides a theoretic

foundation for us to interpret that the interfirmmutual share-holding ratios of the member-firms within the familial-typelogistic supply chains aremuch larger than those ratioswithinthe public-type logistic supply chains At the same time italso means that the customized production efficiency of theformer is higher than that of the latter Although there is roomfor improvement we still firmly believe that the success ofChinese logistic industry should be mainly attributed to theadvantage of owner-managed efficiency

To be mentioned the mechanism of partial ownershipundoubtedly improves the cooperative efficiency of twotrade parties Although social welfare level this arrangementprovides is not optimal the cooperative mechanism helpsto enhance Pareto improvement of the return of two tradeparties compared with simple contract system

6 Conclusions

The phenomena that one consignor holds equity ownershipof one carrier within logistic supply chain are often observedDespite its importance the existing interpretations for inter-firm partial ownership scheme remain relatively unexploredIn this paper a theoretical explanation for equity partici-pation arrangement existing between member-firms withinlogistic supply chain is provided under the background ofcustomized production

Based on the models in which we view the parame-ter for customization level as the selective variable of thecarrier we figure out that the simple contract cannot solvethe low-efficient customized production problem Equityparticipation mechanism together with simple contract canimprove the efficiency of customized transportation Thepartial ownership mechanism supported by customized pro-duction plays a role as a bond in keeping the relationaltransactions among member-firms but not a role as theefficiency-enhancing mechanism resulting from outside arti-ficial personsrsquo supervision in some literature about equityownership structure

What is more on the basis of keeping the logic deductiveconsistency we obtain the outcome of the optimal partialownership affected by the relative bargaining power 120582 ofthe consignor and the other outside income 120587

0of the

carrier under two cases of owner-managed firm type andpublic-firm type respectively and showwhy the familial-typelogistic supply chains may choose more efficient customizedproduction level than public-type logistic supply chains

To be mentioned our theory provides few cases inwhich we can verify the interfirm equity participation ratioAlthough many important conclusions we obtain seem to beconsistent with some evidences there is a need for furtherstudy such as analyzing bilateral cross-shareholding case andconsidering the relationship between bargaining power andequity participation ratio through extending our models

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Mathematical Problems in Engineering 9

Acknowledgments

We acknowledge financial support from the National NatureScience Foundation of China (Grant nos 71001073 71371127and 71471118) the National Soft Science Research Plan(Grant no 2013GXS4D138) the Humanities and SocialSciences Foundation of Ministry of Education of China(Grant nos 13YJA630050 and 14YJC630096) DevelopmentProgram for Distinguished Young Teachers in Higher Edu-cation of Guangdong Province (Grant no Yq2013140 andYq2013147) and the Open Foundation of Shenzhen KeyLaboratory of Urban Planning and Decision Making (Grantno UPDMHITSZ2014B07) We would like to thank theanonymous referees for their valuable suggestions

References

[1] T M Choi Fashion Supply Chain Management Industry andBusiness Analysis IGI Global Hershey Pa USA 2011

[2] S Guercini and A Runfola ldquoRelational paths in business net-work dynamics evidence from the fashion industryrdquo IndustrialMarketing Management vol 41 no 5 pp 807ndash815 2012

[3] G B Richardson ldquoThe organization of industryrdquo EconomicJournal vol 82 pp 883ndash896 1972

[4] G P Pisano ldquoUsing equity participation to support exchangeevidence from the biotechnology industryrdquo Journal of LawEconomics and Organization vol 5 no 1 pp 109ndash126 1989

[5] TMChoi P S Chow and SC Liu ldquoImplementation of fashionERP systems in China case study of a fashion brand reviewand future challengesrdquo International Journal of ProductionEconomics vol 146 no 1 pp 70ndash81 2013

[6] X D Lin ldquoSpecial investment optimal partial ownership andincentive efficiencyrdquo in Proceedings of the 4th International Con-ference on Wireless Communications Networking and MobileComputing (WiCOM rsquo08) pp 1ndash4 Dalian China October 2008

[7] M Aoki Information Incentives and Bargaining in the JapaneseEconomy Cambridge University Press Cambridge UK 1988

[8] J H Dyer andWGOuchi ldquoJapanese-style partnerships givingcompanies a competitive edgerdquo Sloan Management Review vol14 pp 51ndash63 1993

[9] Y-K Che and D B Hausch ldquoCooperative investments and thevalue of contractingrdquo The American Economic Review vol 89no 1 pp 125ndash147 1999

[10] O E Williamson ldquoCredible commitments using hostages tosupport exchangerdquo American Economic Review vol 73 no 2pp 519ndash540 1983

[11] O Hart and JMoore ldquoIncomplete contracts and renegotiationrdquoEconometrica vol 56 no 4 pp 755ndash785 1988

[12] S Grossman and O Hart ldquoThe costs and benefits of ownershipa theory of vertical and lateral integrationrdquo Journal of PoliticalEconomy vol 94 no 2 pp 691ndash719 1989

[13] O E Williamson The Economic Institutions of CapitalismFirms Markets Relational Contracting Macmillan PrincetonNJ USA 1985

[14] B Klein R Crawford and A Alchian ldquoVertical integrationappropriable rents and the competitive contracting processrdquoThe Journal of Law and Economics vol 21 no 1 pp 297ndash3261978

[15] P Milgrom and J Roberts Economics Organization andManagement Prentice Hall Englewood Cliffs NJ USA 1992

[16] M R Scheffer ldquoTrends in textile markets and their implicationsfor textile products and processesrdquo in The Global Textile andClothing Industry pp 8ndash28 2012

[17] P Bolton and M D Whinston ldquoIncomplete contracts verticalintegration and supply assurancerdquoReview of Economics Studiesvol 60 no 1 pp 121ndash148 1993

[18] R G Rajan and L Zingales ldquoPower in a theory of the firmrdquoQuarterly Journal of Economics vol 113 no 1 pp 387ndash432 1998

[19] S Dasgupta and Z Tao ldquoBargaining bonding and partialownershiprdquo International Economic Review vol 41 no 3 pp609ndash635 2000

[20] P Aghion and J Tirole ldquoThe management of innovationrdquoQuarterly Journal of Economics vol 109 no 3 pp 1185ndash12091994

[21] T Y Chung ldquoIncomplete contracts specific investments andrisk sharingrdquo Review of Economic Studies vol 58 pp 1031ndash10421991

[22] Y Yu T-M Choi C-L Hui and T-K Ho ldquoA new andefficient intelligent collaboration scheme for fashion designrdquoIEEE Transactions on Systems Man and Cybernetics A Systemsand Humans vol 41 no 3 pp 463ndash475 2011

[23] T-M Choi C-L Hui N Liu S-F Ng and Y Yu ldquoFast fashionsales forecasting with limited data and timerdquo Decision SupportSystems vol 59 no 1 pp 84ndash92 2014

[24] W K Wong and S Y S Leung ldquoGenetic optimization of fabricutilization in apparel manufacturingrdquo International Journal ofProduction Economics vol 114 no 1 pp 376ndash387 2008

[25] B Asanuma ldquoManufacturer-supplier relationships in Japan andthe concept of relation-specific skillrdquo Journal of The Japaneseand International Economies vol 3 no 1 pp 1ndash30 1989

[26] M C Jensen and W H Meckling ldquoTheory of the firmmanagerial behavior agency costs and ownership structurerdquoJournal of Financial Economics vol 3 no 4 pp 305ndash360 1976

[27] T-M Choi C-L Hui S-F Ng and Y Yu ldquoColor trendforecasting of fashionable products with very few historicaldatardquo IEEE Transactions on Systems Man and Cybernetics PartC Applications and Reviews vol 42 no 6 pp 1003ndash1010 2012

[28] P Aghion and P Bohton ldquoAn incomplete contracts approach tofinancial contractingrdquo Review of Economic Studies vol 59 no3 pp 473ndash494 1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

lowast 119881 (119886) minus 119875119879

+ 119903 [119875119879

minus 119862 (119886)]

minus 119903 [119875119873

+ 119892 (1 minus 119886) minus 119862 (119886)] + 119875119873

120582

(2)

The first order condition of 119875119879demands

(1 minus 120582) (1 minus 119903)

(1 minus 119903) [119875119879

minus 119875119873

minus 119892 (1 minus 119886)]

+120582 (119903 minus 1)

119881 (119886) minus 119875119879

+ 119903 [119875119879

minus 119875119873

minus 119892 (1 minus 119886)] + 119875119873

= 0

(3)

Then

119875119879

=[119890119886

minus 119903 (1 minus 119886) + (1 minus 119886 minus 119890119886

) 120582] 119892

1 minus 119903+ 119875119873

(4)

Using payoff matrix we know that when transactionoccurs the revenues of carrier and consignor are (1 minus 119903)[119875

119879minus

119862(119886)] and (119881(119886) minus 119875119879

+ 119903[119875119879

minus 119862(119886)]) respectively expressedby 119878119879(119903 119875119873

) and 119861119879(119903 119875119873

) So we have

119878119879

(119903 119875119873

) = [119890119886

minus 119903 (1 minus 119886) + (1 minus 119886 minus 119890119886

) 120582] 119892

+ (1 minus 119903) [119875119873

minus 1205731198862

]

119861119879

(119903 119875119873

) = [119890119886

120582 + (1 minus 119886) (119903 minus 120582)] 119892

minus (1 minus 119903) 119875119873

minus 1199031205731198862

(5)

The socially optimal customization level choice mustsatisfy

max119886

[119881 (119886) minus 119862 (119886)] (6)

The first order condition demands119890119886

119886=

2120573

119892 (7)

That is the first-best customization level parameter 119886fb =

arg[119890119886

119886 = 2120573119892] But if 119903 = 0 can (119875119879 119875119873

) make sure thatthe entrepreneur chooses 119886fb

For simplicity of the analyses let 119875119873

= 0 and then itdemands that the manager chooses 119886

lowast to maximize carrierrsquosrevenue as follows

119886lowast

= argmax119886

119878119879

(119903 119875119873

) (8)

Then we have

119886lowast

= argmax [119890119886

119886=

120582 minus 119903

(1 minus 120582) 119886+

2 (1 minus 119903) 120573

(1 minus 120582) 119892] (9)

When 119903 = 0 above equation can be changed into

119886lowast

= argmax [119890119886

119886=

120582

(1 minus 120582) 119886+

2120573

(1 minus 120582) 119892] (10)

Apparently from 120582 isin [0 1] we can deduce

120582

(1 minus 120582) 119886+

2120573

(1 minus 120582) 119892ge

2120573

119892 (11)

The function [119881(119886) minus 119862(119886)] is concave so119886lowast

le 119886fb (12)It means when the entrepreneur of the upstream carrier

has the whole bargaining power (120582 = 0) simple contract(119875119879 119875119873

) can induce the entrepreneur to choose the optimalcustomization level It is not difficult to understand thatwhen the entrepreneur with an overwhelming bargainingpower can obtain all of investment surplus he or she willmake the choice of the fist-best customization level It isconsistent with the interpretation of Choi et al [19ndash22] thatthe incomplete contract can also lead to efficient outcomesunder some special conditions

But when 120582 gt 0 (119875119879 119875119873

) contract cannot ensure thatthe entrepreneur would make the efficient customizationinvestment Then how many ration of equity participationcan result in efficient outcomes

If 119886lowast

= 119886fb then 1198811015840

(119886lowast

) = 1198621015840

(119886lowast

) This means120573119897

119892=

120582 minus 119903

(1 minus 120582) 119886+

2 (1 minus 119903) 120573

(1 minus 120582) 119892 (13)

Obviously only when 119903 = 120582 may (14) hold Since 119875119879

=

119881(119886fb) then (119875119879 119875119873

) = (119881(119886fb) 0)Integrating the above analyses we can conclude the

following

Proposition 1 (i) Only when the entrepreneur of carrieroccupies all of bargaining power (eg 120582 = 1) can simplecontract (119881(119886

119891119887) 0) result in the socially optimal customization

level chosen by carrier (ii) but if 0 lt 120582 lt 1 theefficient customization investment outcome can be obtainedonly through equity participation 119903 = 120582 plus simple contract(119881(119886119891119887

) 0)

Proposition 1 does not mean the consignor 119889 must makethe decision of equity participation 119903 = 120582 at 119905 = 0 becauseas a rational entity maximizing its benefit the consignorwould not only consider the customization efficiency of theupstream carrier but alsomake benefit-cost analyses of equityparticipation Hence the optimal equity participation rationeed not satisfy the condition under which the managerwould choose the socially optimal customization level Innext section we will discuss the problem about optimalequity participation ratio

3 Equity Participation by Consignor inOwner-Managed Carrier

This section aims at obtaining the comparative static outcomeaffecting the equity participation ratio factors so we willinstall the cost items related to the equity participation inorder to obtain the internal angle solution about the optimalpartial ownership

31 Optimal Equity Participation Ratio Given 119903 theentrepreneur will choose 119886

lowast to maximize the customizationinvestment revenue that is

119886lowast

= argmax119886

119878119879

(119903) (14)

Mathematical Problems in Engineering 5

Given 119886 chosen by carrier at 119905 = 1 the managerof consignor would at 119905 = 0 decide on optimal equityparticipation ratio 119903 to maximize its total net income Aswe all know under the mechanism of partial ownershipthe consignor can get a lot of benefits from customizedtransportation but must pay for obtaining partial ownershipof carrierThe reason why complete vertical integration is notalways the optimal choice lies in the fact that the integrationcost is likely to exceed the added-value benefits of customizedtransportation

Assuming that other outside income of the upstreamcarrier is 120587

0 we express 119875(119903) that the consignor pays for

obtaining an equity ratio 119903 of the carrier in the followingequation

119875 (119903) = (1 + 120579) [(119878119879

(119900) + 1205870) minus (119878

119879(119903) + (1 minus 119903) 120587

0)] (15)

In this equation (119878119879(119900)+120587

0) term represents total income

of entrepreneur when 119903 = 0 and (119878119879(119903) + (1 minus 119903)120587

