min h.-international intermodal choices via chance-constrained

7/27/2019 Min H.-international Intermodal Choices via Chance-constrained

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Tonspn Res:A Vo. ZSA No 6 pp 351362, 1991Primed in Great Brnain.

0191260791 S3W + .OO@ 1991 Pergamon Press plc

INTERNATIONAL INTERMODAL CHOICES VIACHANCE-CONSTRAINED GOAL PROGRAMMINGHOKEYMINManagement Science Group, 314 Hayden Hall, College of Business Administration,Northeastern University, Boston, MA 02115, U.S.A.

(Receiv ed 30 June 1990; in revisedform 16November 1990)Abstract-Over the years, an increasing interdependence of the world economy has led to the consider-able growth of international trade. Due to the lengthy distribution channel, international trade is oftencharacterized by intermodal shipment which moves products across national boundaries via more thanone mode of transportation. Consequently, the intermodal choice is of vital importance to the success ofinternational trade. The intermodal choice, however, has never been a simple matter for any distributionmanager because it can be affected by the multitude of conflicting factors such as cost, on-time service,and risk. This article develops a chance-constrained goal programming model to aid the distributionmanager in choosing the most effective intermodal mix that not only minimizes cost and risk, but alsosatisfies various on-time service requirements.

1. INTRODUCTIONSince the Reciprocal Trade Agreement Act of 1934reduced tariffs and encouraged free trade for U.S.companies, there has been a tremendous increase inforeign trade volume and value. Anderson (1984) re-ports that overall U.S. trade as a share of GNP hasdoubled from 1960 to 1985, and is expected to re-main at 12% through 1990. As foreign trade esca-lates each year, many distribution managers have re-alized the importance of international logistics to thecompanys competitiveness in the world market-place. The importance of international logistics isevident from a recent article in Purchasing WorldMagazine (1987) indicating that international logisticcosts account for 30 to 50% of the companys pro-duction costs.

Over the past decade, the increasing awareness ofinternational logistics has forced many companies toreassess the design of their current transportationsystems. Perhaps the most significant trend towardinternational logistics may be utilization of inter-modalism. Intermodalism is generally referred to asthe movement of products from origin to destinationusing a mixture of various transportation modessuch as air, ocean liner, barge, rail, and truck. Inter-modalism is a key part of international logistics be-cause surface transportation (truck or rail) alonecannot cross the ocean that often separates one na-tion from another. Therefore, with the exception ofcross-border trade with Canada and Mexico, inter-modalism is indispensable to international trade.Intermodalism can provide great opportunitiesfor reducing logistics costs and improving services,but can create a lot of hassles due to a variety ofcomplex options. lntermodalism in international en-vironments is more complicated than intermodalismin domestic environments because of increased ship-ping distances, additional document preparations,

greater uncertainties in foreign regulations, and thelike. Intermodalism, which commonly uses contain-ers, can save money and time by unitizing freight,protecting goods from weather, pilferage, and dam-age, and simplifying loading and unloading proce-dures (see e.g., Mahoney, 1985). Intermodalism canalso improve service by using a faster mode, that is,air versus surface, for a segment of the haul (Oss-wald, 1985). On the other hand, intermodalism cancreate problems because goods are subject to differ-ent stresses and conditions in each mode due to thedifferent shape of each mode (Mahoney, 1985). Ad-ditionally, intermodalism through containerizationcan limit certain international routes because not ev-ery port in the world is equipped to handle contain-ers, restricting possible routings through noncon-tainer ports (Schary, 1984; Stock and Lambert,1987).In light of the above discussion, the main focus ofthis study is to set a decision rule that best combinesdifferent modes of transportation and best maintainsa continuous flow of products during intermodaltransfer. In so doing, the distribution manager cantake advantage of the full benefits of intermodalismwhile minimizing its disadvantages. As a powerfultool in setting such a decision rule, we propose anddevelop a chance-constrained goal programming(GP) model.

In the next section, the international intermodalchoice problem and its related issues will be clearlydefined and illustrated with a hypothetical scenario.Then, underlying assumptions and chance-con-strained GP formulation will be presented with justi-fications for the GP formulation. Also, to illustratethe validity of modelling efforts, a hypotheticalproblem mimicking real-world situations will besolved by the model. Finally, the research effortswill be summarized with implications of the currentresearch and suggestions for future research.TR(A) 25: 6-C 351


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352 H.2. PROBLEM SCENARIO

Let us consider the problem that a typical multi-national firm faces in shipping goods across interna-tional boundaries via different modes of transporta-tion. These transportation modes can be air, rail,ocean carrier, barge, and truck. Each of these modescan be combined to various intermodal mixes suchas truck-rail, truck-water (barge or ocean carrier),truck-air, and rail-water. Some of these mixes havetheir own names (see Fig. 1). For example, truck-rail combination is dubbed piggybock. Specifically,piggyback refers to trailer-on-flatcar (TOFC) orcontainer-on-flatcar (COFC). Piggyback has beenthe most widely used intermodal mix in the U.S.since it was deregulated on March 23, 1981, by theInterstate Commerce Commission (ICC) (Foster,1981). Regardless of the popularity of such a mode,the distribution manager has to make intermodalchoices by considering a variety of factors affecting.the efficiency of intermodalism. Examples of thesefactors include speed, reliability, capacity, andfreight rate of each mode involved in intermodalism,and size of cargo (freight). Unfortunately, many ofthese factors are conflicting against one another. Forexample, water transportation is slower and less fre-quent, but substantially cheaper than air transporta-tion. Also, water transportation, which is larger incapacity, is more ideal for shipments of heavy andbulky cargoes than air transportation. By the sametoken, similar comparisons can be made amongother transportation modes (rail vs. truck, rail vs.barge, truck vs. air). Refer to Table 1 for generalcomparisons of the modes.

