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Int. J. Production Economics

Int. J. Production Economics 122 (2009) 319–328

0925-52

doi:10.1

� Cor

E-m

(S.G. De

journal homepage: www.elsevier.com/locate/ijpe

Dynamic supply chain modeling using a new fuzzy hybridnegotiation mechanism

Vipul Jain a,�, S.G. Deshmukh b

a Mechanical Engineering Department, Indian Institute of Technology Delhi, New Delhi 110 016, Indiab ABV-Indian Institute of IT and Management, Gwalior, Morena Link Road, Gwalior 474010, India

a r t i c l e i n f o

Available online 2 July 2009

Keywords:

Coordination

Negotiation

Fuzzy logic

Agents

Supply chain management

73/$ - see front matter & 2009 Elsevier B.V. A

016/j.ijpe.2009.06.034

responding author. Fax: +9111 26582053.

ail addresses: vjain@mech.iitd.ac.in (V. Jain),

shmukh).

a b s t r a c t

The key part of dynamic supply chain management is negotiating with suppliers and

with buyers. Coordination is essential for successful supply chain management. In order

to model coordination among suppliers and buyers in a dynamic supply chain, this

paper takes a step further and proposes a new fuzzy- logic-based hybrid negotiation

mechanism. In most real-world negotiation situations, agents have a common interest

to cooperate, but have conflicting interests over exactly how to cooperate. These

situations involve restrictions and preferences that may be vaguely and partly defined.

Therefore, this study takes the advantage of fuzzy logic and develops a hybrid

negotiation-based mechanism, that combines both cooperative and competitive

negotiations. Achieving effective coordination in a multi-agent system is non-trivial as

no agent possesses the global view of the problem space. Moreover, the different

strategies adopted by agents may produce conflicts. While agents coordinate with each

other in the operations, they will negotiate about their strategies to reduce conflicts. The

proposed fuzzy hybrid negotiation mechanism allows negotiation agents more

flexibility and robustness in an automated negotiation system. The proposed mechan-

ism not only helps sellers and buyers to explore various new choices and opportunities

that the e-markets offer but also allows them to identify and analyze their resource

constraints in a given schedule, and helps them to explore and exploit many alternatives

for a better solution. The efficacy of the proposed approach is demonstrated through an

illustrative example.

& 2009 Elsevier B.V. All rights reserved.

1. Introduction and motivations

Traditionally, marketing, distribution, planning, man-ufacturing, and purchasing of organizations along thesupply chain operate independently. These organizationshave their own objectives and they are often conflicting.Marketing objectives of high customer service and max-imum sales dollars conflict with the manufacturing anddistribution goals (Jain et al., 2007b). Many manufacturing

ll rights reserved.

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operations are designed to maximize throughput andlower costs with little consideration for the impact oninventory levels and distribution capabilities. Purchasingcontracts are often negotiated with very little informationbeyond historical buying patterns. The result of thesefactors is that there is no single, integrated plan for theorganization. Clearly, there is a need for a mechanismthrough which these different functions can be integratedtogether (Jain, 2006a). Supply chain management is astrategy through which such integration can be achieved.Supply chain management is typically viewed to liebetween fully vertically integrated firms, where the entirematerial flow is owned by a single firm, and where eachchannel member operates independently. Therefore,

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coordination between the various players to the chain isthe key in its effective management (Gan et al., 2004;Fung and Chen, 2005, Jain et al., 2007a).

Effective supply chain management requires creatingsynergistic relationships between the supply and distri-bution partners with the objective of maximizing custo-mer value and providing a profit for each supply chainmember. However, often there is no effective control

mechanism to coordinate the actions of the individual supply

chain members such that their decisions are aligned with

global supply chain objectives (Taylor, 2001; Chan andChan, 2004). In this case, each supply chain memberattempts to optimize a part of the system without givingfull consideration to the impact of their myopic decisionson total system performance. This decentralized decision-making process is the traditional mode of operation intoday’s business environment. Optimizing the portions ofthe system often yields sub-optimal performance, result-ing in an inefficient allocation of scarce resources, highersystem costs, compromised customer service, and aweakened strategic position (Jain et al., 2006b; Jenningset al., 2001).

Supply chains are complex operations and theiranalysis requires a carefully defined approach. Moreover,with on increase in technological complexity, supplychains have become more dynamic and complex to solve.Consequently, it is easy to get lost in details and spend alarge amount of effort for analyzing the supply chain.There is growing interest from industry and academic

disciplines regarding coordination in supply chains, particu-

larly addressing the potential coordination mechanisms

available to eliminate sub-optimization within supply chains

(Wang and Gerchak, 2001; Fung and Chen, 2005; Jain,2006a). Coordination, the process by which an agentreasons about its local actions and the actions of others totry to ensure that the community acts in a coherentmanner (Toledo Excelente and Jennings, 2002), is animportant issue in multi-agent systems (MASs). There arethree main reasons why it is necessary for agents tocoordinate. First, there are dependencies between agents’tasks or goals; second, there is a need to meet globalconstraints such as cost and time limits; and third, noindividual agent has sufficient competence, resources, orinformation to solve the entire problem (Parunak et al.,1998; Toledo Excelente and Jennings, 2002).