0) is the

correspondent revenue that entrepreneur earns when equityparticipation ratio is 119903 The surplus between these two termscan be regarded as the real value of the equity fraction 119903

of the upstream carrier Let 120579 denote the average premium(discount) price coefficient at which the consignor acquires afraction 119903 of the carrier where 120579 gt 0 represents purchasingat premium 120579 = 0 represents purchasing at par and 120579 lt 0

represents purchasing at discount In order to accord with theactual scenarios of equity fight we install 120579-coefficient intothe formula to calculate 119875(119903)

Let 120587119889denote net income of the downstream consignor

then120587119889

= 119861119879

(119903) + 1199031205870

minus 119875 (119903) (16)

Substituting 119861119879(119903) and 119875(119903) into above equation we get

120587119889

= 119890119886

119892 minus 1205731198862

+ 120579119878119879

(119903) minus 1205791205870119903 minus (1 + 120579) 119878

119879(0) (17)

Anticipating that the entrepreneur chooses 119886lowast based on

equity participation ratio 119903 that is 119886lowast

= 119886lowast

(119903) the managerof the downstream consignor will try to acquire optimalequity ratio 119903

lowast for maximizing 120587119889 that is

119903lowast

= argmax119903

120587119889 (18)

The first order condition demands120597119886lowast

120597119903[1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)]

+ 120579 [119862 (119886lowast

) minus 119892 (1 minus 119886lowast

)] minus 1205791205870

= 0

(19)

Without loss of generality suppose 1205731198862

fb minus 119892(1 minus 119886fb) le 0we will discuss the results in the cases of different 120579-values

32 The Effects of 120579 on 119886lowast and 119903

lowast

(1) 120579 gt 0 which means purchasing at premiumBy (9) we know

1205972

119878119879

(119903)

120597(119886lowast)2

lt 0 (20)

Moreover 1205972119878119879(119903)120597119886

lowast

120597119903 = 2120573 gt 0

Thus 120597119886lowast

120597119903= (minus1205972

119878119879(119903)120597119886

lowast

120597119903)(1205972

119878119879(119903)120597(119886

lowast

)2

) gt

0Since 119881

1015840

(119886lowast

) minus 1198621015840

(119886lowast

) lt 0 when 120579 is sufficientlysmaller we have

120597120587119889

120597119903|119903=0

gt 0

120597120587119889

120597119903|119903=120582

= 120579 [119862 (119886fb) minus (1 minus 119886fb) 119892 minus 1205870] lt 0

(21)

Thus the optimal partial ownership 119903lowast

isin (0 120582) andwe can get 119886

lowast

gt 119886fbIf 120579 is sufficiently larger forall119903 isin [0 1] 120597120587

119889120597119903 lt 0 then

119903lowast

= 0

(2) 120579 = 0 which means purchasing at parObviously for (19) to hold it requires

1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

) = 0 (22)

Then 119903lowast = 120582 and 119886lowast

= 119886fb(3) 120579 lt 0 which means purchasing at discount

Evidently when the value of the upstream fabric supplieris underestimated the consignor will buy as much equity aspossible to maximize its total net income Although over-incentive effects of equitymay lead to customized productionlevel exceeding the social optimality and the increase ofthe equity investment revenue renders the manager of theconsignor to purchase the share of 119903

lowast greatly exceedingsocial optimal level that is 119903

lowast

gt 120582 Besides when theshare-holding ratio of the downstream consignor exceeds theentrepreneurrsquos the customization level of carrier should equalthe social optimal one So we have

119886lowast

= 119886fb if 119903lowast

ge1

2

lt 119886fb if 119903lowast

lt1

2

(23)

If 120579 is sufficiently negative then 119903lowast

= 1 and 119886lowast

= 119886fbNotably we regard 120579 as a constant in this paper which doesnot affect our analyses about the optimal equity participationratio

But what we must pay attention to is that with 119903

vibrating average discount (or premium) price parameter 120579

may also be changeable The exact magnitude of the optimalcustomization level 119886 and partial ownership 119903 will depend on120579-value

The three-dimension chart (see Figure 1) shows thatwhen 120579 drops from 04 to minus04 120587

119889(119886 119903) the equilibrium

path demonstrates an increasing trend and the optimalcustomization level 119886 is increasing in 119903 With equity purchaseshifting from discount price to premium price the drop ofoptimal equity participation ratiowill result in the customiza-tion transportation level and the net income of consignordecreasing simultaneously

6 Mathematical Problems in Engineering

0 01 02 03 04 05 06 07 08 09 1

001020304050607minus02minus01

00102030405

ar

120579 = minus04120579 = minus02120579 = 0

120579 = 02120579 = 04

120587d

Figure 1 The relationship chart among 120587119889 119886 and 119903 given 120582 = 05

120573 = 2 and 119892 = 2

Concluding the above analyses we get the following

Proposition 2 (i) If 120579 is a sufficiently small positive value119862(119886119891119887

)minus119892(1minus119886119891119887

) le 0 the consignor holds the optimal partialequity of the carrier 119903

lowast

isin (0 120582) and the customization levelwhich the entrepreneur chooses is below social optimal levelthat is 119886

lowast

lt 119886119891119887 If 120579 is sufficiently larger choosing 119903

lowast

= 0 willbe beneficial for the consignor

(ii) In the case when purchasing at par (120579 = 0) 119903lowast

= 120582

and 119886lowast

= 119886119891119887

hold and the efficient customization level can beobtained

(iii) In the case when purchasing at discount 119903lowast

gt 120582 and119886lowast

gt 119886119891119887

hold and optimal partial ownership can motivate theentrepreneur to choose the socially optimal customization type

Proposition 2 demonstrates that only when purchasing atpar can optimal equity participation mechanism make surethat themost efficient outcome is obtainedWhen purchasingat premium or discount price the distortion effects of wealthtransfer will make the customization outcome brought upby optimal partial ownership deviate from social optimalinvestment type

According to Proposition 2 we can interpret why theaverage equity ratios Chinese consignors hold of carriersrsquoequity ownership exceed the corresponding value of Amer-ican firms under the condition of the same technologyparameters In China majority equity ownership of the firmsis under the control of individual investors or institutioninvestors the exchange ratio of the stock is very low and theexchange of stock is often solved by private negotiation [22]Generally in this case 119875(119903) will not deviate seriously from itsreal value and 120579 is likely to be bigger than zero slightly Butin the United States whose capital markets are very matureequity ownership of firms is widely dispersed the publicshareholders hold the majority equities the ownership 119903 isobtained by exchange in the stock market and the bids ofmany trade entities lead to 120579-value exceeding zero greatly[23ndash25] Therefore when other technical parameters arenot changed the mechanism that the greater 120579-value wouldlead to the smaller 119903

lowast will result in the interfirm equityparticipation ratio in China to be obviously higher than thatof the same industry in the United States

4 Equity Participation by the Consignor inthe Public-Type Carrier

In this section we will expand our analyses of the opti-mal partial ownership to the public carrier operated byprofessional managers When the carrier is not owner-managed but is a public-firm the analyses of last sectiondo not apply completely in that professional managers inthe interest of the stockholders will not be affected directlyby the dispersive equities when considering investmentincome Even so our analyses belowdemonstrates that partialownership still affects the customization choice of managersand a conclusion similar to the last section will be obtained

For simplicity of analyses besides the assumption that themanager of carrier is risk neutral we also assume that thereexists nomanagerrsquosmoral hazard about reward compensatingmechanism and endeavor choice problem Assume thatrewards of manager are a minority part of the whole profit ofcarrier which ensures that manager makes decisions in theinterest of the stockholders Based on these assumptions wecan attain the bargaining outcome below

Lemma 3 Given r and 120582 let 119875119873

= 0 then the consignor pays

119879

=(1 minus 120582) 119890

119886

119892 + (120582 minus 119903) 119892 (1 minus 119886)

1 minus 119903

(24)

to the public-type carrier

And the incomes obtained by the two trade parties arerespectively

119878119879

(119903) =(1 minus 120582) 119890

119886

119892 + (120582 minus 119903) 119892 (1 minus 119886)

1 minus 119903minus 1205731198862

119861119879

(119903) = 120582119892119890119886

minus (120582 minus 119903) 119892 (1 minus 119886) minus 1199031205731198862

(25)

From the payoff matrix of two trade parties we canobtain

119879= 119875119879 that is no matter what type the carrier

belongs to the payoffs of the consignor are the same Thereexist differences between two types of carrierrsquo trade incomefunction But for the consignor the function formof the tradeincome remains unchanged

Observing that the manager of the carrier will choosethe customization level 119886

lowast to maximize its utility given themanagerrsquos risk neutrality we know

119886lowast

= arg[120597119878119879

(119903)

120597119886= 0] (26)

Given 119903 the manager would choose 119886lowast

(119903) to maximizethe earnings of the carrier then decision-makers of consignorcan decide on equity participation ratio to maximize its netincome

119889 Here we adopt the form below to describe

119889

119889

= 119861119879

(119903) + 1199031205870

minus (119903) (27)

where (119903) denotes the price at which the consignor buys afraction 119903 of equity of the carrier Assuming that the faction119903 of equity is purchased through tender offers the real value

Mathematical Problems in Engineering 7

120575(119903) of the carrier based on the partial ownership 119903 can beexpressed as

120575 (119903) = 119878119879

(119903) + 1205870 (28)

(119903) can be denoted as follows

(119903) = (1 + 120579) 119903120575 (119903) (29)

Therefore the total net income of the consignor can bedescribed as

119889

= 119861119879

(119903) + 1199031205870

minus 119903 (1 + 120579) [119878119879

(119903) + 1205870] (30)

The optimal partial ownership 119903lowast must satisfy the first-

order condition

120597119889

120597119903 | 119903 = 119903lowast

= 0 (31)

We further have

(120597119886lowast

120597119903) [1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)] minus 120579119878119879

(119903) minus 1205791205870

minus(1 + 120579119903) (1 minus 119886) 119892

(1 minus 119903)2

= 0

(32)

Obviously when 120579 gt 0 and is sufficiently small 119903lowast

isin

(0 120582) Similar to the conclusions of the last section the valuesof 119886lowast and 119903

lowast will be adjusted to correspond to positive ornegative 120579-value In this paper we will only analyze the caseof 120579 gt 0

By (32) we get

1205972

119889

120597119903120597120582= [

120597119886lowast

120597119903] [11988110158401015840

(119886lowast

) minus 11986210158401015840

(119886lowast

)] [120597119886lowast

120597120582] minus

1 + 120573119903

(1 minus 119903)2

lowast [minus (1 minus 119886lowast

) 119881 (119886lowast

) minus (1 minus 120582) 119881 (119886lowast

) (120597119886lowast

120597120582)

+ (1 minus 119886) (1 minus 120582) 119881 (119886lowast

) (120597119886lowast

120597120582)]

+ [1205972

119886lowast

120597119903120597120582] [1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)] +120573 (1 minus 119886

lowast

) 119881 (119886lowast

)

1 minus 119903

(33)

By 120597119878119879(119903)(120597119886 | 119886 = 119886

lowast

) = 0 we know

120597119886lowast

120597119903gt 0

120597119886lowast

120597120582lt 0

1205972

119886lowast

120597119903120597120582lt 0 (34)

Then in (33) all the right-hand terms exceed zero thus

1205972

120587119889

120597119903120597120582gt 0 (35)

Since Sign(120597119903lowast

120597120582) = Sign(1205972

119889120597119903120597120582) we can get

120597119903lowast

120597120582gt 0

120597119903lowast

1205971205870

lt 0 (36)

0 01 02 03 04 05 06 07 08 090

010203040506070809

1

r

a

120582 = 02120582 = 05120582 = 08

Figure 2 The relationship chart between 119886 and 119903 given 120573 = 2 119892 =

12

Given the values of 120582 120573 and 119892 we can find out therelationship between 119886 and 119903 through numerical simulationin Figure 2

Our numerical result shows that parameters 119886 and 119903 areincreasing function of 120582 and 119886 increases nonlinearly in r

From the above analyses we can conclude the following

Proposition 4 Assuming that the carrier is a public-firmmanaged by the manager in the interest of the share-holderswhen purchasing at premium price the optimal equity partic-ipation ratio 119903

lowast by the consignor increases in 120582 but decreasesin 1205870

5 Discussions about Customized ProductionEfficiency and Policy Implications

The theory of optimal ownership structure extracts thedistillate of two stream academic ideas the financial structuretheory and the managerial motivation theory which havebeen agreed on in economic literature [19] For exampleJensen andMeckling [26] pointed out that agent costs causedby dilution of ownership are derived from the fact thatthe incentive of inside controllers cannot keep track withthat of the ownerrsquos On the other hand many academicpapers demonstrate that an outside artificial person whoholds a major part of ownership has a positive effect onthe firmrsquos value [10 17 26ndash28] These papers emphasizedthe supervising function of the outside artificial personsrsquoshare-holders to the firmrsquos managers Compared with theseexisting articles we provide a theoretical interpretation whyoutside artificial persons hold partial ownership under thecircumstance of vertical transaction relationship Our resultis if the downstream firm holds partial ownership of theupstream firm it may function as a bonding mechanismwhich improves the performance of twoparties Itmeans thatcompared with 119903 = 0 the mechanism of partial ownershipimproves the efficiency of customization service

However can the optimal partial ownership result insocial optimal customized transportation level

As we know no matter what type the carrier is eitherowner-managed one or a public-firm managed by managers119903lowast

= 120582 or 119903lowast

= 05 is the necessary condition bringing in

8 Mathematical Problems in Engineering

social optimal customization level If the carrier is an owner-managed one only when the purchasing of partial ownershipat par price occursmay choosing 119903

lowast

= 120582 be a rational decisionfor the consignor aiming at maximizing its total net incomeBut purchasing at premium price is dominant in reality ifcalculated under general case of 120582 = 05 the optimal partialownership 119903

lowast is less than 120582 not large enough to motivatethe decision-maker of the carrier to choose the most efficientcustomized production level The marginal return obtainedby the consignor through enlarging equity participation ratiowill be offset by marginal costs of purchasing the equityownership and premium price distorting effects lead to theefficiency loss of the carrierrsquos customization investment (119903

lowast

lt

05)On the opposite when purchasing at discount overmoti-

vation leads to 119903lowast

gt 120582 and the customization efficiency lossmay still occur Therefore we hold that the effect of wealthtransfer in the purchase of equity ownership is the mainreason that leads to efficiency loss of customized productionwhich shows our theory about partial ownership differentfrom the entrepreneur endeavor choice interpretation byDasgupta and Tao but similar to the conclusion of Aghionand Tirolersquos that partial ownership arrangement can motivatespecial investment but cannot solve the investorsrsquo underin-vestment problem totally