a cost/service tradeoff analysis is always an underly-ing premise for any form of intermodal problemsincluding international intermodalism. To performthe cost/service tradeoff analysis, we need to exam-ine all the cost/service elements involved in interna-tional intermodal choices and, if appropriate, inves-tigate their functional relationships with each mode.The following lists represent typical cost/service ele-ments for international intermodalism.

From Table 1, it is obvious that there is no domi-nant mode of transportation that is the cheapest andfastest one among the various modes. Consequently,

1.

2.

3.

4.

AIRwIRDYBACK53RUCKPIGGYBACK FISHYBACK

RAIL WATER

Fig. 1.Types of intermodal services.Source: Adapted from Coyle, J. J., Bardi, E. J., Lang-ley, C. J., (1988), The M anagement of Business Logi sti cs,4th edition, West Publishing Co., St. Paul, MN, p. 346.

5.

6.

7.

Transportation cost-This is mainly based onfreight rates which are determined by the type ofthe mode, size of cargo, and shipping distances.In-transit inventory carrying cost -This is propor-tional to speed of the mode and size of cargo. Thiscost can be computed by the following formulasuggested by Bender (1985a).

IICC = TT x %ICC x UF x FSwhere IICC = in-transit inventory carrying cost;TT = transit time of the mode; %ICC = unit in-ventory carrying charge (in percent); UF = unitvalue of freight; FS = freight size (in unitnumber).Packaging cost-This cost is influenced by thetype and speed of the mode. As a rule of thumb,the slower the mode used, the more expensive thepacking cost is (Bender, 1985a). The reason maybe that slower journey requires better packagingto withstand more shocks and bumps. Also, pack-aging cost for less-than-truckload (LTL) or less-than-carload (LCL) shipment is known to behigher than that for full truckload or full carloadbecause LTL or LCL shipment is more vulnerableto physical stress and pilferage (Cox and Van Tas-sel, 1985).Insurance cost -This cost is related to the typeand speed of the mode, and the value of freight.Consequently, the slower the mode and the moreexpensive the freight, the higher the insurancecost.Documentation cost-This is affected by themode used. The faster the mode used, the shorterthe time available to prepare documentation,therefore, the higher the document preparationcost (Bender, 1985a).Miscellaneous cost -This cost includes customsduty, handling cost, and loading and unloadingcost at the port.Transit time-This includes the time required forpickup and delivery, for terminal handling, andfor shipment between origin and destination(Coyle et al., 1988). Because longer transit timeresults in higher inventory and frequent stockouts,short transit time is usually desired by many cosig-nees. However, on-time delivery is more crucialto international intermodalism than faster deliv-ery in two different ways. First, faster transit timehas often led to the arrival of products at the portlong before the arrival of documentation needed


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Chance-constrained goal programmjngTable 1. General comparison of transportation modes

353

Characteristics Truck Rail Air Barge*1. cost Moderate Low High Low2. Market Coveraae Point-to-point Terminal-to-terminal Terminal-to-terminal Terminal-to-terminal3. Average Length of Haul(miles) 515 617 885 376-1.3674. Equipment Capacity

(tons)5. Speed6. Availability7. Reliability (delivery timevariability)8. Damage

IO-25 50-12,000 5-125 1 OOO-60,000Moderate Slow Fast SlowHigh Moderate Moderate LowHigh Moderate High LowLow Moderate-high Low Low-Moderate

*Ocean carrier has similar characteristics to barge.Source: Adapted from Stock J.R. and Lambert D.M. (1987) Strategic L ogistics Management, 2nd Ed, RichardD. Irwin, Inc., Homewood, IL, p. 185.

to release them. This undermines the efficiency ofinternational intermodalism (Harrington, 1983).Second, with the increasing commitment of U.S.companies to just-in-time (JIT) systems, nearly90% of U.S. managers surveyed by Lieb and Mil-len (1988) opted for on-time delivery rather thanother services.

8 Reliability -This usually represents the consis-tency of the transit time that relates to risks ofdelay. Because unreliable services increase safetystock levels, reliability is one of the most impor-tant factors in choosing the mode.