Member enterprises in the chain need to cooperatewith their business partners in order to meet customers’needs and to maximize their profit. Managing multi-party

collaboration in a supply chain, however, is a very difficult

task because there are so many parties involved in the supply

chain operation, each with its own resources and objectives.There is no single authority over all the chain members.Cooperation is through negotiation rather than centralmanagement and control. The interdependence of multi-stage processes also requires real-time cooperation inoperation and decision making across different tasks,functional areas, and organizational boundaries in orderto deal with problems and uncertainties. The strategic shift

of focus for mass customization, quick response, and high-

quality service cannot be achieved without more sophisti-

cated cooperation and dynamic formation of supply chains

(Chan et al., 2004). One solution to this problem is to haveintelligent interacting entities that can provide domain-specific information to validate the decision-makingsystem. Therefore, MAS-based approaches for supplychain modeling are proposed (Swaminathan et al., 1998;Ertogral and Wu, 2000; Julka et al., 2002; Jain et al.,2007a; etc.).

Agent-based modeling can be assumed to be a reason-able methodology for the examination of supply chainsbecause in a supply chain a number of individualcompanies interact with each other using specific internaldecision structures (Choi et al., 2001). Each of the players inthe supply chain is modeled as an agent who negotiateswith its immediate neighbor in pushing/pulling the part orproduct through the chain. The agents operate in MASs andsituations often arise in which their plans conflict with theplans of other agents. For achieving effective multi-agent

coordination, conflict resolution is crucial. Negotiation is a

predominant tool for resolving conflict of interests (Jain et al.,2007a). However, with recent technological advances, the

mechanisms available to carry out such activities have become

increasingly sophisticated, and the environment in which

these activities take place has become highly dynamic. A

higher-level coordination mechanism with respect to distrib-

uted modeling of supply chains is generally not specified in the

reported literature (Chan and Chan, 2004).A variety of research work exists on negotiation

strategies in the areas of social science, game theory,negotiation support systems, agent technologies, andmachine learning. Unfortunately, automated negotiationagents based on any of these techniques usually face twoproblems. First, agents are not as flexible and adaptive todifferent negotiation environments as desired. Negotia-tion environment is a set of pre-defined negotiationfeatures that are not negotiable. This means an agentmay work well under one set of negotiation features, butperform worse in others. Second, a fixed strategy or astatic group of strategies may become known by compet-ing agents as a result of negotiation processes, after whichthose agents can potentially exploit this knowledge infuture negotiations (Jennings, 2000; Fung and Chen,2005). The interacting network formation of a supplychain is inherently complex (Wilding, 1998), with themajority of firms operating simultaneously in multiplesupply chains. The operational complexity of supplychains further complicates the structural complexity,which shows itself in supply chains as consistent andunpredictable materials and information flow. Knowledgein expert system is vague and modified frequently (Jain etal., 2005). Hence, there is a strong urge to design a dynamic

knowledge inference system that is adaptable according to

knowledge variation as human cognition and thinking (Jainet al., 2005).

Therefore, unlike other researches, in this paper wetake the advantage of fuzzy logic and develop a hybridnegotiation-based mechanism that combines both coop-erative and competitive negotiations. The proposed fuzzyhybrid negotiation mechanism allows negotiation agentsmore flexibility and robustness in an automated negotia-tion system. The proposed mechanism not only helpssellers and buyers to explore various new choices and

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opportunities that the e-markets offer but also allowsthem to identify and analyze their resource constraints ina given schedule, and helps them to explore and exploitmany alternatives for a better solution. Moreover, in theproposed hybrid fuzzy negotiation mechanism agents

learn and make decisions on when to negotiate, with whom

to negotiate, and how to negotiate based on the past

negotiation experiences, current activities, and predictions.We choose the fuzzy negotiation framework for the

following reasons:

�

Consider the trade-off involved in agents decidingwhether they prefer to acquire exactly the preferredvalue of an attribute that is very important or severalsets of less-good values for attributes that are lessimportant to it. Such a trade-off can be modeled byfuzzy constraints. One of the primary things innegotiation is to represent trade-offs between thedifferent possible values for parameters. A buyer’spreferences on trade-offs between different attributesof the desired product can be easily modeled by fuzzyconstraints. � For a single characteristic of the preferred product, a

buyer might prefer certain values over others. Such apreference can be expressed as a fuzzy constraint overa single attribute, and the preference level at a certainvalue of the attribute is the constraint satisfactiondegree for that value. Likewise, for multiple productattributes, a buyer might favor certain combinations ofvalues over others. Such preferences can be expressedas fuzzy constraint over multiple attributes, and thepreference level at a certain combination value of theseattributes is the constraint satisfaction degree for thecombination value.