However when the carrier is public-managed even ifthere exist 120579 = 0 and the optimal partial ownership 119903

lowast

lt

120582 social optimal customization level cannot be obtainedbecause the benefit of the consignor does not keep consistentwith the trade partiesrsquo common benefit When 120579 gt 0119903lowast will become smaller and the higher loss degree of thecustomization investment efficiency will occur Obviouslyunder the second-order condition constraint that we can getthe optimal solution satisfying (32) the larger the averagepremium price parameter is the smaller 119903

lowast is the lowercustomized production efficiency becomes and the greatersocial welfare loss will be which holds true in the caseof owner-managed carrier As for the case of 120579 lt 0 itaccords with the aforementioned analyses that is the over-motivation of equity ownership may lead to customizedproduction efficiency loss

In China the state-owned equity reform in logisticindustry just began with unclear ownership partition andmany social functions assumed by firms are not peeled offThe high premium-price acquisitions may make carriers tochoose 119903

lowast

= 0 which leads to the undermotivation of thecustomization investment of consignors and the social opti-mal customized transportation cannot be realizedThereforein the developing process of logistic supply chains in Chinait is necessary that the logistic firms should become theentities that can be self-managed self-constricted and self-motivated and the burden of the social functions will lead tothe loss of the transportation efficiency which are all what wemust pay attention to

In addition when all technical parameters keep constantcomparing optimal partial ownership in the cases of twodifferent types of carrier we can discover that in theorythe ratio of optimal equity participation by the consignor inthe owner-managed carrier should exceed the ratio in the

public-managed firm that is 119903lowast

gt 119903lowast It provides a theoretic

foundation for us to interpret that the interfirmmutual share-holding ratios of the member-firms within the familial-typelogistic supply chains aremuch larger than those ratioswithinthe public-type logistic supply chains At the same time italso means that the customized production efficiency of theformer is higher than that of the latter Although there is roomfor improvement we still firmly believe that the success ofChinese logistic industry should be mainly attributed to theadvantage of owner-managed efficiency

To be mentioned the mechanism of partial ownershipundoubtedly improves the cooperative efficiency of twotrade parties Although social welfare level this arrangementprovides is not optimal the cooperative mechanism helpsto enhance Pareto improvement of the return of two tradeparties compared with simple contract system

6 Conclusions

The phenomena that one consignor holds equity ownershipof one carrier within logistic supply chain are often observedDespite its importance the existing interpretations for inter-firm partial ownership scheme remain relatively unexploredIn this paper a theoretical explanation for equity partici-pation arrangement existing between member-firms withinlogistic supply chain is provided under the background ofcustomized production

Based on the models in which we view the parame-ter for customization level as the selective variable of thecarrier we figure out that the simple contract cannot solvethe low-efficient customized production problem Equityparticipation mechanism together with simple contract canimprove the efficiency of customized transportation Thepartial ownership mechanism supported by customized pro-duction plays a role as a bond in keeping the relationaltransactions among member-firms but not a role as theefficiency-enhancing mechanism resulting from outside arti-ficial personsrsquo supervision in some literature about equityownership structure

What is more on the basis of keeping the logic deductiveconsistency we obtain the outcome of the optimal partialownership affected by the relative bargaining power 120582 ofthe consignor and the other outside income 120587

0of the

carrier under two cases of owner-managed firm type andpublic-firm type respectively and showwhy the familial-typelogistic supply chains may choose more efficient customizedproduction level than public-type logistic supply chains

To be mentioned our theory provides few cases inwhich we can verify the interfirm equity participation ratioAlthough many important conclusions we obtain seem to beconsistent with some evidences there is a need for furtherstudy such as analyzing bilateral cross-shareholding case andconsidering the relationship between bargaining power andequity participation ratio through extending our models

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Mathematical Problems in Engineering 9

Acknowledgments

We acknowledge financial support from the National NatureScience Foundation of China (Grant nos 71001073 71371127and 71471118) the National Soft Science Research Plan(Grant no 2013GXS4D138) the Humanities and SocialSciences Foundation of Ministry of Education of China(Grant nos 13YJA630050 and 14YJC630096) DevelopmentProgram for Distinguished Young Teachers in Higher Edu-cation of Guangdong Province (Grant no Yq2013140 andYq2013147) and the Open Foundation of Shenzhen KeyLaboratory of Urban Planning and Decision Making (Grantno UPDMHITSZ2014B07) We would like to thank theanonymous referees for their valuable suggestions

References

[1] T M Choi Fashion Supply Chain Management Industry andBusiness Analysis IGI Global Hershey Pa USA 2011

[2] S Guercini and A Runfola ldquoRelational paths in business net-work dynamics evidence from the fashion industryrdquo IndustrialMarketing Management vol 41 no 5 pp 807ndash815 2012

[3] G B Richardson ldquoThe organization of industryrdquo EconomicJournal vol 82 pp 883ndash896 1972

[4] G P Pisano ldquoUsing equity participation to support exchangeevidence from the biotechnology industryrdquo Journal of LawEconomics and Organization vol 5 no 1 pp 109ndash126 1989

[5] TMChoi P S Chow and SC Liu ldquoImplementation of fashionERP systems in China case study of a fashion brand reviewand future challengesrdquo International Journal of ProductionEconomics vol 146 no 1 pp 70ndash81 2013

[6] X D Lin ldquoSpecial investment optimal partial ownership andincentive efficiencyrdquo in Proceedings of the 4th International Con-ference on Wireless Communications Networking and MobileComputing (WiCOM rsquo08) pp 1ndash4 Dalian China October 2008

[7] M Aoki Information Incentives and Bargaining in the JapaneseEconomy Cambridge University Press Cambridge UK 1988

[8] J H Dyer andWGOuchi ldquoJapanese-style partnerships givingcompanies a competitive edgerdquo Sloan Management Review vol14 pp 51ndash63 1993

[9] Y-K Che and D B Hausch ldquoCooperative investments and thevalue of contractingrdquo The American Economic Review vol 89no 1 pp 125ndash147 1999

[10] O E Williamson ldquoCredible commitments using hostages tosupport exchangerdquo American Economic Review vol 73 no 2pp 519ndash540 1983

[11] O Hart and JMoore ldquoIncomplete contracts and renegotiationrdquoEconometrica vol 56 no 4 pp 755ndash785 1988

[12] S Grossman and O Hart ldquoThe costs and benefits of ownershipa theory of vertical and lateral integrationrdquo Journal of PoliticalEconomy vol 94 no 2 pp 691ndash719 1989

[13] O E Williamson The Economic Institutions of CapitalismFirms Markets Relational Contracting Macmillan PrincetonNJ USA 1985

[14] B Klein R Crawford and A Alchian ldquoVertical integrationappropriable rents and the competitive contracting processrdquoThe Journal of Law and Economics vol 21 no 1 pp 297ndash3261978

[15] P Milgrom and J Roberts Economics Organization andManagement Prentice Hall Englewood Cliffs NJ USA 1992

[16] M R Scheffer ldquoTrends in textile markets and their implicationsfor textile products and processesrdquo in The Global Textile andClothing Industry pp 8ndash28 2012

[17] P Bolton and M D Whinston ldquoIncomplete contracts verticalintegration and supply assurancerdquoReview of Economics Studiesvol 60 no 1 pp 121ndash148 1993

[18] R G Rajan and L Zingales ldquoPower in a theory of the firmrdquoQuarterly Journal of Economics vol 113 no 1 pp 387ndash432 1998

[19] S Dasgupta and Z Tao ldquoBargaining bonding and partialownershiprdquo International Economic Review vol 41 no 3 pp609ndash635 2000

[20] P Aghion and J Tirole ldquoThe management of innovationrdquoQuarterly Journal of Economics vol 109 no 3 pp 1185ndash12091994

[21] T Y Chung ldquoIncomplete contracts specific investments andrisk sharingrdquo Review of Economic Studies vol 58 pp 1031ndash10421991

[22] Y Yu T-M Choi C-L Hui and T-K Ho ldquoA new andefficient intelligent collaboration scheme for fashion designrdquoIEEE Transactions on Systems Man and Cybernetics A Systemsand Humans vol 41 no 3 pp 463ndash475 2011

[23] T-M Choi C-L Hui N Liu S-F Ng and Y Yu ldquoFast fashionsales forecasting with limited data and timerdquo Decision SupportSystems vol 59 no 1 pp 84ndash92 2014

[24] W K Wong and S Y S Leung ldquoGenetic optimization of fabricutilization in apparel manufacturingrdquo International Journal ofProduction Economics vol 114 no 1 pp 376ndash387 2008

[25] B Asanuma ldquoManufacturer-supplier relationships in Japan andthe concept of relation-specific skillrdquo Journal of The Japaneseand International Economies vol 3 no 1 pp 1ndash30 1989

[26] M C Jensen and W H Meckling ldquoTheory of the firmmanagerial behavior agency costs and ownership structurerdquoJournal of Financial Economics vol 3 no 4 pp 305ndash360 1976

[27] T-M Choi C-L Hui S-F Ng and Y Yu ldquoColor trendforecasting of fashionable products with very few historicaldatardquo IEEE Transactions on Systems Man and Cybernetics PartC Applications and Reviews vol 42 no 6 pp 1003ndash1010 2012

[28] P Aghion and P Bohton ldquoAn incomplete contracts approach tofinancial contractingrdquo Review of Economic Studies vol 59 no3 pp 473ndash494 1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

Given 119886 chosen by carrier at 119905 = 1 the managerof consignor would at 119905 = 0 decide on optimal equityparticipation ratio 119903 to maximize its total net income Aswe all know under the mechanism of partial ownershipthe consignor can get a lot of benefits from customizedtransportation but must pay for obtaining partial ownershipof carrierThe reason why complete vertical integration is notalways the optimal choice lies in the fact that the integrationcost is likely to exceed the added-value benefits of customizedtransportation

Assuming that other outside income of the upstreamcarrier is 120587

0 we express 119875(119903) that the consignor pays for

obtaining an equity ratio 119903 of the carrier in the followingequation

119875 (119903) = (1 + 120579) [(119878119879

(119900) + 1205870) minus (119878

119879(119903) + (1 minus 119903) 120587

0)] (15)

In this equation (119878119879(119900)+120587

0) term represents total income

of entrepreneur when 119903 = 0 and (119878119879(119903) + (1 minus 119903)120587

0) is the

correspondent revenue that entrepreneur earns when equityparticipation ratio is 119903 The surplus between these two termscan be regarded as the real value of the equity fraction 119903

of the upstream carrier Let 120579 denote the average premium(discount) price coefficient at which the consignor acquires afraction 119903 of the carrier where 120579 gt 0 represents purchasingat premium 120579 = 0 represents purchasing at par and 120579 lt 0

represents purchasing at discount In order to accord with theactual scenarios of equity fight we install 120579-coefficient intothe formula to calculate 119875(119903)

Let 120587119889denote net income of the downstream consignor

then120587119889

= 119861119879

(119903) + 1199031205870

minus 119875 (119903) (16)

Substituting 119861119879(119903) and 119875(119903) into above equation we get

120587119889

= 119890119886

119892 minus 1205731198862

+ 120579119878119879

(119903) minus 1205791205870119903 minus (1 + 120579) 119878

119879(0) (17)

Anticipating that the entrepreneur chooses 119886lowast based on

equity participation ratio 119903 that is 119886lowast

= 119886lowast

(119903) the managerof the downstream consignor will try to acquire optimalequity ratio 119903

lowast for maximizing 120587119889 that is

119903lowast

= argmax119903

120587119889 (18)

The first order condition demands120597119886lowast

120597119903[1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)]

+ 120579 [119862 (119886lowast

) minus 119892 (1 minus 119886lowast

)] minus 1205791205870

= 0

(19)

Without loss of generality suppose 1205731198862

fb minus 119892(1 minus 119886fb) le 0we will discuss the results in the cases of different 120579-values

32 The Effects of 120579 on 119886lowast and 119903

lowast

(1) 120579 gt 0 which means purchasing at premiumBy (9) we know

1205972

119878119879

(119903)

120597(119886lowast)2

lt 0 (20)

Moreover 1205972119878119879(119903)120597119886

lowast

120597119903 = 2120573 gt 0

Thus 120597119886lowast

120597119903= (minus1205972

119878119879(119903)120597119886

lowast

120597119903)(1205972

119878119879(119903)120597(119886

lowast

)2

) gt

0Since 119881

1015840

(119886lowast

) minus 1198621015840

(119886lowast

) lt 0 when 120579 is sufficientlysmaller we have

120597120587119889

120597119903|119903=0

gt 0

120597120587119889

120597119903|119903=120582

= 120579 [119862 (119886fb) minus (1 minus 119886fb) 119892 minus 1205870] lt 0

(21)

Thus the optimal partial ownership 119903lowast

isin (0 120582) andwe can get 119886

lowast

gt 119886fbIf 120579 is sufficiently larger forall119903 isin [0 1] 120597120587

119889120597119903 lt 0 then

119903lowast

= 0

(2) 120579 = 0 which means purchasing at parObviously for (19) to hold it requires

1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

) = 0 (22)

Then 119903lowast = 120582 and 119886lowast

= 119886fb(3) 120579 lt 0 which means purchasing at discount

Evidently when the value of the upstream fabric supplieris underestimated the consignor will buy as much equity aspossible to maximize its total net income Although over-incentive effects of equitymay lead to customized productionlevel exceeding the social optimality and the increase ofthe equity investment revenue renders the manager of theconsignor to purchase the share of 119903

lowast greatly exceedingsocial optimal level that is 119903

lowast

gt 120582 Besides when theshare-holding ratio of the downstream consignor exceeds theentrepreneurrsquos the customization level of carrier should equalthe social optimal one So we have

119886lowast

= 119886fb if 119903lowast

ge1

2

lt 119886fb if 119903lowast

lt1

2

(23)

If 120579 is sufficiently negative then 119903lowast

= 1 and 119886lowast

= 119886fbNotably we regard 120579 as a constant in this paper which doesnot affect our analyses about the optimal equity participationratio