9. Intermodal compatibility-Consignors may faceserious difficulties in transferring goods betweentransportation modes operating in different inter-change points such as ocean liners and rails. Ac-cordingly, the most prevalent form of modal com-binations for intermodal transfer have been thetruck-rail, truck-water, and truck-air, which arecompatible (accessible) to each other because oftrucks point-to-point coverage (Coyle er al.,1988).In addition to the cost/service tradeoff analysis,international intermodal choice problem presents

unique situations one does not encounter in domesticintermodalism due to the involvement of exporting/importing ports and Foreign Trade Zones (FTZs) inthe multilevel distribution channel shown in Fig. 2.These unique situations occur in selecting ports andutilizing FTZs.To elaborate, unlike domestic intermodalism,port selection is crucial for international intermodal-ism in that inefficient port operations and/or facili-ties may delay intermodal transfer, and, more seri-ously, the absence of equipment for handlingcontainers may prevent intermodal transfer at a cer-tain port.

As opposed to domestic intermodalism that neverrequires customs clearance, international intermod-alism can benefit from FTZs. FTZs are areas, adja-cent to a port of entry, that are set aside by thegovernment for packaging, sorting, storing, labeling,

exhibiting, manufacturing, and reshipping importedgoods without paying customs duty until the goodsare sent into the domestic territory (Leenders ef al.,1989). The FTZ offers some potential benefits forinternational intermodal shippers because passagethrough customs is known to be usually faster froma FTZ than from the port of entry, and goods aremore secure from pilferage in a FTZ than in a typicalwarehouse, thereby lowering insurance rates in-volved in intermodal shipments (Tansuhaj and Jack-son, 1989). Undoubtedly, port selection and Foreign

Fig. 2. Typical international logistics flow.Source: Adapted with modifications from Bender P.(1988) The international dimensions of physical distribu-tion management. In J. Robson and R. House (Eds.), TheDistribution H andbook, p. 783. The Free Press, New York.


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354 H. MINTrade Zone usage constitute the important compo-nents of the international intermodal choice prob-lem.

With the above in mind, the international inter-modal choice problem must tackle the following is-sues:1. How to choose the most cost-service-effective

transportation mode for each segment of the in-ternational distribution channel and how to blendintermodal combinations for the entire distribu-tion channel so as to minimize disruption at inter-change points?

2. How to select exporting/importing ports? Morespecifically, does the port have special equipmentfor handling containers? Does the port providesecure operations for minimizing cargo loss anddamage? Does the port have greater accessibilityto domestic inland transportation? Does the portprovide low cargo handling charges?3. How to utilize FTZs in an effort to strategicallyposition imported goods in advance of quotaopenings or demand increases without paying cus-toms duties?

3.MODELDEVELOPMEN.lTo help distribution managers set rational andconsistent guidelines for evaluating the cost-service-

effectiveness of intermodal choices in internationalenvironments, we develop a chance-constrained goalprogramming (GP) model. Generally speaking,chance-constrained GP is referred to as a multipleobjective technique for determining solutions thatsatisfice multiple goals where there are elements ofrisk and uncertainty associated with parameters(technological coefficients) and/or constraints (See,e.g., Wynne, 1978).We decided to employ a chance-constrained GPapproach for both practical and technical reasons.From a practical standpoint, a GP aspect of themodel developed in this study reflects the diverse andconflicting nature of goals (e.g., minimizing trans-portation costs versus maximizing on-time deliveryservices) associated with international intermodal-ism. A chance-constrained aspect of the model re-flects the dynamic and uncertain nature of con-straints (e.g., just-in-time requirements) associatedwith international intermodalism. Hence, a chance-constrained GP model is suitable for solving interna-tional intermodal problems.From a technical standpoint, we preferredchance-constrained GP to other multiple objectivetechniques because the computational complexity ofGP is less severe than that of other multiobjectiveprogramming techniques (so-called generating tech-niques) such as weighting, constraint, noninferior setestimation (NISE), and multiobjective simplex meth-ods. In particular, Cohon (1978) observed that thecomputational burden of the generating techniquesincrease exponentially with the number of objectives(goals). Therefore, the generating techniques can

pose onerous computational difficulties even for sol-ving the moderate-sized problem. On the other hand,in GP formulation, an addition of one more objec-tive to the problem is nothing more than an additionof one more constraint; consequently, the computa-tional complexity of GP would not increase signifi-cantly with the number of objectives. Also, due tothe special structure of GP, a new objective (in theform of a new goal constraint) can always be addedto the problem without violating the feasibility re-quirements of a given solution [Zeleny (1982)]. Forthese reasons, GP can better accommodate a largenumber of conflicting objectives than other alterna-tive methods. Furthermore, the chance-constrainedGP model can be formulated within a standard linearprogramming (LP) framework. Thus, it can besolved using a variety of inexpensive and easily acces-sible commercial codes such as LINDO (1984). Thisfeature of chance-constrained GP would not requireextensive computer programming efforts that, other-wise, might have been needed by some generat-ing techniques, such as the multiobjective simplexmethod.

Prior to developing the model, we make the fol-lowing underlying assumptions.

1. The term of shipping agreement is based on exworks (EXW). The term ex-works stipulates thatthe quoted purchasing price applies only at thepoint of origin (see, e.g., Coyle et al., 1988).Hence, the buyer (consignee) is fully responsiblefor all of the costs and risks involved in shippinggoods from the origin (the door of suppliers) tothe final destination (the door of a buyers com-pany). This assumption is necessary to make themodel more useful for other shipping optionsbecause other terms of shipping agreements suchas F.O.B. (free on board) and C.I.F. (cost, insur-ance, freight) are subsets of EXW.2. Intermodal transfers are always online transfers(moving freight between transportation modes ofthe same company) rather than interline transfers(between two different companies).3. Freight rates are proportional to shipment sizes.