� In several cases, buyers do not know the precise details

of the products they want to buy, and so theirrequirements are often expressed by constraints overmultiple issues.

� A buyer’s constraints are not for all time equally

important. In order to deal with different levels ofimportance of different fuzzy constraints, researchershave introduced the concept of fuzzy in negotiationmechanisms.

� When buyers and sellers negotiate, it is hardly ever the

case that an offer is totally acceptable or totallyinconsistent with their respective constraints. Rela-tively, an offer usually satisfies the buyer’s constraintsmore or less. The proposed fuzzy negotiation frame-work is suited for capturing constraints of this kindbecause fuzzy constraints can be partially satisfied orviolated.

The rest of the paper is arranged as follows: Section 2deals with supply chains and fuzzy system modeling.Section 3 addresses an exhaustive literature review.Section 4 presents the proposed fuzzy hybrid negotiationmechanism. Section 5 discusses an illustrative numericalexample. Finally, Section 6 concludes the paper with someperspectives.

2. Supply chain systems and fuzzy system modeling

A supply chain is also a network of facilities anddistribution options that functions to procure materials,transform these materials into intermediate and finishedproducts, and distribute these finished products tocustomers. Supply chains exist in both service andmanufacturing organizations, although the complexity ofthe chain may vary greatly from industry to industry andfirm to firm. Realistic supply chains have multiple endproducts with shared components, facilities, and capa-cities. The flow of materials is not always along anarborescent network; various modes of transportationmay be considered, and the bill of materials for the enditems may be both deep and large (Jain et al., 2004).

Petrovic et al. (1999) highlighted the uncertainties insupply chain system as follows: ‘‘A real supply chainoperates in an uncertain environment. Different sourcesand types of uncertainty exist along the supply chain.They are random events uncertainty in judgment, lack ofevidence, lack of certainty in judgment, lack of evidence,lack of certainty of evidence that appear in customerdemand, production, and supply. Each facility in thesupply chain must deal with uncertainty demand imposedby succeeding facilities and uncertain delivery of thepreceding facilities in the supply chain’’. Generally, supplychain networks include several subsystems with unlim-ited interfaces and relations.

Every subsystem usually contains uncertainties. Ob-viously, uncertainties associated with each subsystem orcomponents make the whole system vague. Also, thenature of interfaces in dynamic supply chains causessupply chains to function in completely imprecise anduncertain environment. These interfaces are rooted in theinformation flows, material flows, and supplier–buyerrelations Goyal and Gopalakrishnan (1996). Moreover,relations among entities of dynamic supply chainscritically depend on human activities. This fact formsthe main reason why emergent dynamic supply chainsnecessitate fuzzy system modeling. Sugeno and Yasukawa(1993) state ‘‘Fuzzy algorithms are nothing but qualitativedescriptions of human actions in decision making’’.

Zadeh (1973) also states ‘‘As the complexity of a systemincreases, our ability to make precise and yet significantstatements about its behavior diminishes until a thresholdis reached beyond which precision and significance (orrelevance) become almost mutually exclusive characteris-tics. It is in this sense that precise quantitative analyses ofthe behavior of humanistic systems are not likely to havemuch relevance to the real-world societal, political,economic, and other types of problems, which involvehumans either as individuals or in groups’’. Sun (1999)develops a distribution constraint satisfaction problemformulation in the modeling of the supply chain as a totalsystem using the fuzzy technology. Petrovic et al. (1999)examine uncertainties in supply chains by focusing ondecentralized control of each inventory and partial co-ordination in the inventories. Turksen and Zarandi (1999)discussed many advantages of fuzzy system approach in

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real-world applications that motivate the authors to applyfuzzy modeling in dynamic supply chains.

1.

Fuzzy system models are flexible, and with any givensystem like dynamic supply chains, it is easy to handleit with fuzzy system models.

2.

Nearly all nonlinear functions of arbitrary complexitycan be captured by fuzzy system models. Also fuzzymodels are conceptually simple to understand.

3.

Superior communication between experts and man-agers is provided by Fuzzy system models. Moreover,these are based on natural languages and are tolerantof imprecise and vague data.

4.

Fuzzy system models can be constructed on the top ofthe experience of experts and can be mingled withconventional control techniques.

Dynamic supply chain network problems are character-ized by their complexity and inherent decentralization.The application of fuzzy logic and MAS techniques to thisproblem seems appropriate. Therefore, in this paper, wehave tapped the properties of fuzzy logic and proposefuzzy negotiation mechanism to capture dynamic nego-tiation between sellers and buyers.