But what we must pay attention to is that with 119903

vibrating average discount (or premium) price parameter 120579

may also be changeable The exact magnitude of the optimalcustomization level 119886 and partial ownership 119903 will depend on120579-value

The three-dimension chart (see Figure 1) shows thatwhen 120579 drops from 04 to minus04 120587

119889(119886 119903) the equilibrium

path demonstrates an increasing trend and the optimalcustomization level 119886 is increasing in 119903 With equity purchaseshifting from discount price to premium price the drop ofoptimal equity participation ratiowill result in the customiza-tion transportation level and the net income of consignordecreasing simultaneously

6 Mathematical Problems in Engineering

0 01 02 03 04 05 06 07 08 09 1

001020304050607minus02minus01

00102030405

ar

120579 = minus04120579 = minus02120579 = 0

120579 = 02120579 = 04

120587d

Figure 1 The relationship chart among 120587119889 119886 and 119903 given 120582 = 05

120573 = 2 and 119892 = 2

Concluding the above analyses we get the following

Proposition 2 (i) If 120579 is a sufficiently small positive value119862(119886119891119887

)minus119892(1minus119886119891119887

) le 0 the consignor holds the optimal partialequity of the carrier 119903

lowast

isin (0 120582) and the customization levelwhich the entrepreneur chooses is below social optimal levelthat is 119886

lowast

lt 119886119891119887 If 120579 is sufficiently larger choosing 119903

lowast

= 0 willbe beneficial for the consignor

(ii) In the case when purchasing at par (120579 = 0) 119903lowast

= 120582

and 119886lowast

= 119886119891119887

hold and the efficient customization level can beobtained

(iii) In the case when purchasing at discount 119903lowast

gt 120582 and119886lowast

gt 119886119891119887

hold and optimal partial ownership can motivate theentrepreneur to choose the socially optimal customization type

Proposition 2 demonstrates that only when purchasing atpar can optimal equity participation mechanism make surethat themost efficient outcome is obtainedWhen purchasingat premium or discount price the distortion effects of wealthtransfer will make the customization outcome brought upby optimal partial ownership deviate from social optimalinvestment type

According to Proposition 2 we can interpret why theaverage equity ratios Chinese consignors hold of carriersrsquoequity ownership exceed the corresponding value of Amer-ican firms under the condition of the same technologyparameters In China majority equity ownership of the firmsis under the control of individual investors or institutioninvestors the exchange ratio of the stock is very low and theexchange of stock is often solved by private negotiation [22]Generally in this case 119875(119903) will not deviate seriously from itsreal value and 120579 is likely to be bigger than zero slightly Butin the United States whose capital markets are very matureequity ownership of firms is widely dispersed the publicshareholders hold the majority equities the ownership 119903 isobtained by exchange in the stock market and the bids ofmany trade entities lead to 120579-value exceeding zero greatly[23ndash25] Therefore when other technical parameters arenot changed the mechanism that the greater 120579-value wouldlead to the smaller 119903

lowast will result in the interfirm equityparticipation ratio in China to be obviously higher than thatof the same industry in the United States

4 Equity Participation by the Consignor inthe Public-Type Carrier

In this section we will expand our analyses of the opti-mal partial ownership to the public carrier operated byprofessional managers When the carrier is not owner-managed but is a public-firm the analyses of last sectiondo not apply completely in that professional managers inthe interest of the stockholders will not be affected directlyby the dispersive equities when considering investmentincome Even so our analyses belowdemonstrates that partialownership still affects the customization choice of managersand a conclusion similar to the last section will be obtained

For simplicity of analyses besides the assumption that themanager of carrier is risk neutral we also assume that thereexists nomanagerrsquosmoral hazard about reward compensatingmechanism and endeavor choice problem Assume thatrewards of manager are a minority part of the whole profit ofcarrier which ensures that manager makes decisions in theinterest of the stockholders Based on these assumptions wecan attain the bargaining outcome below

Lemma 3 Given r and 120582 let 119875119873

= 0 then the consignor pays

119879

=(1 minus 120582) 119890

119886

119892 + (120582 minus 119903) 119892 (1 minus 119886)

1 minus 119903

(24)

to the public-type carrier

And the incomes obtained by the two trade parties arerespectively

119878119879

(119903) =(1 minus 120582) 119890

119886

119892 + (120582 minus 119903) 119892 (1 minus 119886)

1 minus 119903minus 1205731198862

119861119879

(119903) = 120582119892119890119886

minus (120582 minus 119903) 119892 (1 minus 119886) minus 1199031205731198862

(25)

From the payoff matrix of two trade parties we canobtain

119879= 119875119879 that is no matter what type the carrier

belongs to the payoffs of the consignor are the same Thereexist differences between two types of carrierrsquo trade incomefunction But for the consignor the function formof the tradeincome remains unchanged

Observing that the manager of the carrier will choosethe customization level 119886

lowast to maximize its utility given themanagerrsquos risk neutrality we know

119886lowast

= arg[120597119878119879

(119903)

120597119886= 0] (26)

Given 119903 the manager would choose 119886lowast

(119903) to maximizethe earnings of the carrier then decision-makers of consignorcan decide on equity participation ratio to maximize its netincome

119889 Here we adopt the form below to describe

119889

119889

= 119861119879

(119903) + 1199031205870

minus (119903) (27)

where (119903) denotes the price at which the consignor buys afraction 119903 of equity of the carrier Assuming that the faction119903 of equity is purchased through tender offers the real value

Mathematical Problems in Engineering 7

120575(119903) of the carrier based on the partial ownership 119903 can beexpressed as

120575 (119903) = 119878119879

(119903) + 1205870 (28)

(119903) can be denoted as follows

(119903) = (1 + 120579) 119903120575 (119903) (29)

Therefore the total net income of the consignor can bedescribed as

119889

= 119861119879

(119903) + 1199031205870

minus 119903 (1 + 120579) [119878119879

(119903) + 1205870] (30)

The optimal partial ownership 119903lowast must satisfy the first-

order condition

120597119889

120597119903 | 119903 = 119903lowast

= 0 (31)

We further have

(120597119886lowast

120597119903) [1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)] minus 120579119878119879

(119903) minus 1205791205870

minus(1 + 120579119903) (1 minus 119886) 119892

(1 minus 119903)2

= 0

(32)

Obviously when 120579 gt 0 and is sufficiently small 119903lowast

isin

(0 120582) Similar to the conclusions of the last section the valuesof 119886lowast and 119903

lowast will be adjusted to correspond to positive ornegative 120579-value In this paper we will only analyze the caseof 120579 gt 0

By (32) we get

1205972

119889

120597119903120597120582= [

120597119886lowast

120597119903] [11988110158401015840

(119886lowast

) minus 11986210158401015840

(119886lowast

)] [120597119886lowast

120597120582] minus

1 + 120573119903

(1 minus 119903)2

lowast [minus (1 minus 119886lowast

) 119881 (119886lowast

) minus (1 minus 120582) 119881 (119886lowast

) (120597119886lowast

120597120582)

+ (1 minus 119886) (1 minus 120582) 119881 (119886lowast

) (120597119886lowast

120597120582)]

+ [1205972

119886lowast

120597119903120597120582] [1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)] +120573 (1 minus 119886

lowast

) 119881 (119886lowast

)

1 minus 119903

(33)

By 120597119878119879(119903)(120597119886 | 119886 = 119886

lowast

) = 0 we know

120597119886lowast

120597119903gt 0

120597119886lowast

120597120582lt 0

1205972

119886lowast

120597119903120597120582lt 0 (34)

Then in (33) all the right-hand terms exceed zero thus

1205972

120587119889

120597119903120597120582gt 0 (35)

Since Sign(120597119903lowast

120597120582) = Sign(1205972

119889120597119903120597120582) we can get

120597119903lowast

120597120582gt 0

120597119903lowast

1205971205870

lt 0 (36)

0 01 02 03 04 05 06 07 08 090

010203040506070809

1

r

a

120582 = 02120582 = 05120582 = 08

Figure 2 The relationship chart between 119886 and 119903 given 120573 = 2 119892 =

12

Given the values of 120582 120573 and 119892 we can find out therelationship between 119886 and 119903 through numerical simulationin Figure 2

Our numerical result shows that parameters 119886 and 119903 areincreasing function of 120582 and 119886 increases nonlinearly in r

From the above analyses we can conclude the following

Proposition 4 Assuming that the carrier is a public-firmmanaged by the manager in the interest of the share-holderswhen purchasing at premium price the optimal equity partic-ipation ratio 119903

lowast by the consignor increases in 120582 but decreasesin 1205870

5 Discussions about Customized ProductionEfficiency and Policy Implications

The theory of optimal ownership structure extracts thedistillate of two stream academic ideas the financial structuretheory and the managerial motivation theory which havebeen agreed on in economic literature [19] For exampleJensen andMeckling [26] pointed out that agent costs causedby dilution of ownership are derived from the fact thatthe incentive of inside controllers cannot keep track withthat of the ownerrsquos On the other hand many academicpapers demonstrate that an outside artificial person whoholds a major part of ownership has a positive effect onthe firmrsquos value [10 17 26ndash28] These papers emphasizedthe supervising function of the outside artificial personsrsquoshare-holders to the firmrsquos managers Compared with theseexisting articles we provide a theoretical interpretation whyoutside artificial persons hold partial ownership under thecircumstance of vertical transaction relationship Our resultis if the downstream firm holds partial ownership of theupstream firm it may function as a bonding mechanismwhich improves the performance of twoparties Itmeans thatcompared with 119903 = 0 the mechanism of partial ownershipimproves the efficiency of customization service

However can the optimal partial ownership result insocial optimal customized transportation level

As we know no matter what type the carrier is eitherowner-managed one or a public-firm managed by managers119903lowast

= 120582 or 119903lowast

= 05 is the necessary condition bringing in

8 Mathematical Problems in Engineering

social optimal customization level If the carrier is an owner-managed one only when the purchasing of partial ownershipat par price occursmay choosing 119903

lowast

= 120582 be a rational decisionfor the consignor aiming at maximizing its total net incomeBut purchasing at premium price is dominant in reality ifcalculated under general case of 120582 = 05 the optimal partialownership 119903

lowast is less than 120582 not large enough to motivatethe decision-maker of the carrier to choose the most efficientcustomized production level The marginal return obtainedby the consignor through enlarging equity participation ratiowill be offset by marginal costs of purchasing the equityownership and premium price distorting effects lead to theefficiency loss of the carrierrsquos customization investment (119903

lowast

lt

05)On the opposite when purchasing at discount overmoti-

vation leads to 119903lowast

gt 120582 and the customization efficiency lossmay still occur Therefore we hold that the effect of wealthtransfer in the purchase of equity ownership is the mainreason that leads to efficiency loss of customized productionwhich shows our theory about partial ownership differentfrom the entrepreneur endeavor choice interpretation byDasgupta and Tao but similar to the conclusion of Aghionand Tirolersquos that partial ownership arrangement can motivatespecial investment but cannot solve the investorsrsquo underin-vestment problem totally

However when the carrier is public-managed even ifthere exist 120579 = 0 and the optimal partial ownership 119903

lowast

lt

120582 social optimal customization level cannot be obtainedbecause the benefit of the consignor does not keep consistentwith the trade partiesrsquo common benefit When 120579 gt 0119903lowast will become smaller and the higher loss degree of thecustomization investment efficiency will occur Obviouslyunder the second-order condition constraint that we can getthe optimal solution satisfying (32) the larger the averagepremium price parameter is the smaller 119903

lowast is the lowercustomized production efficiency becomes and the greatersocial welfare loss will be which holds true in the caseof owner-managed carrier As for the case of 120579 lt 0 itaccords with the aforementioned analyses that is the over-motivation of equity ownership may lead to customizedproduction efficiency loss

In China the state-owned equity reform in logisticindustry just began with unclear ownership partition andmany social functions assumed by firms are not peeled offThe high premium-price acquisitions may make carriers tochoose 119903

lowast

= 0 which leads to the undermotivation of thecustomization investment of consignors and the social opti-mal customized transportation cannot be realizedThereforein the developing process of logistic supply chains in Chinait is necessary that the logistic firms should become theentities that can be self-managed self-constricted and self-motivated and the burden of the social functions will lead tothe loss of the transportation efficiency which are all what wemust pay attention to

In addition when all technical parameters keep constantcomparing optimal partial ownership in the cases of twodifferent types of carrier we can discover that in theorythe ratio of optimal equity participation by the consignor inthe owner-managed carrier should exceed the ratio in the

public-managed firm that is 119903lowast

gt 119903lowast It provides a theoretic

foundation for us to interpret that the interfirmmutual share-holding ratios of the member-firms within the familial-typelogistic supply chains aremuch larger than those ratioswithinthe public-type logistic supply chains At the same time italso means that the customized production efficiency of theformer is higher than that of the latter Although there is roomfor improvement we still firmly believe that the success ofChinese logistic industry should be mainly attributed to theadvantage of owner-managed efficiency

To be mentioned the mechanism of partial ownershipundoubtedly improves the cooperative efficiency of twotrade parties Although social welfare level this arrangementprovides is not optimal the cooperative mechanism helpsto enhance Pareto improvement of the return of two tradeparties compared with simple contract system

6 Conclusions

The phenomena that one consignor holds equity ownershipof one carrier within logistic supply chain are often observedDespite its importance the existing interpretations for inter-firm partial ownership scheme remain relatively unexploredIn this paper a theoretical explanation for equity partici-pation arrangement existing between member-firms withinlogistic supply chain is provided under the background ofcustomized production

Based on the models in which we view the parame-ter for customization level as the selective variable of thecarrier we figure out that the simple contract cannot solvethe low-efficient customized production problem Equityparticipation mechanism together with simple contract canimprove the efficiency of customized transportation Thepartial ownership mechanism supported by customized pro-duction plays a role as a bond in keeping the relationaltransactions among member-firms but not a role as theefficiency-enhancing mechanism resulting from outside arti-ficial personsrsquo supervision in some literature about equityownership structure

What is more on the basis of keeping the logic deductiveconsistency we obtain the outcome of the optimal partialownership affected by the relative bargaining power 120582 ofthe consignor and the other outside income 120587