4. Transit time of the mode is proportional to thedistance traveled by the mode.5. There are no differing load and size restrictionsfor inland road and rail transport in foreigncountries.6. Consolidated shipments (e.g., TL or CL ship-ments) imply containerized shipments.7. For containerization, only the 20 x 8 x 8-footcontainer, which is the most prominent containerin use today, is considered because it can be car-ried out by both air and surface transportation.For example, it is very difficult to insert a larger40 x 8 x 8-foot container into even a Boeing747 air freight (Mahoney, 1985).8. All the trucks considered in this study are 40x 8 x 8-foot trailers with 2,560 cubic feet ofspace.9. Distribution centers in an importing country are


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Chance-constrained goal programming 355break-bulk terminals which separate consoli-dated shipments. Consequently, when there isonly one consignee (customer), the distributioncenter is excluded from the international distri-bution channel because it is not necessary tobreak bulk.10. All the importing ports considered in this studyhave FTZs. This assumption makes sense to usbecause at least 91 ports in the U.S. have theFTZs, as of February 1984.

Within the aforementioned model framework,the final model formulation is presented in the Ap-pendix.

4. MODEL APPLICATION

To illustrate how the proposed model works, weapply the model to a hypothetical intermodal choiceproblem that may occur in typical international dis-tribution operations.4.1 Background of the illustrative problem

A multinational firm located in Needham, Massa-chusetts- high-tech belt area around Route 128 ofBoston-manufactures and sells personal computers(PCs). Recently, increasing competition from FarEastern countries coupled with rising labor costs inthe New England area forced the company to changeits product line. Rather than manufacturing all thecomponents/parts (e.g., computer chips, video mon-itors, and hard disks) for the PCs, the company de-cided to explore the possibility of importing thesehigh quality components/parts from some Japanesesuppliers at cheaper prices. Particularly, based onthe past sales record, the company estimated that1,200 units of video monitors would be neededwithin the next 30 days. The company also figuredthat three Japanese suppliers with different locationswere ready to provide a needed number of the moni-tors. The locations and current production capacityof these suppliers are as follows:

1. Supplier 1 is located in Kobe, Japan, with theproduction capacity of 500 units of the monitors.

2. Supplier 2 is located in Osaka, Japan, with theproduction capacity of 400 units of the monitors.

3. Supplier 3 is located in Kyoto, Japan, with theproduction capacity of 300 units of the monitors.However, the executive group of the companyworried that high distribution costs and long lead-

time, resulting from the international distributionchannel, might offset cost savings gained throughthe inexpensive international sourcing. So, the logis-tics division of the company initiated a comprehen-sive study of the companys international distribu-tion. After the study, the distribution manager foundthree major issues facing the company: (a) How tochoose and combine transportation modes whenshipping the monitors from the Japanese suppliersto the U.S. manufacturing plant? (b) How to selectexporting/importing ports? (c) How to utilize aFTZ?

Prior to further analysis of these issues, the distri-bution manager identified the potential productflows in the international distribution network (seeFig. 3). He also prepared a list of key factors whichgreatly influence the international intermodal choiceproblem (see Fig. 4). Then, in consultation with afreight forwarder, he collected data pertinent to theproblem. The volume, weight, value (purchasingprice), and unit inventory carrying charge of eachmonitor are summarized as follows:1. Volume of the monitor - 2 cubic feet per unit.2. Weight of the monitor - 5 kilograms per unit.3. Value (purchasing price) of the monitor - $100 perunit.4. Unit inventory carrying charge of the monitor-1%.

Transportation, consolidation, packaging, load-ing, and unloading costs associated with the variousmodes are given in Tables 2, 3, and 4. These tables

Fig. 3. Alternative international routes.


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Cost Factorssize/type/value orfreightfreight rateshwlng route(distance)speed/typeof the modeConsolldatlon(LTLvsTLor LCL v-3 CL)

ervlce Factorstranslt timeIntermodalcompatlbllityJust-In-Timerequirementloadlng/unloadlng

Risk Factorsdamage/lossmodeavallabilltyegulpmentavallabllltyclaimsspeed/typeof the modelabor strikes

lnternatlonalFactor;

documentationcustoms dutyForeign TradeZonefrelghtforwarderforeignregulationlicensereowrement

Modal CholCeand f-11xtruckrail

water (barge/ocean carrier)airPIggybackflshybackblrdyback

t

Port Selectionlocatlonfacllltyweatheroroxlmlty tolocaldlstrlbutloncenters

t

transshipmentquota opening

status of US

1I International Intermodalism I

Fig. 4. Key factors of international intermodalism.