3. Literature review

Traditionally, supply chains have been formed andmaintained over long periods of time by means ofextensive human interactions. But the increasing demandfor accelerated commercial decision making in the face ofexploding growth and complexity of information iscreating a need for more advanced support for automatedsupply chain formation (Reaidy et al., 2006). Companiesranging from auto makers to computer manufacturers arebasing their business models on rapid development, buildto order, and customized products to satisfy ever-changingconsumer demand, and fluctuations in resource costs andavailability mean that companies must respond rapidly tomaintain production capabilities and profits. As thesechanges increasingly occur at speeds, scales, and complex-ity unmanageable by humans, the need for automatedsupply chain formation becomes acute (Durfee et al.,1989; Chopra and Meindl, 2007; Lo et al., 2008). Thegeneral agent-based modeling method is not new and ithas already been applied in many different economic andsocial contexts. There has been much research work thatdeals with coordination in MASs. A framework is pre-sented in (Toledo Excelente and Jennings, 2002) thatenables agents to dynamically select the mechanism theyemploy in order to coordinate their inter-related activities.The agents also learn when and how to coordinate. InXuan et al. (2001), various coordination aspects and acooperative, multi-step negotiation mechanism are dis-cussed.

Collaboration and partnership are new leitmotivs inorganizations and supply chain management, with em-phasis on collaborative design and planning. Several majorresearch projects emphasize the manufacturing andlogistic aspects of the collaboration, addressing the

problem of enterprise and enterprise-wide modeling andintegration. Examples are the CIMOSA project, the TOVEproject (Fox et al., 2000), and the NetMan project (Sophieet al., 1999; Frayret et al., 2001). Yung and Yang (1999)proposed the integration of multi-agent technology andconstraint network for solving supply chain managementproblems. Yan et al. (2000) developed a multi-agent-based negotiation support system for distributed electricpower transmission cost allocation based on a networkflow model and KQML. Gjerdrumm et al. (2001) showedhow expert system techniques for distributed decisionmaking can be combined with contemporary numericaltechniques for supply chain optimization. Though theapplications of MASs in networked manufacturing andsupply chains are not brand new, the analytical modelsand algorithms for integrating the planning and coordi-nating the operations of these agents have not been fullyaddressed.

An MAS consists of a group of agents that can takespecific roles within an organizational structure. Differenttypes of agents may represent different objects, withdifferent authorities and capabilities, and perform differ-ent functions or tasks. MAS enhances performance alongthe dimensions of (1) computational efficiency becauseconcurrency of computation is exploited (as long ascommunication is kept minimal, for example, by trans-mitting high-level information and results rather thanlow-level data); (2) reliability, that is, graceful recovery ofcomponent failures, because agents with redundantcapabilities or appropriate inter-agent coordination arefound dynamically (for example, taking up responsibilitiesof agents who fail); (3) extensibility because the numberand the capabilities of agents working on a problem canbe altered; (4) robustness, the system’s ability to tolerateuncertainty, because suitable information is exchangedamong agents; (5) maintainability because it is easier tomaintain a system composed of multiple-componentagents because of its modularity; (6) responsiveness

because modularity can handle anomalies locally, notpropagate them to the whole system; (7) flexibility

because agents with different abilities can adaptivelyorganize to solve the current problem; and (8) reuse

because functionally specific agents can be reused indifferent agent teams to solve different problems. Withthese properties, MAS then becomes a research areaattracting a great amount of research efforts, especially,for a problem domain that is characterized by complexity,large scale, distribution and uncertainty (Jain, 2006a).

Moreover, the agent system is an alternative technol-ogy for supply chain management because of the featuressuch as distributed collaboration, autonomy, and intelli-gence (Nissen, 2001; Chan and Chan, 2004). The ability tomeet the changing needs of customers requires changingthe supply of product, including mix, volume, productvariations, and new products. Meeting these needs in thesupply chain requires flexibility in sourcing product fromraw materials to outsourced finished product. Swami-nathan et al. (1998) present a modeling and simulationframework for developing customized decision supporttools for supply chain re-engineering. Agents may repre-sent various supply chain entities, viz. customers,

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manufactures, and transportation. These agents usedifferent protocols and help in simulation of material,information, and cash flows. The research findings of Tsay(2002) highlights how risk aversion affects both sides ofthe supplier-retailer relationships under various scenariosof relative strategic power, and how these dynamics arealtered by the introduction of a return policy. Jennings etal. (1998) provide an overview of research and develop-ments in the field of autonomous agents and multi-agentsystems.

Negotiation is a process by which a group of entitiestry and come to a mutually acceptable agreement on somematter (Pruitt, 1981). According to the cardinality andnature of the interaction, automated negotiation modelscan be classified into three main categories (Jennings etal., 2001). The first consists of many-to-one or many-to-many models in which multiple agents negotiate witheither a single or many other agents. This category ispredominantly handled using various auction-basedmodels (Sandholm, 1999) and these models are widelyused in the field of on-line retail, e.g., eBay (http://www.ebay.com) and eMediator (Sandholm, 1999). Thesecond category consists of one-to-one models in which apair of agents negotiate directly with one another (Faratinet al., 2002). These models typically use a range ofheuristic methods to cope with the uncertainties. Thethird category consists of argumentation/persuasion--based models (Kraus et al., 1998) in which agents usevarious types of argument, such as threats, rewards, andappeals, to persuade their opponent to accept a deal theywould not previously have countenanced. For each of thethree categories, the negotiation domain could be asingle-issue one (e.g., price) or a multiple-issue one (e.g.,price, quality, model, volume, delivery date, expiry date,after-sale service, warranty, and return policy).