0of the

carrier under two cases of owner-managed firm type andpublic-firm type respectively and showwhy the familial-typelogistic supply chains may choose more efficient customizedproduction level than public-type logistic supply chains

To be mentioned our theory provides few cases inwhich we can verify the interfirm equity participation ratioAlthough many important conclusions we obtain seem to beconsistent with some evidences there is a need for furtherstudy such as analyzing bilateral cross-shareholding case andconsidering the relationship between bargaining power andequity participation ratio through extending our models

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Mathematical Problems in Engineering 9

Acknowledgments

We acknowledge financial support from the National NatureScience Foundation of China (Grant nos 71001073 71371127and 71471118) the National Soft Science Research Plan(Grant no 2013GXS4D138) the Humanities and SocialSciences Foundation of Ministry of Education of China(Grant nos 13YJA630050 and 14YJC630096) DevelopmentProgram for Distinguished Young Teachers in Higher Edu-cation of Guangdong Province (Grant no Yq2013140 andYq2013147) and the Open Foundation of Shenzhen KeyLaboratory of Urban Planning and Decision Making (Grantno UPDMHITSZ2014B07) We would like to thank theanonymous referees for their valuable suggestions

References

[1] T M Choi Fashion Supply Chain Management Industry andBusiness Analysis IGI Global Hershey Pa USA 2011

[2] S Guercini and A Runfola ldquoRelational paths in business net-work dynamics evidence from the fashion industryrdquo IndustrialMarketing Management vol 41 no 5 pp 807ndash815 2012

[3] G B Richardson ldquoThe organization of industryrdquo EconomicJournal vol 82 pp 883ndash896 1972

[4] G P Pisano ldquoUsing equity participation to support exchangeevidence from the biotechnology industryrdquo Journal of LawEconomics and Organization vol 5 no 1 pp 109ndash126 1989

[5] TMChoi P S Chow and SC Liu ldquoImplementation of fashionERP systems in China case study of a fashion brand reviewand future challengesrdquo International Journal of ProductionEconomics vol 146 no 1 pp 70ndash81 2013

[6] X D Lin ldquoSpecial investment optimal partial ownership andincentive efficiencyrdquo in Proceedings of the 4th International Con-ference on Wireless Communications Networking and MobileComputing (WiCOM rsquo08) pp 1ndash4 Dalian China October 2008

[7] M Aoki Information Incentives and Bargaining in the JapaneseEconomy Cambridge University Press Cambridge UK 1988

[8] J H Dyer andWGOuchi ldquoJapanese-style partnerships givingcompanies a competitive edgerdquo Sloan Management Review vol14 pp 51ndash63 1993

[9] Y-K Che and D B Hausch ldquoCooperative investments and thevalue of contractingrdquo The American Economic Review vol 89no 1 pp 125ndash147 1999

[10] O E Williamson ldquoCredible commitments using hostages tosupport exchangerdquo American Economic Review vol 73 no 2pp 519ndash540 1983

[11] O Hart and JMoore ldquoIncomplete contracts and renegotiationrdquoEconometrica vol 56 no 4 pp 755ndash785 1988

[12] S Grossman and O Hart ldquoThe costs and benefits of ownershipa theory of vertical and lateral integrationrdquo Journal of PoliticalEconomy vol 94 no 2 pp 691ndash719 1989

[13] O E Williamson The Economic Institutions of CapitalismFirms Markets Relational Contracting Macmillan PrincetonNJ USA 1985

[14] B Klein R Crawford and A Alchian ldquoVertical integrationappropriable rents and the competitive contracting processrdquoThe Journal of Law and Economics vol 21 no 1 pp 297ndash3261978

[15] P Milgrom and J Roberts Economics Organization andManagement Prentice Hall Englewood Cliffs NJ USA 1992

[16] M R Scheffer ldquoTrends in textile markets and their implicationsfor textile products and processesrdquo in The Global Textile andClothing Industry pp 8ndash28 2012

[17] P Bolton and M D Whinston ldquoIncomplete contracts verticalintegration and supply assurancerdquoReview of Economics Studiesvol 60 no 1 pp 121ndash148 1993

[18] R G Rajan and L Zingales ldquoPower in a theory of the firmrdquoQuarterly Journal of Economics vol 113 no 1 pp 387ndash432 1998

[19] S Dasgupta and Z Tao ldquoBargaining bonding and partialownershiprdquo International Economic Review vol 41 no 3 pp609ndash635 2000

[20] P Aghion and J Tirole ldquoThe management of innovationrdquoQuarterly Journal of Economics vol 109 no 3 pp 1185ndash12091994

[21] T Y Chung ldquoIncomplete contracts specific investments andrisk sharingrdquo Review of Economic Studies vol 58 pp 1031ndash10421991

[22] Y Yu T-M Choi C-L Hui and T-K Ho ldquoA new andefficient intelligent collaboration scheme for fashion designrdquoIEEE Transactions on Systems Man and Cybernetics A Systemsand Humans vol 41 no 3 pp 463ndash475 2011

[23] T-M Choi C-L Hui N Liu S-F Ng and Y Yu ldquoFast fashionsales forecasting with limited data and timerdquo Decision SupportSystems vol 59 no 1 pp 84ndash92 2014

[24] W K Wong and S Y S Leung ldquoGenetic optimization of fabricutilization in apparel manufacturingrdquo International Journal ofProduction Economics vol 114 no 1 pp 376ndash387 2008

[25] B Asanuma ldquoManufacturer-supplier relationships in Japan andthe concept of relation-specific skillrdquo Journal of The Japaneseand International Economies vol 3 no 1 pp 1ndash30 1989

[26] M C Jensen and W H Meckling ldquoTheory of the firmmanagerial behavior agency costs and ownership structurerdquoJournal of Financial Economics vol 3 no 4 pp 305ndash360 1976

[27] T-M Choi C-L Hui S-F Ng and Y Yu ldquoColor trendforecasting of fashionable products with very few historicaldatardquo IEEE Transactions on Systems Man and Cybernetics PartC Applications and Reviews vol 42 no 6 pp 1003ndash1010 2012

[28] P Aghion and P Bohton ldquoAn incomplete contracts approach tofinancial contractingrdquo Review of Economic Studies vol 59 no3 pp 473ndash494 1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

0 01 02 03 04 05 06 07 08 09 1

001020304050607minus02minus01

00102030405

ar

120579 = minus04120579 = minus02120579 = 0

120579 = 02120579 = 04

120587d

Figure 1 The relationship chart among 120587119889 119886 and 119903 given 120582 = 05

120573 = 2 and 119892 = 2

Concluding the above analyses we get the following

Proposition 2 (i) If 120579 is a sufficiently small positive value119862(119886119891119887

)minus119892(1minus119886119891119887

) le 0 the consignor holds the optimal partialequity of the carrier 119903

lowast

isin (0 120582) and the customization levelwhich the entrepreneur chooses is below social optimal levelthat is 119886

lowast

lt 119886119891119887 If 120579 is sufficiently larger choosing 119903

lowast

= 0 willbe beneficial for the consignor

(ii) In the case when purchasing at par (120579 = 0) 119903lowast

= 120582

and 119886lowast

= 119886119891119887

hold and the efficient customization level can beobtained

(iii) In the case when purchasing at discount 119903lowast

gt 120582 and119886lowast

gt 119886119891119887

hold and optimal partial ownership can motivate theentrepreneur to choose the socially optimal customization type

Proposition 2 demonstrates that only when purchasing atpar can optimal equity participation mechanism make surethat themost efficient outcome is obtainedWhen purchasingat premium or discount price the distortion effects of wealthtransfer will make the customization outcome brought upby optimal partial ownership deviate from social optimalinvestment type

According to Proposition 2 we can interpret why theaverage equity ratios Chinese consignors hold of carriersrsquoequity ownership exceed the corresponding value of Amer-ican firms under the condition of the same technologyparameters In China majority equity ownership of the firmsis under the control of individual investors or institutioninvestors the exchange ratio of the stock is very low and theexchange of stock is often solved by private negotiation [22]Generally in this case 119875(119903) will not deviate seriously from itsreal value and 120579 is likely to be bigger than zero slightly Butin the United States whose capital markets are very matureequity ownership of firms is widely dispersed the publicshareholders hold the majority equities the ownership 119903 isobtained by exchange in the stock market and the bids ofmany trade entities lead to 120579-value exceeding zero greatly[23ndash25] Therefore when other technical parameters arenot changed the mechanism that the greater 120579-value wouldlead to the smaller 119903

lowast will result in the interfirm equityparticipation ratio in China to be obviously higher than thatof the same industry in the United States

4 Equity Participation by the Consignor inthe Public-Type Carrier

In this section we will expand our analyses of the opti-mal partial ownership to the public carrier operated byprofessional managers When the carrier is not owner-managed but is a public-firm the analyses of last sectiondo not apply completely in that professional managers inthe interest of the stockholders will not be affected directlyby the dispersive equities when considering investmentincome Even so our analyses belowdemonstrates that partialownership still affects the customization choice of managersand a conclusion similar to the last section will be obtained

For simplicity of analyses besides the assumption that themanager of carrier is risk neutral we also assume that thereexists nomanagerrsquosmoral hazard about reward compensatingmechanism and endeavor choice problem Assume thatrewards of manager are a minority part of the whole profit ofcarrier which ensures that manager makes decisions in theinterest of the stockholders Based on these assumptions wecan attain the bargaining outcome below

Lemma 3 Given r and 120582 let 119875119873

= 0 then the consignor pays

119879

=(1 minus 120582) 119890

119886

119892 + (120582 minus 119903) 119892 (1 minus 119886)

1 minus 119903

(24)

to the public-type carrier

And the incomes obtained by the two trade parties arerespectively

119878119879

(119903) =(1 minus 120582) 119890

119886

119892 + (120582 minus 119903) 119892 (1 minus 119886)

1 minus 119903minus 1205731198862

119861119879

(119903) = 120582119892119890119886

minus (120582 minus 119903) 119892 (1 minus 119886) minus 1199031205731198862

(25)

From the payoff matrix of two trade parties we canobtain

119879= 119875119879 that is no matter what type the carrier

belongs to the payoffs of the consignor are the same Thereexist differences between two types of carrierrsquo trade incomefunction But for the consignor the function formof the tradeincome remains unchanged

Observing that the manager of the carrier will choosethe customization level 119886

lowast to maximize its utility given themanagerrsquos risk neutrality we know

119886lowast

= arg[120597119878119879

(119903)

120597119886= 0] (26)

Given 119903 the manager would choose 119886lowast

(119903) to maximizethe earnings of the carrier then decision-makers of consignorcan decide on equity participation ratio to maximize its netincome

119889 Here we adopt the form below to describe

119889

119889

= 119861119879

(119903) + 1199031205870

minus (119903) (27)

where (119903) denotes the price at which the consignor buys afraction 119903 of equity of the carrier Assuming that the faction119903 of equity is purchased through tender offers the real value

Mathematical Problems in Engineering 7

120575(119903) of the carrier based on the partial ownership 119903 can beexpressed as

120575 (119903) = 119878119879

(119903) + 1205870 (28)

(119903) can be denoted as follows

(119903) = (1 + 120579) 119903120575 (119903) (29)

Therefore the total net income of the consignor can bedescribed as

119889

= 119861119879

(119903) + 1199031205870

minus 119903 (1 + 120579) [119878119879

(119903) + 1205870] (30)

The optimal partial ownership 119903lowast must satisfy the first-

order condition

120597119889

120597119903 | 119903 = 119903lowast

= 0 (31)

We further have

(120597119886lowast

120597119903) [1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)] minus 120579119878119879

(119903) minus 1205791205870

minus(1 + 120579119903) (1 minus 119886) 119892

(1 minus 119903)2

= 0

(32)

Obviously when 120579 gt 0 and is sufficiently small 119903lowast

isin

(0 120582) Similar to the conclusions of the last section the valuesof 119886lowast and 119903

lowast will be adjusted to correspond to positive ornegative 120579-value In this paper we will only analyze the caseof 120579 gt 0

By (32) we get

1205972

119889

120597119903120597120582= [

120597119886lowast

120597119903] [11988110158401015840

(119886lowast

) minus 11986210158401015840

(119886lowast

)] [120597119886lowast

120597120582] minus

1 + 120573119903

(1 minus 119903)2

lowast [minus (1 minus 119886lowast

) 119881 (119886lowast

) minus (1 minus 120582) 119881 (119886lowast

) (120597119886lowast

120597120582)

+ (1 minus 119886) (1 minus 120582) 119881 (119886lowast

) (120597119886lowast

120597120582)]

+ [1205972

119886lowast

120597119903120597120582] [1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)] +120573 (1 minus 119886

lowast

) 119881 (119886lowast

)

1 minus 119903

(33)

By 120597119878119879(119903)(120597119886 | 119886 = 119886

lowast

) = 0 we know

120597119886lowast

120597119903gt 0

120597119886lowast

120597120582lt 0

1205972

119886lowast

120597119903120597120582lt 0 (34)

Then in (33) all the right-hand terms exceed zero thus

1205972

120587119889

120597119903120597120582gt 0 (35)

Since Sign(120597119903lowast

120597120582) = Sign(1205972

119889120597119903120597120582) we can get

120597119903lowast

120597120582gt 0

120597119903lowast

1205971205870

lt 0 (36)

0 01 02 03 04 05 06 07 08 090

010203040506070809

1

r

a

120582 = 02120582 = 05120582 = 08

Figure 2 The relationship chart between 119886 and 119903 given 120573 = 2 119892 =

12

Given the values of 120582 120573 and 119892 we can find out therelationship between 119886 and 119903 through numerical simulationin Figure 2

Our numerical result shows that parameters 119886 and 119903 areincreasing function of 120582 and 119886 increases nonlinearly in r