Table 2. Export distribution cost estimation(in $/cubic foot) in JapanFreight Charges in Japan

Truck (LTL) Truck (TL) Rail (CL)Kobe to TokyoOsaka to TokyoKyoto to TokyoKobe to NagoyaOsaka to NagoyaKyoto to NagoyaNagoya toYokohama

5.00 -4.90 -4.10 - -2.00 - -1.95 - -1.80 - -1.90 1.20

Packaging and Handling Costsin JapanTruck (LTL) Truck (TL) Rail (CL)

Export PackagingStorage andConsolidation atNagoyaLoading andUnloading atYokohamaLoading andUnloading atTokyoLoss and Damage

3.50 2.50 3.20

- 1.00 1.10

2.00 3.00

2.500.20 0.10 0.30

Table 3. Ocean distribution cost estimation(in $/cubic foot)Ocean Freight Charges(including insurance)

Water AirTokyo to New York 100Yokohama to San Francisco 6.00Yokohama to New Orleans(through Panama) 6.30 -Yokohama to Boston 6.40

Import StorageandHandling CostsWater Air

Unloading and Loading at New YorkUnloading and Loading at - 4.00

San FranciscoUnloading and Loading atNew OrleansUnloading and Loading at BostonFTi! Storage at New YorkFTZ Storage at San FranciscoFTZ Storage at New OrleansFTZ Storage at BostonUSA Customs DutyUSA Internal Revenue TaxImport Documentation andLicense FeeWharfage Charge at the SeaportAirport-Usage Charge

5.00 -4.00 -4.80 -0.30+0.20* -0.15. -0.25* -2.50 2.501.20 1.201.10 3.000.50 -0.75

*All FTZ storage rates are based on daily storagecharges.356


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Chance-constrained goal programming 357Table 4. Import distribution cost estimation (in %/cubic foot) in the United States

Freight Charges in U.S.Truck (LTL) Truck (TL) Piggyback Fishyback Birdyback

NewYork to Needham 4 - - 25San Francisco to Needham - 30 20 - 90New Orleans to Needham - 15 10 7 50Local Delivery fromBoston Seaport to Needham - 2.50 - -All the freight charges include local delivery charges, which includes costs of loading and unloading.

also provide information about other associatedcosts including insurance, documentation, import-license fee, customs duty, storage, and wharfagecharges.

Estimates of average transit times along withtransit time variability for the various modes aregiven in Tables 5, 6, and 7.

Based on the analysis of factors and data, thedistribution manager developed two major transpor-tation strategies:

Direct (LTL) shipments from the Japanese suppli-ers to an exporting port (e.g., Tokyo Narita air-port) via trucks and overseas shipments from theexporting port to an importing port (e.g., NewYork Kennedy airport) via air and finally domes-tic shipments from the importing port to the com-panys plant in Needham via trucks or combina-tions of other modes such as birdybacks.Consolidated (TL or CL) shipments from the Jap-anese suppliers via trucks or piggybacks, andoverseas shipments from the exporting port (e.g.,Yokohama seaport) to an importing port (e.g.,San Francisco seaport) via ocean carriers and fi-nally domestic shipments from the importing portto the companys plant via trucks or combinationsof other modes.

These strategies can be further complicated bytaking into account the usage of a FTZ and variousinternational shipping channels (see Fig. 5). The SUC-cess of these strategies hinges on how fully the fol-lowing goals of the company can be achieved.1. Minimize all the distribution costs involved in in-

ternational intermodalism.2. Minimize delay of shipments, that is, minimizetransit times to prevent stockout situations.3. Minimize in-transit inventories at the consolida-

tion center, exporting/importing ports, and FTZs.4. Forbid early shipments to the fullest extent in or-der to satisfy the JIT manufacturing requirement.

4.2. Model test and resultsThe base-line model using the hypothetical datalisted in Tables 2 through 7 resulted in a mixed inte-ger chance-constrained GP problem with 26 con-straints and 37 variables, which include 29 zero-oneinteger variables. The model was tested on theVAX-l l/785 system. To solve the model, the ZOOMversion of XMP mathematical programming (Mars-ten, 1981) was used. For an experimental purpose,the model was run 10 times by altering model param-eters and reassigning goal weights. The model solu-tion required only 0.53 through 0.94 ss of CPU time.

Table 5. Export transit time estimation (hours) in JapanAverage Transit Timeand Transit Time Variability

Truck (LTL)Truck

(TL) Rail (CL)Kobe to Tokyoa 5.00 (2.30) -Osaka to Tokyoa 4.50 (2.00)Kyoto to Tokyo 4.30 (1.30) - -Kobe to Nagoyab 25.00 (3.00) -Osaka to Nagoyab 24.50 (2.00) - -Kyoto to Nagoyab 24.30 (1.00)Nagoya to Yokohama - 3.00 (1.00) 4.00 (3.00)

Transit times include loading/unloading and waiting time at the Tokyo(Narita) international airport.bTransit times include loading/unloading, consolidation, and storage timeat the Nagoya consolidation terminal.Transit time includes loading/unloading and waiting time at the Yokohamaseaport.Numbers in parentheses represent transit time variability.