Agents in open and dynamic environments likedynamic supply chains would aim to produce the bestpossible result given their available processing, commu-nication, and information resources to maximize systemoutput (Garcıa-Flores et al., 2000; Julka et al., 2002;Emerson and Piramuthu, 2004). While designing agentsystems, it may be difficult to foresee all the potentialsituations an agent may encounter and specify an agentbehavior optimally in advance. Agents therefore have tolearn from, and adapt to, their environment, especially inmulti-agent setting. However to build autonomous agentswho improve their negotiation competence based onlearning from their interaction with other agents is stillan emerging area Mundhe and Sen (2000). The mostintelligent agents will be able to learn, and will be able toadapt to their environment, in terms of user requests andthe resources available to the agent (Papazoglou, 2001;Yoo and Kim, 2002). There are already a variety ofinformation systems and networks working within andbetween chain members to facilitate the flows ofmaterials, information, and funds. However, there is lackof coordination and integration between these systems.

Pappas et al. (1996) presented conflict resolutionarchitecture for multi-agent hybrid systems with empha-sis on air traffic management systems, which has theability to detect conflict dynamically by sensory informa-

tion available to aircraft. Wagner et al. (1999) presenteddifferent solutions to inter-agent, intra-agent, and meta-level conflicts: conversations and negotiations are used toresolve inter-agent conflicts that occur during the ex-change of information, constraints, and formation ofcommitments among agents. Therefore, it is quite possiblethat no solution can be reached among a group of non-cooperative agents in that the agent might be better offacting alone if no benefit is obtained from the negotiation.Therefore, the effectiveness of such systems in resolvingconflicts among non-cooperative agents is questionable.Even in collaborative MASs, since no single agent hasaccurate and complete global knowledge, it is inevitablethat agents enter into conflicts over actions, plans, orresources (that they select; Muller and Dieng, 2000).

In addition, the uncertainties associated with supplychain networks result in an inefficient manufacturingenterprise. This is principally due to its impreciseinterfaces and its real-world character, where uncertain-ties in various activities right from raw material procure-ment to the end user may make the supply chainimprecise. The true nature of the problem involves datathat are often vague and imprecise. For example, in theproduction scenario, various elements like set-up time,processing time, mean time between failure, mean time torepair, etc. will be better expressed as fuzzy variables, asthey are often expressed in imprecise, vague terms like‘Processing time is high’ or ‘Set-up time is low’. Therefore,real-world production planning, inventory control, andscheduling problems are usually imprecise. However,managers are to interact in an intelligent way in thisenvironment. Thus, they have to reach out for a new kindof reasoning based on imprecise knowledge. In real-world

situations there is variability in order type, quantity, or

frequency. There are effects due to incentives, lack of

information, capacity constraints, demand forecasting er-

rors, uncertainties in information flows, transportation scale

economies, set-up and ordering costs. Henceforth, it is

essential to be able to cope up dynamically with variations

in the environment, i.e. inventory, demand, supply, spatial,

temporal, monetary constraints, to overcome both costly

interruption stock-out as well as over- stock problems. Thus,it can be seen that the dynamic supply chain networkproblems are characterized by their complexity andinherent decentralization. The application of fuzzy logicand MAS techniques to this problem seems appropriate.

4. Proposed fuzzy hybrid negotiation mechanism

In this section, we discuss in detail the proposed fuzzyhybrid negotiation mechanism. First, we define thefollowing notations for the fuzzy negotiation framework:

VATITSEL value of attribute I at time T for the Seller agent.

Its acceptable range is [VATIT(Low)SEL, VATIT(High)

SEL]VATIT

BUY value of attribute I at time T for the Buyer agent.Its acceptable range is [VATIT(Low)

BUY, VATIT(High)BUY]

RANI range of negotiation issues. It is given asRANI ¼ VATI1

SEL�VATI1

BUY as shown in Fig. 1.

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CRANITSEL appropriation range of attribute I at time T. It is

given as CRANITBUY¼ VATIT

SEL�VATI1

SEL for thebuyer and CRANIT

SEL¼ VATIT

BUY�VATI1

BUY for theseller.

WTI weight associated with the attribute I, 0oW-

TIo1 and sum of weights ¼ 1. The weightassociated with seller agent and buyer agent isdenoted as WTI

SEL and WTIBUY respectively.

ARANI acceptable range for attribute I. For buyer,ARANI

BUY¼ VATI(High)

BUY�VATI(Low)

BUY and for sellerit is given as ARANI

SEL¼ VATI(High)

SEL�VATI(Low)

SEL asshown in Fig. 2.