From the above analyses we can conclude the following

Proposition 4 Assuming that the carrier is a public-firmmanaged by the manager in the interest of the share-holderswhen purchasing at premium price the optimal equity partic-ipation ratio 119903

lowast by the consignor increases in 120582 but decreasesin 1205870

5 Discussions about Customized ProductionEfficiency and Policy Implications

The theory of optimal ownership structure extracts thedistillate of two stream academic ideas the financial structuretheory and the managerial motivation theory which havebeen agreed on in economic literature [19] For exampleJensen andMeckling [26] pointed out that agent costs causedby dilution of ownership are derived from the fact thatthe incentive of inside controllers cannot keep track withthat of the ownerrsquos On the other hand many academicpapers demonstrate that an outside artificial person whoholds a major part of ownership has a positive effect onthe firmrsquos value [10 17 26ndash28] These papers emphasizedthe supervising function of the outside artificial personsrsquoshare-holders to the firmrsquos managers Compared with theseexisting articles we provide a theoretical interpretation whyoutside artificial persons hold partial ownership under thecircumstance of vertical transaction relationship Our resultis if the downstream firm holds partial ownership of theupstream firm it may function as a bonding mechanismwhich improves the performance of twoparties Itmeans thatcompared with 119903 = 0 the mechanism of partial ownershipimproves the efficiency of customization service

However can the optimal partial ownership result insocial optimal customized transportation level

As we know no matter what type the carrier is eitherowner-managed one or a public-firm managed by managers119903lowast

= 120582 or 119903lowast

= 05 is the necessary condition bringing in

8 Mathematical Problems in Engineering

social optimal customization level If the carrier is an owner-managed one only when the purchasing of partial ownershipat par price occursmay choosing 119903

lowast

= 120582 be a rational decisionfor the consignor aiming at maximizing its total net incomeBut purchasing at premium price is dominant in reality ifcalculated under general case of 120582 = 05 the optimal partialownership 119903

lowast is less than 120582 not large enough to motivatethe decision-maker of the carrier to choose the most efficientcustomized production level The marginal return obtainedby the consignor through enlarging equity participation ratiowill be offset by marginal costs of purchasing the equityownership and premium price distorting effects lead to theefficiency loss of the carrierrsquos customization investment (119903

lowast

lt

05)On the opposite when purchasing at discount overmoti-

vation leads to 119903lowast

gt 120582 and the customization efficiency lossmay still occur Therefore we hold that the effect of wealthtransfer in the purchase of equity ownership is the mainreason that leads to efficiency loss of customized productionwhich shows our theory about partial ownership differentfrom the entrepreneur endeavor choice interpretation byDasgupta and Tao but similar to the conclusion of Aghionand Tirolersquos that partial ownership arrangement can motivatespecial investment but cannot solve the investorsrsquo underin-vestment problem totally

However when the carrier is public-managed even ifthere exist 120579 = 0 and the optimal partial ownership 119903

lowast

lt

120582 social optimal customization level cannot be obtainedbecause the benefit of the consignor does not keep consistentwith the trade partiesrsquo common benefit When 120579 gt 0119903lowast will become smaller and the higher loss degree of thecustomization investment efficiency will occur Obviouslyunder the second-order condition constraint that we can getthe optimal solution satisfying (32) the larger the averagepremium price parameter is the smaller 119903

lowast is the lowercustomized production efficiency becomes and the greatersocial welfare loss will be which holds true in the caseof owner-managed carrier As for the case of 120579 lt 0 itaccords with the aforementioned analyses that is the over-motivation of equity ownership may lead to customizedproduction efficiency loss

In China the state-owned equity reform in logisticindustry just began with unclear ownership partition andmany social functions assumed by firms are not peeled offThe high premium-price acquisitions may make carriers tochoose 119903

lowast

= 0 which leads to the undermotivation of thecustomization investment of consignors and the social opti-mal customized transportation cannot be realizedThereforein the developing process of logistic supply chains in Chinait is necessary that the logistic firms should become theentities that can be self-managed self-constricted and self-motivated and the burden of the social functions will lead tothe loss of the transportation efficiency which are all what wemust pay attention to

In addition when all technical parameters keep constantcomparing optimal partial ownership in the cases of twodifferent types of carrier we can discover that in theorythe ratio of optimal equity participation by the consignor inthe owner-managed carrier should exceed the ratio in the

public-managed firm that is 119903lowast

gt 119903lowast It provides a theoretic

foundation for us to interpret that the interfirmmutual share-holding ratios of the member-firms within the familial-typelogistic supply chains aremuch larger than those ratioswithinthe public-type logistic supply chains At the same time italso means that the customized production efficiency of theformer is higher than that of the latter Although there is roomfor improvement we still firmly believe that the success ofChinese logistic industry should be mainly attributed to theadvantage of owner-managed efficiency

To be mentioned the mechanism of partial ownershipundoubtedly improves the cooperative efficiency of twotrade parties Although social welfare level this arrangementprovides is not optimal the cooperative mechanism helpsto enhance Pareto improvement of the return of two tradeparties compared with simple contract system

6 Conclusions

The phenomena that one consignor holds equity ownershipof one carrier within logistic supply chain are often observedDespite its importance the existing interpretations for inter-firm partial ownership scheme remain relatively unexploredIn this paper a theoretical explanation for equity partici-pation arrangement existing between member-firms withinlogistic supply chain is provided under the background ofcustomized production

Based on the models in which we view the parame-ter for customization level as the selective variable of thecarrier we figure out that the simple contract cannot solvethe low-efficient customized production problem Equityparticipation mechanism together with simple contract canimprove the efficiency of customized transportation Thepartial ownership mechanism supported by customized pro-duction plays a role as a bond in keeping the relationaltransactions among member-firms but not a role as theefficiency-enhancing mechanism resulting from outside arti-ficial personsrsquo supervision in some literature about equityownership structure

What is more on the basis of keeping the logic deductiveconsistency we obtain the outcome of the optimal partialownership affected by the relative bargaining power 120582 ofthe consignor and the other outside income 120587

0of the

carrier under two cases of owner-managed firm type andpublic-firm type respectively and showwhy the familial-typelogistic supply chains may choose more efficient customizedproduction level than public-type logistic supply chains

To be mentioned our theory provides few cases inwhich we can verify the interfirm equity participation ratioAlthough many important conclusions we obtain seem to beconsistent with some evidences there is a need for furtherstudy such as analyzing bilateral cross-shareholding case andconsidering the relationship between bargaining power andequity participation ratio through extending our models

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Mathematical Problems in Engineering 9

Acknowledgments

We acknowledge financial support from the National NatureScience Foundation of China (Grant nos 71001073 71371127and 71471118) the National Soft Science Research Plan(Grant no 2013GXS4D138) the Humanities and SocialSciences Foundation of Ministry of Education of China(Grant nos 13YJA630050 and 14YJC630096) DevelopmentProgram for Distinguished Young Teachers in Higher Edu-cation of Guangdong Province (Grant no Yq2013140 andYq2013147) and the Open Foundation of Shenzhen KeyLaboratory of Urban Planning and Decision Making (Grantno UPDMHITSZ2014B07) We would like to thank theanonymous referees for their valuable suggestions

References

[1] T M Choi Fashion Supply Chain Management Industry andBusiness Analysis IGI Global Hershey Pa USA 2011

[2] S Guercini and A Runfola ldquoRelational paths in business net-work dynamics evidence from the fashion industryrdquo IndustrialMarketing Management vol 41 no 5 pp 807ndash815 2012

[3] G B Richardson ldquoThe organization of industryrdquo EconomicJournal vol 82 pp 883ndash896 1972

[4] G P Pisano ldquoUsing equity participation to support exchangeevidence from the biotechnology industryrdquo Journal of LawEconomics and Organization vol 5 no 1 pp 109ndash126 1989

[5] TMChoi P S Chow and SC Liu ldquoImplementation of fashionERP systems in China case study of a fashion brand reviewand future challengesrdquo International Journal of ProductionEconomics vol 146 no 1 pp 70ndash81 2013

[6] X D Lin ldquoSpecial investment optimal partial ownership andincentive efficiencyrdquo in Proceedings of the 4th International Con-ference on Wireless Communications Networking and MobileComputing (WiCOM rsquo08) pp 1ndash4 Dalian China October 2008

[7] M Aoki Information Incentives and Bargaining in the JapaneseEconomy Cambridge University Press Cambridge UK 1988

[8] J H Dyer andWGOuchi ldquoJapanese-style partnerships givingcompanies a competitive edgerdquo Sloan Management Review vol14 pp 51ndash63 1993

[9] Y-K Che and D B Hausch ldquoCooperative investments and thevalue of contractingrdquo The American Economic Review vol 89no 1 pp 125ndash147 1999

[10] O E Williamson ldquoCredible commitments using hostages tosupport exchangerdquo American Economic Review vol 73 no 2pp 519ndash540 1983

[11] O Hart and JMoore ldquoIncomplete contracts and renegotiationrdquoEconometrica vol 56 no 4 pp 755ndash785 1988

[12] S Grossman and O Hart ldquoThe costs and benefits of ownershipa theory of vertical and lateral integrationrdquo Journal of PoliticalEconomy vol 94 no 2 pp 691ndash719 1989

[13] O E Williamson The Economic Institutions of CapitalismFirms Markets Relational Contracting Macmillan PrincetonNJ USA 1985

[14] B Klein R Crawford and A Alchian ldquoVertical integrationappropriable rents and the competitive contracting processrdquoThe Journal of Law and Economics vol 21 no 1 pp 297ndash3261978

[15] P Milgrom and J Roberts Economics Organization andManagement Prentice Hall Englewood Cliffs NJ USA 1992

[16] M R Scheffer ldquoTrends in textile markets and their implicationsfor textile products and processesrdquo in The Global Textile andClothing Industry pp 8ndash28 2012

[17] P Bolton and M D Whinston ldquoIncomplete contracts verticalintegration and supply assurancerdquoReview of Economics Studiesvol 60 no 1 pp 121ndash148 1993

[18] R G Rajan and L Zingales ldquoPower in a theory of the firmrdquoQuarterly Journal of Economics vol 113 no 1 pp 387ndash432 1998

[19] S Dasgupta and Z Tao ldquoBargaining bonding and partialownershiprdquo International Economic Review vol 41 no 3 pp609ndash635 2000

[20] P Aghion and J Tirole ldquoThe management of innovationrdquoQuarterly Journal of Economics vol 109 no 3 pp 1185ndash12091994

[21] T Y Chung ldquoIncomplete contracts specific investments andrisk sharingrdquo Review of Economic Studies vol 58 pp 1031ndash10421991

[22] Y Yu T-M Choi C-L Hui and T-K Ho ldquoA new andefficient intelligent collaboration scheme for fashion designrdquoIEEE Transactions on Systems Man and Cybernetics A Systemsand Humans vol 41 no 3 pp 463ndash475 2011

[23] T-M Choi C-L Hui N Liu S-F Ng and Y Yu ldquoFast fashionsales forecasting with limited data and timerdquo Decision SupportSystems vol 59 no 1 pp 84ndash92 2014

[24] W K Wong and S Y S Leung ldquoGenetic optimization of fabricutilization in apparel manufacturingrdquo International Journal ofProduction Economics vol 114 no 1 pp 376ndash387 2008

[25] B Asanuma ldquoManufacturer-supplier relationships in Japan andthe concept of relation-specific skillrdquo Journal of The Japaneseand International Economies vol 3 no 1 pp 1ndash30 1989

[26] M C Jensen and W H Meckling ldquoTheory of the firmmanagerial behavior agency costs and ownership structurerdquoJournal of Financial Economics vol 3 no 4 pp 305ndash360 1976

[27] T-M Choi C-L Hui S-F Ng and Y Yu ldquoColor trendforecasting of fashionable products with very few historicaldatardquo IEEE Transactions on Systems Man and Cybernetics PartC Applications and Reviews vol 42 no 6 pp 1003ndash1010 2012

[28] P Aghion and P Bohton ldquoAn incomplete contracts approach tofinancial contractingrdquo Review of Economic Studies vol 59 no3 pp 473ndash494 1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

120575(119903) of the carrier based on the partial ownership 119903 can beexpressed as

120575 (119903) = 119878119879

(119903) + 1205870 (28)

(119903) can be denoted as follows

(119903) = (1 + 120579) 119903120575 (119903) (29)

Therefore the total net income of the consignor can bedescribed as

119889

= 119861119879

(119903) + 1199031205870

minus 119903 (1 + 120579) [119878119879

(119903) + 1205870] (30)

The optimal partial ownership 119903lowast must satisfy the first-

order condition

120597119889

120597119903 | 119903 = 119903lowast

= 0 (31)

We further have

(120597119886lowast

120597119903) [1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)] minus 120579119878119879

(119903) minus 1205791205870

minus(1 + 120579119903) (1 minus 119886) 119892

(1 minus 119903)2

= 0

(32)

Obviously when 120579 gt 0 and is sufficiently small 119903lowast

isin

(0 120582) Similar to the conclusions of the last section the valuesof 119886lowast and 119903

lowast will be adjusted to correspond to positive ornegative 120579-value In this paper we will only analyze the caseof 120579 gt 0

By (32) we get

1205972

119889

120597119903120597120582= [

120597119886lowast

120597119903] [11988110158401015840

(119886lowast

) minus 11986210158401015840

(119886lowast

)] [120597119886lowast

120597120582] minus

1 + 120573119903

(1 minus 119903)2

lowast [minus (1 minus 119886lowast

) 119881 (119886lowast

) minus (1 minus 120582) 119881 (119886lowast

) (120597119886lowast

120597120582)

+ (1 minus 119886) (1 minus 120582) 119881 (119886lowast

) (120597119886lowast

120597120582)]

+ [1205972

119886lowast

120597119903120597120582] [1198811015840

(119886lowast

) minus 1198621015840

(119886lowast

)] +120573 (1 minus 119886

lowast

) 119881 (119886lowast

)

1 minus 119903

(33)

By 120597119878119879(119903)(120597119886 | 119886 = 119886

lowast

) = 0 we know

120597119886lowast

120597119903gt 0

120597119886lowast

120597120582lt 0

1205972

119886lowast

120597119903120597120582lt 0 (34)

Then in (33) all the right-hand terms exceed zero thus

1205972

120587119889

120597119903120597120582gt 0 (35)

Since Sign(120597119903lowast

120597120582) = Sign(1205972

119889120597119903120597120582) we can get

120597119903lowast

120597120582gt 0

120597119903lowast

1205971205870

lt 0 (36)

0 01 02 03 04 05 06 07 08 090

010203040506070809

1

r

a

120582 = 02120582 = 05120582 = 08

Figure 2 The relationship chart between 119886 and 119903 given 120573 = 2 119892 =