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358 HTable 6. Ocean transit time estimation (hours)

Tokyo to New York 15 (2)Yokohama to San Francisco 720 (120) -Yokohama to New Orleans 1080 (168) -Yokohama to Boston 1200 (240) -

Numbers in parentheses represent time variability.Transit time includes loading/unloading and waiting timeat the port. Transit time variability includes unexpecteddelay at the port due to labor strikes or severe weatherconditions.

First, we carried out sensitivity analyses to examinethe response of model solutions to changes of themodel parameters such as freight rates, inventory car-rying charges, other related distribution costs, transittimes, and transit-time variability. When we supposedsubstantial (e.g., 100%) increases in distribution costsand then modified the related parameters such asfreight rates, inventory carrying charges, packaging,handling and storage costs, the model test revealed nochange in the base-line solution shown in Table 8. Fur-ther, we tested the model with dramatic changes (e.g.,100% increases) in either transit times or their vari-ability. The model solution still remained the same.Therefore, we can conclude that the model solutionwas somewhat robust to even drastic changes incosts, time, and variability.

In addition, we conducted sensitivity analyses ofgoal weights (i.e., relative importance of goals) toexplore the response of model solutions to changesof the companys business policy (e.g., cost-containment, JIT, or consistent service). When thecompany heavily emphasized the cost-cutting policy,the model solution is no different from the resultshown in Table 8. This test was actually done byassigning a three times heavier weight for the goal ofcost-minimization (i.e., W, = 3) than other goalweights. By the same token, to evaluate the robust-ness of the consistent delivery policy, we assigned athree times heavier weight for the goal of minimumtransit time variability (i.e., W,+ = 3) than othergoal weights. We still obtained the same result. How-ever, when the prevention of early shipments wasconsidered much more important than cost reductionor service consistency, the model resulted in a differ-ent solution summarized in Table 9.

MI N

Average Transit Timeand Transit Time

VariabilityWater Air

Table 7. Import transit time estimation (hours)

Table 9 suggests that a slower route throughocean was chosen over a faster route through airbecause the company might decide that early ship-ments were more undesirable than late shipments.Such a situation may occur when the company pre-dicts a substantial price increase of the importeditems in the near future or a temporary decrease indemand requirements. Specifically, Table 9 showsthat the company may allow a minor shipping delayof about 64 h.

From Table 8, we found that faster modes suchas LTL truck, air, and piggyback were chosen overslower modes. This result could be explained in twoways. First, faster modes are not necessarily moreexpensive than slower modes because faster modescan save a substantial amount of in-transit carryingcosts, thereby reducing total distribution costs byspeedy and often safer deliveries. Second, early ship-ments resulting from faster deliveries can be offsetby a lengthy stay in a FTZ. To be specific, Table 8indicates that the imported monitors should bestored in the New York FTZ for approximately 28days so that the company can not only delay thepayment of customs duty until the monitors leavethe zone, but also deliver the monitors just when thecompany needs them.

Finally, we investigated the response of model so-lutions to simultaneous changes of model parametersand goal weights. Once again, changes of both modelparameters and goal weights associated with transittimes resulted in a different solution as shown inTable 10, whereas other changes produced the samesolution. The result shown in Table 10 is virtuallythe same as the one shown in Table 9 with the excep-tion of the length of shipping delay and distributioncosts. The increases in shipping delay and distribu-tion costs are due to changes in estimated transittimes that, in turn, affected total transit times as wellas in-transit inventory carrying costs. To sum up, themodal choice is greatly affected by the speed of amode rather than either the freight rate or thedelivery-time variability of a mode. More impor-tantly, the companys shifts in priority of goals hadmuch greater impact on the modal choice than para-metric changes of cost, time, and variability.

Average Transit Time and Transit Time VariabilityTruck (LTL) Truck (TL) Piggyback Fishyback Birdyback

New York to NeedhamSan Francisco to NeedhamNew Orleans to NeedhamLocal Delivery from

Boston Seaport to Needham

4 (1) - - 2 (I)- 144 (24) 192 (28) 7 (2)- 48 (12) 72 (24) 144 (48) 4 (1)- 1 (0.5) - -

Numbers in parentheses represent time variability.


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Fig. 5. Alternative distribution flow.

359hance-constrained goal programmingConsolidation Exporting Importing

cuut Epct eQd

5. CONCLUSION managers. Perhaps one of the most significant chal-lenges and opportunities may be international inter-

During the past decade, the rapid growth of modalism. Yet, an analytical study dealing with in-U.S.-based multinational firms has revolutionally ternational intermodalism is almost nonexistent upchanged the current distribution concept from do- until today. This article has made an attempt to initi-mestic to international. The transfer from domestic ate such an analytical study by developing a chance-to international distribution provides a new set of constrained GP model that was designed to evaluatechallenges and opportunities for many distribution various distribution strategies with different modal

Table 8. The result of a baseline modelDistribution Channels(1) (2) (3)Kobe Osaka Kyoto

J J 1

Chosen Modes

All LTL trucks

Chosen Shipping Options

Direct and separateshipments

Nonconsolidated andseparate shipments

New York Airportt f +Usage of the New York Total length of stay at the New York FTZ is 669 h (approximately 28

i \ 1 days)Cu/omsOfr I j LTL trucks for channel (l), (2), and (3) Nonconsoiidated and

separate shipments

NeedhamTotal distribution cost = $342,124Total transit time variability = 14.6 h

For the initial run, equal weights of WY = W; = W; = W; = 1 were assigned, presuming thatthe company equally emphasizes the goals of minimum cost, on-time delivery, and consistent delivery.