SCRANISELscore gained from appropriation ratio of attri-

butes I for the sellerSPRANI

BUY score gained from preference ratio of attri-butes I for the buyer

The proposed negotiation mechanism uses two fea-tures, appropriation degree and preference degree, as areference to find a new offer to the buyer. We tap theproperties of fuzzy logic to develop two membershipfunctions for these two features. Based on their fuzzyvalues, we allot fuzzy rules for the new offer to the buyersand sellers.

4.1. Calculation of appropriation degree

During a negotiation process, if the appropriation of anattribute from the buyer is high, we would respond with a

Seller’sinitial offer

SELIVAT 1

Buyer’s current offer

BUYIVAT 1

Buyer’s initial offer

BUYIVAT 1

Range of negotiation IRAN

Fig. 1. Concept of appropriation (from seller’s viewpoint).

Acceptable Range ARANI

Seller’s lower limit SEL

I (Low)VAT

Buyer’s current offer BUYIT

VAT

Seller’s higher limit SELI (High)

VAT

Fig. 2. Concept of Preference (from seller’s viewpoint).

Table 1Triangular fuzzy membership function.

Very low Low Medium High

Very low L,L,L L,L,M L,L,H L,M,L

Low L,M,H L,H,L L,H,M L,H,H

Medium M,L,M M,L,H M,M,L M,M,M

High M,H,L M,H,M M,H,H H,L,L

Very high H,L,H H,M,L H,M,M H,M,H

better value for the issue to the buyer. The step-by-stepprocedure for calculating the appropriation degree is asfollows:

Step 1: Find the value of every attribute, from thepresent offer of the buyers and the sellers.

Step 2: Calculate the range of appropriation CRANITSEL.

Step 3: Calculate the appropriation ratio ACRANIT ¼ -CRANST

SEL/RANS. From the appropriation ratio, find itscorresponding score SCRANI

SEL as shown in Table 1Step 4: Compute the total appropriation degree TCDT

SEL

for seller from the buyer’s offer using the formulaTCDT

SEL¼P

IWTISELSCRANIT

SEL

4.2. Calculation of preference degree

Each attribute has its acceptable range, from which wecan divide the range into different proportions to showdifferent preference degrees to opponent’s offer. Theprocedure for calculating the preference degree is asfollows:

Step 1: Every seller and buyer can find his/heracceptable range ARANI for each attributes like cost,quality, lead time, flexibility, etc.

Step 2: From Step 1, seller and buyer can divide theacceptable range into different preference areas to showvarious preferences.

Step 3: We can calculate the preference ratio PRANIT-SEL¼ ((VATIT(High)

SEL�VATIT

BUY)/ARANISEL) and PRANIT-

BUY¼ ((VATIT

SEL�VATIT(Low)

BUY)/ARANIBUY) for seller and

buyer, respectively.Step 4: From Step 3, we can find the corresponding

score SPRANIBUY

Step 5: Calculate the total preference degree TPDTSEL for

seller from the buyer’s offer using the equationTPDT

SEL¼ ¼

PIWTI

SELSPRANITSEL

4.3. Calculations of counter offers

For the above two parameters, appropriation degreeand preference degree, we define two fuzzy membershipfunctions. Each function has five values: very low (VL),low (L), medium (M), high (H), and very high (VH).Triangular membership functions are used to representthese two functions as shown in Figs. 3 and 4, respectively,and their universe of discourse for each fuzzy value isshown in Table 1.

The step-by-step procedure for finding a counter-offeris as follows:

Step 1: We can find the membership function values foreach TCD and TPD, that is, m1(TCD), m2(TCD), m1(TPD), and

Very high Left (m ¼ 0) Center (m ¼ 1) Right (m41)

L,M,M – 0.30 3.2

M,L,L 0.4 3.8 5.4

M,M,H 4.0 6.0 8.0

H,L,M 6.5 8.5 10.1

H,H,L 7.7 10.7 –

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0 1 10

µ

0

1µVL(TCD) µL(TCD) µM(TCD) µH(TCD) µVH(TCD)

Very Low

Low Medium High Very High

2 3 4 5 6 7 8 9

Fig. 3. Fuzzy membership function for appropriation degree.

0 1 4 6 10

µ

0

1

µVL(TPD) µL(TPD) µM(TPD) µH(TPD) µVH(TPD)

VeryLow

Low Medium High VeryHigh

2 3 5 7 8 9

Fig. 4. Fuzzy membership function for preference degree.

V. Jain, S.G. Deshmukh / Int. J. Production Economics 122 (2009) 319–328 325

m2(TPD). Each of these values can be either one of the fivevalues: VL, L, M, H, and VH.

Step 2: Calculate the fuzzy firing strength. The jointmembership function between the two membershipfunctions can be expressed as JMFV ¼ min(mm(TCD),mn(TPD)), where m, n ¼ 1 or 2, and n ¼ 1–4.

Step 3: Each JMFv value corresponds to a fuzzy rule, asshown in Table 1, where each capital letters (L, M, and H)in each column stands for three different rules for threeattributes.