12

Given the values of 120582 120573 and 119892 we can find out therelationship between 119886 and 119903 through numerical simulationin Figure 2

Our numerical result shows that parameters 119886 and 119903 areincreasing function of 120582 and 119886 increases nonlinearly in r

From the above analyses we can conclude the following

Proposition 4 Assuming that the carrier is a public-firmmanaged by the manager in the interest of the share-holderswhen purchasing at premium price the optimal equity partic-ipation ratio 119903

lowast by the consignor increases in 120582 but decreasesin 1205870

5 Discussions about Customized ProductionEfficiency and Policy Implications

The theory of optimal ownership structure extracts thedistillate of two stream academic ideas the financial structuretheory and the managerial motivation theory which havebeen agreed on in economic literature [19] For exampleJensen andMeckling [26] pointed out that agent costs causedby dilution of ownership are derived from the fact thatthe incentive of inside controllers cannot keep track withthat of the ownerrsquos On the other hand many academicpapers demonstrate that an outside artificial person whoholds a major part of ownership has a positive effect onthe firmrsquos value [10 17 26ndash28] These papers emphasizedthe supervising function of the outside artificial personsrsquoshare-holders to the firmrsquos managers Compared with theseexisting articles we provide a theoretical interpretation whyoutside artificial persons hold partial ownership under thecircumstance of vertical transaction relationship Our resultis if the downstream firm holds partial ownership of theupstream firm it may function as a bonding mechanismwhich improves the performance of twoparties Itmeans thatcompared with 119903 = 0 the mechanism of partial ownershipimproves the efficiency of customization service

However can the optimal partial ownership result insocial optimal customized transportation level

As we know no matter what type the carrier is eitherowner-managed one or a public-firm managed by managers119903lowast

= 120582 or 119903lowast

= 05 is the necessary condition bringing in

8 Mathematical Problems in Engineering

social optimal customization level If the carrier is an owner-managed one only when the purchasing of partial ownershipat par price occursmay choosing 119903

lowast

= 120582 be a rational decisionfor the consignor aiming at maximizing its total net incomeBut purchasing at premium price is dominant in reality ifcalculated under general case of 120582 = 05 the optimal partialownership 119903

lowast is less than 120582 not large enough to motivatethe decision-maker of the carrier to choose the most efficientcustomized production level The marginal return obtainedby the consignor through enlarging equity participation ratiowill be offset by marginal costs of purchasing the equityownership and premium price distorting effects lead to theefficiency loss of the carrierrsquos customization investment (119903

lowast

lt

05)On the opposite when purchasing at discount overmoti-

vation leads to 119903lowast

gt 120582 and the customization efficiency lossmay still occur Therefore we hold that the effect of wealthtransfer in the purchase of equity ownership is the mainreason that leads to efficiency loss of customized productionwhich shows our theory about partial ownership differentfrom the entrepreneur endeavor choice interpretation byDasgupta and Tao but similar to the conclusion of Aghionand Tirolersquos that partial ownership arrangement can motivatespecial investment but cannot solve the investorsrsquo underin-vestment problem totally

However when the carrier is public-managed even ifthere exist 120579 = 0 and the optimal partial ownership 119903

lowast

lt

120582 social optimal customization level cannot be obtainedbecause the benefit of the consignor does not keep consistentwith the trade partiesrsquo common benefit When 120579 gt 0119903lowast will become smaller and the higher loss degree of thecustomization investment efficiency will occur Obviouslyunder the second-order condition constraint that we can getthe optimal solution satisfying (32) the larger the averagepremium price parameter is the smaller 119903

lowast is the lowercustomized production efficiency becomes and the greatersocial welfare loss will be which holds true in the caseof owner-managed carrier As for the case of 120579 lt 0 itaccords with the aforementioned analyses that is the over-motivation of equity ownership may lead to customizedproduction efficiency loss

In China the state-owned equity reform in logisticindustry just began with unclear ownership partition andmany social functions assumed by firms are not peeled offThe high premium-price acquisitions may make carriers tochoose 119903

lowast

= 0 which leads to the undermotivation of thecustomization investment of consignors and the social opti-mal customized transportation cannot be realizedThereforein the developing process of logistic supply chains in Chinait is necessary that the logistic firms should become theentities that can be self-managed self-constricted and self-motivated and the burden of the social functions will lead tothe loss of the transportation efficiency which are all what wemust pay attention to

In addition when all technical parameters keep constantcomparing optimal partial ownership in the cases of twodifferent types of carrier we can discover that in theorythe ratio of optimal equity participation by the consignor inthe owner-managed carrier should exceed the ratio in the

public-managed firm that is 119903lowast

gt 119903lowast It provides a theoretic

foundation for us to interpret that the interfirmmutual share-holding ratios of the member-firms within the familial-typelogistic supply chains aremuch larger than those ratioswithinthe public-type logistic supply chains At the same time italso means that the customized production efficiency of theformer is higher than that of the latter Although there is roomfor improvement we still firmly believe that the success ofChinese logistic industry should be mainly attributed to theadvantage of owner-managed efficiency

To be mentioned the mechanism of partial ownershipundoubtedly improves the cooperative efficiency of twotrade parties Although social welfare level this arrangementprovides is not optimal the cooperative mechanism helpsto enhance Pareto improvement of the return of two tradeparties compared with simple contract system

6 Conclusions

The phenomena that one consignor holds equity ownershipof one carrier within logistic supply chain are often observedDespite its importance the existing interpretations for inter-firm partial ownership scheme remain relatively unexploredIn this paper a theoretical explanation for equity partici-pation arrangement existing between member-firms withinlogistic supply chain is provided under the background ofcustomized production

Based on the models in which we view the parame-ter for customization level as the selective variable of thecarrier we figure out that the simple contract cannot solvethe low-efficient customized production problem Equityparticipation mechanism together with simple contract canimprove the efficiency of customized transportation Thepartial ownership mechanism supported by customized pro-duction plays a role as a bond in keeping the relationaltransactions among member-firms but not a role as theefficiency-enhancing mechanism resulting from outside arti-ficial personsrsquo supervision in some literature about equityownership structure

What is more on the basis of keeping the logic deductiveconsistency we obtain the outcome of the optimal partialownership affected by the relative bargaining power 120582 ofthe consignor and the other outside income 120587

0of the

carrier under two cases of owner-managed firm type andpublic-firm type respectively and showwhy the familial-typelogistic supply chains may choose more efficient customizedproduction level than public-type logistic supply chains

To be mentioned our theory provides few cases inwhich we can verify the interfirm equity participation ratioAlthough many important conclusions we obtain seem to beconsistent with some evidences there is a need for furtherstudy such as analyzing bilateral cross-shareholding case andconsidering the relationship between bargaining power andequity participation ratio through extending our models

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Mathematical Problems in Engineering 9

Acknowledgments

We acknowledge financial support from the National NatureScience Foundation of China (Grant nos 71001073 71371127and 71471118) the National Soft Science Research Plan(Grant no 2013GXS4D138) the Humanities and SocialSciences Foundation of Ministry of Education of China(Grant nos 13YJA630050 and 14YJC630096) DevelopmentProgram for Distinguished Young Teachers in Higher Edu-cation of Guangdong Province (Grant no Yq2013140 andYq2013147) and the Open Foundation of Shenzhen KeyLaboratory of Urban Planning and Decision Making (Grantno UPDMHITSZ2014B07) We would like to thank theanonymous referees for their valuable suggestions

References

[1] T M Choi Fashion Supply Chain Management Industry andBusiness Analysis IGI Global Hershey Pa USA 2011

[2] S Guercini and A Runfola ldquoRelational paths in business net-work dynamics evidence from the fashion industryrdquo IndustrialMarketing Management vol 41 no 5 pp 807ndash815 2012

[3] G B Richardson ldquoThe organization of industryrdquo EconomicJournal vol 82 pp 883ndash896 1972

[4] G P Pisano ldquoUsing equity participation to support exchangeevidence from the biotechnology industryrdquo Journal of LawEconomics and Organization vol 5 no 1 pp 109ndash126 1989

[5] TMChoi P S Chow and SC Liu ldquoImplementation of fashionERP systems in China case study of a fashion brand reviewand future challengesrdquo International Journal of ProductionEconomics vol 146 no 1 pp 70ndash81 2013

[6] X D Lin ldquoSpecial investment optimal partial ownership andincentive efficiencyrdquo in Proceedings of the 4th International Con-ference on Wireless Communications Networking and MobileComputing (WiCOM rsquo08) pp 1ndash4 Dalian China October 2008

[7] M Aoki Information Incentives and Bargaining in the JapaneseEconomy Cambridge University Press Cambridge UK 1988

[8] J H Dyer andWGOuchi ldquoJapanese-style partnerships givingcompanies a competitive edgerdquo Sloan Management Review vol14 pp 51ndash63 1993

[9] Y-K Che and D B Hausch ldquoCooperative investments and thevalue of contractingrdquo The American Economic Review vol 89no 1 pp 125ndash147 1999

[10] O E Williamson ldquoCredible commitments using hostages tosupport exchangerdquo American Economic Review vol 73 no 2pp 519ndash540 1983

[11] O Hart and JMoore ldquoIncomplete contracts and renegotiationrdquoEconometrica vol 56 no 4 pp 755ndash785 1988

[12] S Grossman and O Hart ldquoThe costs and benefits of ownershipa theory of vertical and lateral integrationrdquo Journal of PoliticalEconomy vol 94 no 2 pp 691ndash719 1989

[13] O E Williamson The Economic Institutions of CapitalismFirms Markets Relational Contracting Macmillan PrincetonNJ USA 1985

[14] B Klein R Crawford and A Alchian ldquoVertical integrationappropriable rents and the competitive contracting processrdquoThe Journal of Law and Economics vol 21 no 1 pp 297ndash3261978

[15] P Milgrom and J Roberts Economics Organization andManagement Prentice Hall Englewood Cliffs NJ USA 1992

[16] M R Scheffer ldquoTrends in textile markets and their implicationsfor textile products and processesrdquo in The Global Textile andClothing Industry pp 8ndash28 2012

[17] P Bolton and M D Whinston ldquoIncomplete contracts verticalintegration and supply assurancerdquoReview of Economics Studiesvol 60 no 1 pp 121ndash148 1993

[18] R G Rajan and L Zingales ldquoPower in a theory of the firmrdquoQuarterly Journal of Economics vol 113 no 1 pp 387ndash432 1998

[19] S Dasgupta and Z Tao ldquoBargaining bonding and partialownershiprdquo International Economic Review vol 41 no 3 pp609ndash635 2000

[20] P Aghion and J Tirole ldquoThe management of innovationrdquoQuarterly Journal of Economics vol 109 no 3 pp 1185ndash12091994

[21] T Y Chung ldquoIncomplete contracts specific investments andrisk sharingrdquo Review of Economic Studies vol 58 pp 1031ndash10421991

[22] Y Yu T-M Choi C-L Hui and T-K Ho ldquoA new andefficient intelligent collaboration scheme for fashion designrdquoIEEE Transactions on Systems Man and Cybernetics A Systemsand Humans vol 41 no 3 pp 463ndash475 2011

[23] T-M Choi C-L Hui N Liu S-F Ng and Y Yu ldquoFast fashionsales forecasting with limited data and timerdquo Decision SupportSystems vol 59 no 1 pp 84ndash92 2014

[24] W K Wong and S Y S Leung ldquoGenetic optimization of fabricutilization in apparel manufacturingrdquo International Journal ofProduction Economics vol 114 no 1 pp 376ndash387 2008

[25] B Asanuma ldquoManufacturer-supplier relationships in Japan andthe concept of relation-specific skillrdquo Journal of The Japaneseand International Economies vol 3 no 1 pp 1ndash30 1989

[26] M C Jensen and W H Meckling ldquoTheory of the firmmanagerial behavior agency costs and ownership structurerdquoJournal of Financial Economics vol 3 no 4 pp 305ndash360 1976

[27] T-M Choi C-L Hui S-F Ng and Y Yu ldquoColor trendforecasting of fashionable products with very few historicaldatardquo IEEE Transactions on Systems Man and Cybernetics PartC Applications and Reviews vol 42 no 6 pp 1003ndash1010 2012

[28] P Aghion and P Bohton ldquoAn incomplete contracts approach tofinancial contractingrdquo Review of Economic Studies vol 59 no3 pp 473ndash494 1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

social optimal customization level If the carrier is an owner-managed one only when the purchasing of partial ownershipat par price occursmay choosing 119903

lowast

= 120582 be a rational decisionfor the consignor aiming at maximizing its total net incomeBut purchasing at premium price is dominant in reality ifcalculated under general case of 120582 = 05 the optimal partialownership 119903

lowast is less than 120582 not large enough to motivatethe decision-maker of the carrier to choose the most efficientcustomized production level The marginal return obtainedby the consignor through enlarging equity participation ratiowill be offset by marginal costs of purchasing the equityownership and premium price distorting effects lead to theefficiency loss of the carrierrsquos customization investment (119903

lowast

lt

05)On the opposite when purchasing at discount overmoti-

vation leads to 119903lowast

gt 120582 and the customization efficiency lossmay still occur Therefore we hold that the effect of wealthtransfer in the purchase of equity ownership is the mainreason that leads to efficiency loss of customized productionwhich shows our theory about partial ownership differentfrom the entrepreneur endeavor choice interpretation byDasgupta and Tao but similar to the conclusion of Aghionand Tirolersquos that partial ownership arrangement can motivatespecial investment but cannot solve the investorsrsquo underin-vestment problem totally

However when the carrier is public-managed even ifthere exist 120579 = 0 and the optimal partial ownership 119903

lowast

lt

120582 social optimal customization level cannot be obtainedbecause the benefit of the consignor does not keep consistentwith the trade partiesrsquo common benefit When 120579 gt 0119903lowast will become smaller and the higher loss degree of thecustomization investment efficiency will occur Obviouslyunder the second-order condition constraint that we can getthe optimal solution satisfying (32) the larger the averagepremium price parameter is the smaller 119903

lowast is the lowercustomized production efficiency becomes and the greatersocial welfare loss will be which holds true in the caseof owner-managed carrier As for the case of 120579 lt 0 itaccords with the aforementioned analyses that is the over-motivation of equity ownership may lead to customizedproduction efficiency loss