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360 H. MI NTable 9. The model result (with emphasis on on-time delivery)

Distribution Channels(1) (2) (3)Kobe Osaka Kyoto

Chosen Modes

All LTL trucks

Chosen Shipping Options

Indirect and separate shipments

Center

IYokohama Seaport

San Farncisco Seaport

Customs OfficeINeedham

! TL trucksI Ocean carrier Consolidated shipmentsConsolidated shipmentsTL birdyback Consolidated shipments

Total distribution cost = $1,182,030Total transit time variability = 129 hFor this run, different weights of IV: = 1, W; = 3, W: = 2, I+: = 1 were assigned toreflect the relative importance of the on-time delivery goal.The FTZ was not used due to a shipping delay of 64 h.

Table 10. The model result (with changes in transit times and strictly forbidden early shipments)Distribution Channels(1) (2) (3)Kobe Osaka Kyoto

Chosen Modes Chosen Shipping Options

I I INagoya ConsolidationCenterJ

All LTL trucks Indirect and separate shipments

Yokohama Seaport

ISan Francisco Seaport1Customs Office

Needham 1

TL trucks

! Ocean carrierTL birdybackConsolidated shipments

Consolidated shipments

Consolidated shipments

Total distribution cost = $2,087,620Total transit time variability = 129 hFor this run, different weights of WI = 1, W; = 6, I+; = 2, W; = I were assigned and allthe estimated transit times were increased by 100%.The FTZ was not used due to a shipping delay of 36 d and 4 h.


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Chance-constrained goal programming 361combinations, logistics channels, and service require-ments in uncertain (stochastic) environments. Al-though the model was applied to solve the hypotheti-cal intermodal choice problem associated withimporting, it has the capability to handle both im-porting (foreign sourcing) and exporting problemsbecause exporting can be considered as simply a re-verse flow of importing. Furthermore, consideringthe cost and complexity of necessary hardware andsoftware, we have formulated the model in such away that it can be easily solved by standard commer-cial software packages within a reasonable amountof CPU time. For instance, in order to overcome thecomputational difficulty arising from the nonlinearinteger formulation, we used the deterministic equiv-alent form of the chance constraint (Charnes andCooper, 1963) that did not require the nonlinear de-cision variables.

Future research, however, is needed to refine thesuggested model by taking into account foreign regu-latory requirements and the option of a landbridgewhere foreign cargo crosses a country en route toanother country (see, e.g., Stock and Lambert, 1987,for an idea of landbridges).

REFERENCESAnderson D. L. (1984) international logistics strategies for

the eighties. Proceedi ngs of the Tw enty-Second Annu alConference of the Nat ional Council of Physical Dist ri -buti on M anagement. Oak Brook, IL, pp. 355-375.

Bender P. S. (198Sa) Logistics system design. In J. F. Robe-son and R. G. House (Eds.). The Distr i bution Hand-book, pp. 143-224. TheFreePress, New York.

Bender P. S. (1985b) The international dimension of physi-cal distribution management. In J. F. Robeson and R.G. House (Eds.), The Di str ibution Handbook. pp. 777-814. The Free Press, New York.

Charnes A. and Cooper W. W. (1963) Deterministic equiv-alents for optimizing and satisficing under chance con-straints. Ops Res., 11, 18-39.

Cohon J. L. (1978) M ulti objective Programming and Pian-ning. Academic Press, New York.

Cox R. M. and Van Tassel K. G. (1985) The ro le of packag-ing in physical distribution. In J. F: Robeson and R. G.House (Eds.) The Di str ibution Handbook, pp. 737-773.The Free Press, New York.

Coyle J. J., Bardi E. J., and Langley C. J. (1988) TheM anagement of Business Logi sti cs, 4th ed. West Pub-lishing Company, St. Paul, MN.

Foster T. A. (1981) Domestic intermodalism: Radicalchange, rapid progress. Distr ibut ion, 80(11), 34-38.

Harrington L. H. (1983) Plugging into world market. Traf-fi c M gmnt., 22(10), 31-38.

How PMs are going global. (July 1987) Purchasing World,63-69.

Leenders M. R., Fearon H. F., and England W. B. (1989)Purchasing and M aterials M anagement, 9th ed. RichardD. Irwin, Homewood, IL.

Lieb R. C. and Millen R. A. (1988) JIT and corporatetransportation requirements. Trans. J., 27(3), 5-10.Mahoney J. H. (1985) Intermodal Freight Transportation.

EN0 Foundation for Transportation, Inc., Westport,CT.

Marsten R. E. (1981) The design of the XMP linear pro-gramming library. Trans. Mat h. Softw are, 7, 481-497.

Osswald W. C. (1985) lntermodalism as an alternative tech-nology. Proceedings of the Tw enty- thi rd A nnual Con-ference of the Council of Logi sti cs M anagement. OakBrook, IL, pp. 295-303.