Step 4: A new value of attribute I for the counter-offercan be derived from the equation

VATIT ¼ VATIt�1 � ARANI

PvJMFv RLvP

vJMFv

where � is + for the buyer and � for the seller.Because of each agent’s incomplete view of the

uncertain environment, our coordination strategy is notto obtain an optimal solution, but a ‘good enough, soonenough’ one. To increase the chance of success, we installlearning mechanisms to our agents so that each agent canlearn to coordinate better. Agents’ learning mechanismsconsist of reinforcement learning (RL) and case-basedlearning (CBL). RL is helpful to decide with whom tocoordinate while CBL is helpful to decide how to negotiate.To facilitate the two learning mechanisms, each agentdynamically profiles (1) each negotiation task—as a casein the case base, and (2) each neighbor—as a vector in theagent. In our research domain, agents also learn from thepast negotiation results to improve coordination in thefuture since they work in a dynamic supply chainnetwork. In such an environment, the optimal coordina-tion is not guaranteed. To achieve the necessary degree offlexibility in coordination, an agent is required todynamically make decisions on when to coordinate, withwhom to coordinate, and how to coordinate.

A case records the problem description of a task, itssolution, its outcome, and its usage history. The agents

dynamically update their neighbor’s utility value usingthe formula VUa,b(t) ¼ (1�b)VUa,b(t�1)+b(Ca(t)/(Z+Ca(t))),where b is the learning rate (0rbr1), which determinesthe dependency degree of agent b on neighbor a’s currentCPU allocation Ca(t) and Z is the balance parameter to geta percentage value for the computation of VUa,b(t). Theflowchart of the proposed fuzzy negotiation mechanism isshown in Fig. 5.

5. An illustrative numerical example

To exhibit the operation of our proposed negotiationmechanism and to show its practicality, we have gener-ated a hypothetical example for evaluating suppliers. Inthis example, there are two suppliers S1 and S2 withattributes cost ($/item), lead time (days), quantity (items),reward, restrictions, and profit associated with them. Sucha scenario is typical of semi-competitive environment.That is, both supplier agent and buyer agent attempt toacquire the best deal they can since they both are self-interested. Towards this end, they should minimize therevelation of their private information since it couldprevent them from getting good deals. However, as theseller desires to build or preserve his reputation (thisshould associate with more money in long term) and thebuyer needs to settle down as soon as possible, it is alsoessential for them to cooperate to a certain extent in thenegotiation. Table 2 shows the seller product model (i.e.the information about the available suppliers prepared bythe seller agent).

We assume the following ranges for attributes:Cost (in $):MIN ¼ OPT ¼ 12; MAX ¼ 67.Lead time (in days):OPT ¼ 2, 3, 4, 5, 6, 7, 8MIN ¼ 1; MAX ¼ 20.Quantity (in items):MAX: OPT ¼ 127MIN: 1By varying the attributes and balancing with cost, we

randomly generate 10 combinations as shown in Table 3.For different configuration of suppliers, the proposedfuzzy negotiation mechanism will represent trade-offsamong the different probable values of the negotiationissues. The table with generated fuzzy rule is shown inTable 3. From the proposed negotiation procedure, weknow that supplier configurations such as 1(S1), 2 (S1), 3(S1), 4 (S1), 5(S1), 1(S2), 2(S2), 3(S3), and 4(S2) are notacceptable to the buyer agent, but configuration 5(S2) isacceptable. Therefore, from both the seller’s and buyer’sperspective 10 is the best solution. Our agents areautonomous in that they negotiate with each other onbehalf of both sellers and buyers. Thus, they actually makethe contract decision themselves. In this mechanism, theuser’s requirements on attributes of a product/service thatfuzzy constraints can easily capture are represented.

The problem can be extended to m suppliers with n

attributes and the proposed mechanism can be carried outover fuzzy constraints of multiple issues of products,which is more efficient than doing it over single solutions.

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Start

Bid announcement with negotiable tangible and intangible attributes like

cost, quality, lead-time etc

Evaluation of Bid based on both tangible and intangible attributes

Submit Bid

Bid submission

Start Negotiation

Calculate Preference degree

Calculate Appropriation degree

Calculate Membership value

Find negotiation strategy & fuzzy rule

Calculate New Counter offers

Offers

Deal is materialized

End

Learning

Dynamic update EndYes No

Learned Pattern

Training examples YesoN

Fig. 5. Flowchart for the proposed fuzzy hybrid negotiation mechanism.

Table 2Product information held by supplier agent.