In China the state-owned equity reform in logisticindustry just began with unclear ownership partition andmany social functions assumed by firms are not peeled offThe high premium-price acquisitions may make carriers tochoose 119903

lowast

= 0 which leads to the undermotivation of thecustomization investment of consignors and the social opti-mal customized transportation cannot be realizedThereforein the developing process of logistic supply chains in Chinait is necessary that the logistic firms should become theentities that can be self-managed self-constricted and self-motivated and the burden of the social functions will lead tothe loss of the transportation efficiency which are all what wemust pay attention to

In addition when all technical parameters keep constantcomparing optimal partial ownership in the cases of twodifferent types of carrier we can discover that in theorythe ratio of optimal equity participation by the consignor inthe owner-managed carrier should exceed the ratio in the

public-managed firm that is 119903lowast

gt 119903lowast It provides a theoretic

foundation for us to interpret that the interfirmmutual share-holding ratios of the member-firms within the familial-typelogistic supply chains aremuch larger than those ratioswithinthe public-type logistic supply chains At the same time italso means that the customized production efficiency of theformer is higher than that of the latter Although there is roomfor improvement we still firmly believe that the success ofChinese logistic industry should be mainly attributed to theadvantage of owner-managed efficiency

To be mentioned the mechanism of partial ownershipundoubtedly improves the cooperative efficiency of twotrade parties Although social welfare level this arrangementprovides is not optimal the cooperative mechanism helpsto enhance Pareto improvement of the return of two tradeparties compared with simple contract system

6 Conclusions

The phenomena that one consignor holds equity ownershipof one carrier within logistic supply chain are often observedDespite its importance the existing interpretations for inter-firm partial ownership scheme remain relatively unexploredIn this paper a theoretical explanation for equity partici-pation arrangement existing between member-firms withinlogistic supply chain is provided under the background ofcustomized production

Based on the models in which we view the parame-ter for customization level as the selective variable of thecarrier we figure out that the simple contract cannot solvethe low-efficient customized production problem Equityparticipation mechanism together with simple contract canimprove the efficiency of customized transportation Thepartial ownership mechanism supported by customized pro-duction plays a role as a bond in keeping the relationaltransactions among member-firms but not a role as theefficiency-enhancing mechanism resulting from outside arti-ficial personsrsquo supervision in some literature about equityownership structure

What is more on the basis of keeping the logic deductiveconsistency we obtain the outcome of the optimal partialownership affected by the relative bargaining power 120582 ofthe consignor and the other outside income 120587

0of the

carrier under two cases of owner-managed firm type andpublic-firm type respectively and showwhy the familial-typelogistic supply chains may choose more efficient customizedproduction level than public-type logistic supply chains

To be mentioned our theory provides few cases inwhich we can verify the interfirm equity participation ratioAlthough many important conclusions we obtain seem to beconsistent with some evidences there is a need for furtherstudy such as analyzing bilateral cross-shareholding case andconsidering the relationship between bargaining power andequity participation ratio through extending our models

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Mathematical Problems in Engineering 9

Acknowledgments

We acknowledge financial support from the National NatureScience Foundation of China (Grant nos 71001073 71371127and 71471118) the National Soft Science Research Plan(Grant no 2013GXS4D138) the Humanities and SocialSciences Foundation of Ministry of Education of China(Grant nos 13YJA630050 and 14YJC630096) DevelopmentProgram for Distinguished Young Teachers in Higher Edu-cation of Guangdong Province (Grant no Yq2013140 andYq2013147) and the Open Foundation of Shenzhen KeyLaboratory of Urban Planning and Decision Making (Grantno UPDMHITSZ2014B07) We would like to thank theanonymous referees for their valuable suggestions

References

[1] T M Choi Fashion Supply Chain Management Industry andBusiness Analysis IGI Global Hershey Pa USA 2011

[2] S Guercini and A Runfola ldquoRelational paths in business net-work dynamics evidence from the fashion industryrdquo IndustrialMarketing Management vol 41 no 5 pp 807ndash815 2012

[3] G B Richardson ldquoThe organization of industryrdquo EconomicJournal vol 82 pp 883ndash896 1972

[4] G P Pisano ldquoUsing equity participation to support exchangeevidence from the biotechnology industryrdquo Journal of LawEconomics and Organization vol 5 no 1 pp 109ndash126 1989

[5] TMChoi P S Chow and SC Liu ldquoImplementation of fashionERP systems in China case study of a fashion brand reviewand future challengesrdquo International Journal of ProductionEconomics vol 146 no 1 pp 70ndash81 2013

[6] X D Lin ldquoSpecial investment optimal partial ownership andincentive efficiencyrdquo in Proceedings of the 4th International Con-ference on Wireless Communications Networking and MobileComputing (WiCOM rsquo08) pp 1ndash4 Dalian China October 2008

[7] M Aoki Information Incentives and Bargaining in the JapaneseEconomy Cambridge University Press Cambridge UK 1988

[8] J H Dyer andWGOuchi ldquoJapanese-style partnerships givingcompanies a competitive edgerdquo Sloan Management Review vol14 pp 51ndash63 1993

[9] Y-K Che and D B Hausch ldquoCooperative investments and thevalue of contractingrdquo The American Economic Review vol 89no 1 pp 125ndash147 1999

[10] O E Williamson ldquoCredible commitments using hostages tosupport exchangerdquo American Economic Review vol 73 no 2pp 519ndash540 1983

[11] O Hart and JMoore ldquoIncomplete contracts and renegotiationrdquoEconometrica vol 56 no 4 pp 755ndash785 1988

[12] S Grossman and O Hart ldquoThe costs and benefits of ownershipa theory of vertical and lateral integrationrdquo Journal of PoliticalEconomy vol 94 no 2 pp 691ndash719 1989

[13] O E Williamson The Economic Institutions of CapitalismFirms Markets Relational Contracting Macmillan PrincetonNJ USA 1985

[14] B Klein R Crawford and A Alchian ldquoVertical integrationappropriable rents and the competitive contracting processrdquoThe Journal of Law and Economics vol 21 no 1 pp 297ndash3261978

[15] P Milgrom and J Roberts Economics Organization andManagement Prentice Hall Englewood Cliffs NJ USA 1992

[16] M R Scheffer ldquoTrends in textile markets and their implicationsfor textile products and processesrdquo in The Global Textile andClothing Industry pp 8ndash28 2012

[17] P Bolton and M D Whinston ldquoIncomplete contracts verticalintegration and supply assurancerdquoReview of Economics Studiesvol 60 no 1 pp 121ndash148 1993

[18] R G Rajan and L Zingales ldquoPower in a theory of the firmrdquoQuarterly Journal of Economics vol 113 no 1 pp 387ndash432 1998

[19] S Dasgupta and Z Tao ldquoBargaining bonding and partialownershiprdquo International Economic Review vol 41 no 3 pp609ndash635 2000

[20] P Aghion and J Tirole ldquoThe management of innovationrdquoQuarterly Journal of Economics vol 109 no 3 pp 1185ndash12091994

[21] T Y Chung ldquoIncomplete contracts specific investments andrisk sharingrdquo Review of Economic Studies vol 58 pp 1031ndash10421991

[22] Y Yu T-M Choi C-L Hui and T-K Ho ldquoA new andefficient intelligent collaboration scheme for fashion designrdquoIEEE Transactions on Systems Man and Cybernetics A Systemsand Humans vol 41 no 3 pp 463ndash475 2011

[23] T-M Choi C-L Hui N Liu S-F Ng and Y Yu ldquoFast fashionsales forecasting with limited data and timerdquo Decision SupportSystems vol 59 no 1 pp 84ndash92 2014

[24] W K Wong and S Y S Leung ldquoGenetic optimization of fabricutilization in apparel manufacturingrdquo International Journal ofProduction Economics vol 114 no 1 pp 376ndash387 2008

[25] B Asanuma ldquoManufacturer-supplier relationships in Japan andthe concept of relation-specific skillrdquo Journal of The Japaneseand International Economies vol 3 no 1 pp 1ndash30 1989

[26] M C Jensen and W H Meckling ldquoTheory of the firmmanagerial behavior agency costs and ownership structurerdquoJournal of Financial Economics vol 3 no 4 pp 305ndash360 1976

[27] T-M Choi C-L Hui S-F Ng and Y Yu ldquoColor trendforecasting of fashionable products with very few historicaldatardquo IEEE Transactions on Systems Man and Cybernetics PartC Applications and Reviews vol 42 no 6 pp 1003ndash1010 2012

[28] P Aghion and P Bohton ldquoAn incomplete contracts approach tofinancial contractingrdquo Review of Economic Studies vol 59 no3 pp 473ndash494 1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 9

Acknowledgments

We acknowledge financial support from the National NatureScience Foundation of China (Grant nos 71001073 71371127and 71471118) the National Soft Science Research Plan(Grant no 2013GXS4D138) the Humanities and SocialSciences Foundation of Ministry of Education of China(Grant nos 13YJA630050 and 14YJC630096) DevelopmentProgram for Distinguished Young Teachers in Higher Edu-cation of Guangdong Province (Grant no Yq2013140 andYq2013147) and the Open Foundation of Shenzhen KeyLaboratory of Urban Planning and Decision Making (Grantno UPDMHITSZ2014B07) We would like to thank theanonymous referees for their valuable suggestions

References

[1] T M Choi Fashion Supply Chain Management Industry andBusiness Analysis IGI Global Hershey Pa USA 2011

[2] S Guercini and A Runfola ldquoRelational paths in business net-work dynamics evidence from the fashion industryrdquo IndustrialMarketing Management vol 41 no 5 pp 807ndash815 2012

[3] G B Richardson ldquoThe organization of industryrdquo EconomicJournal vol 82 pp 883ndash896 1972

[4] G P Pisano ldquoUsing equity participation to support exchangeevidence from the biotechnology industryrdquo Journal of LawEconomics and Organization vol 5 no 1 pp 109ndash126 1989

[5] TMChoi P S Chow and SC Liu ldquoImplementation of fashionERP systems in China case study of a fashion brand reviewand future challengesrdquo International Journal of ProductionEconomics vol 146 no 1 pp 70ndash81 2013

[6] X D Lin ldquoSpecial investment optimal partial ownership andincentive efficiencyrdquo in Proceedings of the 4th International Con-ference on Wireless Communications Networking and MobileComputing (WiCOM rsquo08) pp 1ndash4 Dalian China October 2008

[7] M Aoki Information Incentives and Bargaining in the JapaneseEconomy Cambridge University Press Cambridge UK 1988

[8] J H Dyer andWGOuchi ldquoJapanese-style partnerships givingcompanies a competitive edgerdquo Sloan Management Review vol14 pp 51ndash63 1993

[9] Y-K Che and D B Hausch ldquoCooperative investments and thevalue of contractingrdquo The American Economic Review vol 89no 1 pp 125ndash147 1999

[10] O E Williamson ldquoCredible commitments using hostages tosupport exchangerdquo American Economic Review vol 73 no 2pp 519ndash540 1983

[11] O Hart and JMoore ldquoIncomplete contracts and renegotiationrdquoEconometrica vol 56 no 4 pp 755ndash785 1988

[12] S Grossman and O Hart ldquoThe costs and benefits of ownershipa theory of vertical and lateral integrationrdquo Journal of PoliticalEconomy vol 94 no 2 pp 691ndash719 1989

[13] O E Williamson The Economic Institutions of CapitalismFirms Markets Relational Contracting Macmillan PrincetonNJ USA 1985

[14] B Klein R Crawford and A Alchian ldquoVertical integrationappropriable rents and the competitive contracting processrdquoThe Journal of Law and Economics vol 21 no 1 pp 297ndash3261978

[15] P Milgrom and J Roberts Economics Organization andManagement Prentice Hall Englewood Cliffs NJ USA 1992

[16] M R Scheffer ldquoTrends in textile markets and their implicationsfor textile products and processesrdquo in The Global Textile andClothing Industry pp 8ndash28 2012

[17] P Bolton and M D Whinston ldquoIncomplete contracts verticalintegration and supply assurancerdquoReview of Economics Studiesvol 60 no 1 pp 121ndash148 1993

[18] R G Rajan and L Zingales ldquoPower in a theory of the firmrdquoQuarterly Journal of Economics vol 113 no 1 pp 387ndash432 1998

[19] S Dasgupta and Z Tao ldquoBargaining bonding and partialownershiprdquo International Economic Review vol 41 no 3 pp609ndash635 2000

[20] P Aghion and J Tirole ldquoThe management of innovationrdquoQuarterly Journal of Economics vol 109 no 3 pp 1185ndash12091994

[21] T Y Chung ldquoIncomplete contracts specific investments andrisk sharingrdquo Review of Economic Studies vol 58 pp 1031ndash10421991

[22] Y Yu T-M Choi C-L Hui and T-K Ho ldquoA new andefficient intelligent collaboration scheme for fashion designrdquoIEEE Transactions on Systems Man and Cybernetics A Systemsand Humans vol 41 no 3 pp 463ndash475 2011

[23] T-M Choi C-L Hui N Liu S-F Ng and Y Yu ldquoFast fashionsales forecasting with limited data and timerdquo Decision SupportSystems vol 59 no 1 pp 84ndash92 2014

[24] W K Wong and S Y S Leung ldquoGenetic optimization of fabricutilization in apparel manufacturingrdquo International Journal ofProduction Economics vol 114 no 1 pp 376ndash387 2008

[25] B Asanuma ldquoManufacturer-supplier relationships in Japan andthe concept of relation-specific skillrdquo Journal of The Japaneseand International Economies vol 3 no 1 pp 1ndash30 1989

[26] M C Jensen and W H Meckling ldquoTheory of the firmmanagerial behavior agency costs and ownership structurerdquoJournal of Financial Economics vol 3 no 4 pp 305ndash360 1976

[27] T-M Choi C-L Hui S-F Ng and Y Yu ldquoColor trendforecasting of fashionable products with very few historicaldatardquo IEEE Transactions on Systems Man and Cybernetics PartC Applications and Reviews vol 42 no 6 pp 1003ndash1010 2012

[28] P Aghion and P Bohton ldquoAn incomplete contracts approach tofinancial contractingrdquo Review of Economic Studies vol 59 no3 pp 473ndash494 1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of