Schary P. B. (1984) Logi sti c Decision s: Text and Cases.The Dryden Press, New York.

Schrage L. (1984) Linear, Integer and Quadratic Program-ming wi th LIN DO: Users M anual. Scientific Press,Palo Alto, CA.

Stock J. R. and Lambert D. M. (1987) Strategic LogisticsM anagement, 2nd ed. Richard D. Irwin, Inc., Home-wood, IL.

Tansuhaj P. S. and Jackson G. C. (1989) Foreign tradezones: A comparative analysis of users and non-users.J. Bus. Log., 10(l), 15-30.

Wynne A. J. (1978) M ult i cr iter ia Opti mizati on wi th Sepa-rabl e and Chance-constrai ned Goal Programm i ng. Un-published PhD dissertation, University of Nebraska,Lincoln, NE.

Zeleny M. (1982) Multiple Criteria Decision Making.McGraw-Hill. New York.

APPENDIX

A.1. Index setsI , J Set of all nodesK Set of all transportation modes01 Set of all consignorsCJ Set of consolidation centersEP Set of exporting portsPF Set of importing ports with FTZsSJ Set of all consigneesLT Set of LTL trucksFT Set of consolidated modes

uT/ kV


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362 H. MI N6 Negative deviational variable that represents the de-gree (in hours) of early arrival of shipments4 Positive deviational variable that represents thelength (in hours) of a shipping delayd, Positive deviational variable that represents the de-gree (in hours) of transit time variability

A.4. FormulationMinimize Z = W,+d,+ + W-d,-

+ W2+dZ+ + W3+di+ 64.1)

Subject to

CCC(U.S,,,(F,,+H,,,+C,,,)+T,,,RP.S,,,)rel ,e, ICAx,,, + c c c S,,, G, Z, - d,- = 0

4CEP /fPf ,e* (8.2)

Prob. i.c c c 7YtX,,X d2- - dz = B] h (Y, (A.3)IE/ IEJ kEKwhere an element o is a statistical significance level that is aprobability measure of the extent to which the violation ofconstraint (A.3) is allowed. That is, it is not strictly requiredthat constraint (A.3) always holds, but constraint (A.3) willbe satisfied if it holds with a prescribed probability of o.If only the right-hand side value, B, of constraint (A.3)is uncertain and normally distributed, the deterministicequivalent form of constraint (A.3) will become (Charnesand Cooper, 1963):

where E(B) = expected value(mean) of random value B;var(B) = variance of random value B; z,, = : score valueof standard normal variable with an area 01.

c c c v,,:,I X,, - A+ = 0,E, ,tJ kEli

I E OIk E L7

x1*, - c x,, = 0, i+h+jrn6CK i E 01h E EPUCJj E EPUPFkELT

i f p f jp E EP

(A.4)(A.5)

(A.6)

(A.7)

c X,,, - N Y = 0, jeEP,EO, kELT1 X,,:,,- N(1 - Y) = 0, j CJ!EOl keLT

,gFZ, 6, (A.ll)

64.8)

(A.9)

(A.lO)

(A.12)

The objective function (A.l) minimizes the weightedsum of deviations from the lowest total distribution cost,targeted on-time (JIT) requirement and the lowest transit-time variability. Constraints (A.2) through (A.4) are goalconstraints. Constraint (A.2) minimizes total distributioncosts including handling, storage, and in-transit inventorycarrying costs. Constraint (A.3) states that, given the pre-scribed significance level of Q, the manager is willing tohave the on-time service requirement unsatisfied at most(I - a) proportion of the time. The reason is that, withoutsome degree of uncertainty, the manager cannot estimatethe desired lead time that may be affected by a variety ofuncertain events such as unexpected changes in the demandlevel, poor weather, and labor strikes. Also, it is noted thattwo-side goals rather than one-side goal are set to preventboth early and late shipments because on-time shipmentsare crucial for the success of JIT manufacturing operations.Constraint (A.4) minimizes transit-time variability. Con-straint sets (A.5) through (A.12) are system (feasibility)constraints. Specifically, constraint set (A.5) insures thatevery shipment should be picked up from every consignor.Constraint set (A.6) assures that any shipments leaving theconsignor must be sent to either an exporting port or aconsolidation center prior to the importing process. Con-straint set (A.7) represents flow-continuity for the consoli-dated transshipment process, that is, any shipments leavingthe consolidation center should be sent to an exporting portand then to an importing port via compatible modes. Con-straint set (A.8) represents flow continuity for the import-ing process, that is, any shipments leaving an exportingport should be delivered to an importing port and then to aconsignee via compatible modes. Constraint sets (A.9) and(A.lO) consider two different shipping options: direct orconsolidation. If consolidation is not needed, only con-straint set (A.9) holds while constraint set (A.lO) does nothold. If consolidation is required, only constraint set (A. 10)holds while constraint set (A.9) does not hold. Constraint(A. 11) counts the total length of stay of imported goods atthe FTZ area. Constraint set (A.12) is introduced to nullifyconstraint (A. 1 ), when there is a shipping delay.

min h.-international intermodal choices via chance-constrained

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