Suppliers Lead time Quantity Cost Quality Appropriation

S1 1–8 1–28 12–67 Low 2 units free

9–14 1.83 12–65 Medium No

15–20 1–128 12–62 High No

S2 1–6 1–13 12–67 Medium No

7–12 1–63 12–64 Low 2 units free

13–20 1–128 12–63 High No

V. Jain, S.G. Deshmukh / Int. J. Production Economics 122 (2009) 319–328326

Since human negotiators are unwilling to disclose privateinformation, decentralized methods for searching Pareto-optimal solutions in negotiation problems are necessary.The proposed mechanism guarantees that the outcome of

the negotiation is Pareto optimal. Thus, it can be seen thatthe proposed mechanism not only helps sellers andbuyers to explore various new choices and opportunitiesthat the e-markets offer but also allows them to identifyand analyze their resource constraints in a given schedule,and helps them to explore and exploit many alternativesfor a better solution.

6. Conclusion and perspectives

Designing efficient business processes throughout thesupply chain, and controlling their speed, timing, andinteraction with one another are decisive factors in acompetitive and dynamic environment. Coordination, theprocess by which agents reason about their local actionsand the actions of others to try to ensure that the

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Table 3The negotiation round for several combinations of numerical example.

Combination of suppliers Lead time Quantity Cost Quality Preference ratio (PRANIT) Score Appropriation ratio (ACRANIT) Score Fuzzy rule

1(S1) 04 77 12 Low PRANITo1/3 0.20 ACRANITo0.25 0.10 VL

2(S1) 10 62 17 Medium 1/3rPRANITo2/3 0.40 0.25rACRANITo0.40 0.30 M

3(S1) 08 127 15 Medium 1/3rPRANITo2/3 0.40 0.40rACRANITo0.55 0.30 M

4(S1) 05 122 18 High 1rPRANIT 0.80 0.70rACRANITo0.85 0.90 H

5(S1) 08 92 12 Low 1/3rPRANITo2/3 0.40 ACRANITo 0.25 0.10 VL

1(S2) 13 122 13 Low PRANITo1/3 0.20 0.25rACRANITo0.40 0.30 L

2(S2) 07 110 12 Medium 2/3rPRANITo1/3 0.80 0.55rACRANITo0.70 0.50 L

3(S2) 08 92 17 Medium 1/3rPRANITo2/3 0.60 0.40rACRANITo0.55 0.30 M

4(S2) 17 127 15 Medium 2/3rPRANITo1/3 0.80 0.55rACRANITo0.70 0.50 H

5(S2) 04 122 12 High 1rPRANIT 1.00 0.85rACRANITo1.00 1.00 VH

V. Jain, S.G. Deshmukh / Int. J. Production Economics 122 (2009) 319–328 327

community acts in a coherent manner is an importantissue in MASs. There are three main reasons why it isnecessary for agents to coordinate. First, there aredependencies between agents’ tasks or goals; second,there is a need to meet global constraints such as cost andtime limits; and third, no individual agent has sufficientcompetence, resources, or information to solve the entireproblem.

Achieving effective coordination in an MAS is non-trivial as no agent possesses the global view of theproblem space. Moreover, the different strategies adoptedby agents may produce conflicts. In order to modelcoordination among suppliers and buyers in a dynamicsupply chain, this paper takes a step further and proposesa new fuzzy-logic-based hybrid negotiation mechanism.In most real-world negotiation situations, agents have acommon interest to cooperate, but have conflictinginterests over exactly how to cooperate. These situationsinvolve restrictions and preferences that may be vaguelyand partly defined. Therefore, this study takes theadvantage of fuzzy logic and develops a hybrid negotia-tion-based mechanism that combines both cooperativeand competitive negotiations. While agents coordinatewith each other in the operations, they will negotiateabout their strategies to reduce conflicts. The proposedfuzzy hybrid negotiation mechanism allows negotiationagents more flexibility and robustness in an automatednegotiation system. The proposed mechanism not onlyhelps sellers and buyers to explore various new choicesand opportunities that the e-markets offer but also allowsthem to identify and analyze their resource constraints ina given schedule, and helps them to explore and exploitmany alternatives for a better solution.

In our research domain, agents also learn from the pastnegotiation results to improve coordination in the futuresince they work in a dynamic and noisy environment. Insuch an environment, the optimal coordination is notguaranteed. To achieve the necessary degree of flexibilityin coordination, an agent is required to dynamically makedecisions on when to coordinate, with whom to coordi-nate, and how to coordinate. The proposed computationalframework based on fuzzy constraints is suited forcapturing the dynamics by modeling trade-offs betweendifferent attributes of a product, leading to a fair andequitable deal for both suppliers and buyers.

The proposed fuzzy negotiation mechanism is genericand can be used for wide range of domains, especially innegotiations pertaining to supply contracts for flexibleproduction networks. The model ensures a high degree offlexibility; it avoids deadlocks and encourages the parties’willingness to a compromise. It guarantees that theoutcome of the negotiation is Pareto optimal, yet theparticipating agents reveal minimal information abouttheir preferences and constraints. Efficacy and intricacy ofthe proposed model are demonstrated with the help ofnumerical examples. In future, the concept of game theorycan be employed to deal with the insight of agentbehavior for effective portrayal of the characteristics ofthe agents, especially in the emerging dynamic B2B e-Commerce environment.

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