A Framework for Designing Effcient Value Chain Networks

Int. J. Production Economics 62 (1999) 133}144

A framework for designing e$cient value chain networks

Srinivas Talluri!,*, R.C. Baker", Joseph Sarkis#

! Department of Information Systems and Sciences, Samuel J. Silberman College of Business Administration, Fairleigh Dickinson University,1000 River Road, Teaneck, NJ 07666, USA

" Department of Information Systems and Management Sciences, Box d 19437, The University of Texas at Arlington, Arlington,TX 76019, USA

# Graduate School of Management, Clark University, 950 Main Street, Worcester, MA 01610, USA

Abstract

Strategic interorganizational networks aid organizations in gaining competitive advantages and improving productione$ciencies. Network organizations, virtual corporations, and value-adding partnerships are envisioned by many expertsas the epitome of interorganizational networks for the 21st century. These multi-organizational structures are viewed asa solution for rapid introduction of products while maintaining high quality and minimal costs. One common key issue indesigning these new forms of organizations is the partner selection process. The business processes, owned byorganizational partners, must be e$cient both individually and as a collective group. This paper proposes a two-phasequantitative framework to aid the decision making process in e!ectively selecting an e$cient and a compatible set ofpartners. Phase 1 identi"es e$cient candidates for each type of business process (e.g. design, manufacturing, distribution,etc.) utilizing data envelopment analysis. Phase 2 involves the execution of an integer goal programming model todetermine the best portfolio of e$cient partners based on a number of compatibility objectives. Model application andinsights are evident through an illustrative example. ( 1999 Elsevier Science B.V. All rights reserved.

Keywords: Value chain networks; Data envelopment analysis; Goal programming

1. Background

Product life cycles for most products are becom-ing increasingly shorter. Customers are becomingmore diverse in their demands, putting more pres-sure on product and service industries to respondto these demands. Manufacturers are constantlyworking towards meeting and balancing cus-tomer oriented performance measures such as high

*Corresponding author. Tel.: #1 201-692-7285; fax: #1 201-692-7219; e-mail: [email protected].

product quality, short lead times, high productvariety, and low cost. It is a monumental task forlarge or small organizations to accomplish all theaforementioned goals in a timely and e$cient man-ner. Large organizations are often very complexand slow to move, while small organizations su!erfrom a scarcity of resources. Network organiza-tions (NOs), virtual corporations (VCs), and value-adding partnerships (VAPs) are envisioned bymany experts as the solution for rapid introductionof a variety of products while maintaining highquality and low costs [1}6]. In this paper, we

0925-5273/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved.PII: S 0 9 2 5 - 5 2 7 3 ( 9 8 ) 0 0 2 2 5 - 4

collectively refer to NOs, VCs, and VAPs as valuechain networks (VCNs).

Snow and Miles [6] have illustrated three typesof network organizations: internal, stable, and dy-namic. In an internal network, "rms own most oftheir assets and have limited exposure to outsourc-ing. A stable network organization engages ina moderate level of outsourcing. Usually, in thistype of network, a set of vendors support a `leada"rm. Dynamic networks are formed by a group ofindependent companies. The lead "rm, actingsomewhat as a broker, identi"es potential partnerswho own a large or sometimes the entire portion ofthe assets in the network. For example, at GaloobToys, a handful of key executives select potentialpartners to design, manufacture, and sell children'stoys. Thus, Galoob acts as broker in forming ane!ective VCN of highly e$cient partners.

VCs are very similar to NOs. They are an al-liance of independent business processes or enter-prises each contributing `core competenciesa inareas such as design, manufacturing, and distribu-tion to the corporation [1}3,5,7,8]. VCs are formedin the event of a market opportunity and are dis-solved when the opportunity passes. Similar toNOs, they do not own any of the individual busi-ness processes that design, produce, and market theproduct. However, the VCs always indulge in tem-porary relationships to take advantage of a speci"cmarket opportunity. For example, Apple Com-puter and Sony Corporation engaged in a similartemporary alliance to manufacture PowerBooknotebooks. TelePad Corporation collaboratedwith more than two dozen partners in bringing itspen-based computer to market. Similarly, IBM,Apple Computer, and Motorola have becomeinvolved in an inter"rm alliance to develop anoperating system and microprocessor for a newgeneration of computers.

According to Johnston and Lawrence [4], theVAPs are à set of independent companies thatwork closely together to manage the #ow of goodsand services along the entire value-added chaina.The primary di!erence between VAPs and VCs isthat, the "rms in a VAP develop lasting ties withothers in the value-added chain. For example,Japanese auto companies are a typical form ofVAPs, producing only about 20% of the value of

their automobiles. Similarly, Chrysler's resurgencemay be attributed to the creation of VAPs with itssuppliers. Other concepts such as extended enter-prises can also be categorized into VAPs [9].

A key factor, emphasized by researchers, in form-ing these new organizations is the selection of agile,competent, and compatible partners [3,6,7,10}13].Although the issues of partnerships are discussed toa great extent in the literature, few, if any, formaldecision making models have been developed fore!ective partner selection process. It is evident thatwithout highly e!ective partners, these VCNs can-not work e$ciently. Therefore, not only is therea need for strong compatibility among the partici-pants, but more importantly they need to be verye$cient in what they contribute individually and asa group. The partner selection process is thereforecritical in the formation of a VCN.

2. Problem complexity and solution technique

As discussed above, one of the key issues encoun-tered in the formation of a VCN is the selection ofpartners. For example, consider a scenario inwhich a VCN with three types of business processesA, B, and C is to be formed. If there are 10potential candidates for the type A process, 10potential candidates for the type B process, and8 potential candidates for the type C businessprocess, then the total number of combinationsunder consideration is 800. Optimally, all thesecombinations need to be evaluated and the mostdesirable one identi"ed. This process is by nomeans a trivial assignment. It can be an extremelytedious and time-consuming process. Moreover, itis very di$cult to incorporate into one decisionmodel both the internal decision variables for anal-ysis of candidates of a given process type, and theexternal (compatibility) analysis of candidates fordi!erent process types.

This paper proposes and introduces a two-stageddecision model for this problem environment.Phase 1 is a "ltering technique based on theinternal relationship decision variables of thecandidates. This technique identi"es è$cientacandidates for each type of business process,which allows for screening and eliminating of the

134 S. Talluri et al. /Int. J. Production Economics 62 (1999) 133}144

ine$cient candidates. This "ltration results in areduced set of possible combinations that areconsidered in Phase 2 of the analysis. A speci"cdata envelopment analysis (DEA) model referred toas the CCR (Charnes, Cooper, and Rhodes) model,developed by Charnes et al. [14], is applied inPhase 1. The CCR model is a fractional program-ming technique that identi"es e$cient candidatesby incorporating a range of internal activity andperformance measures into the model. Phase 2 util-izes an integer goal programming model, which isbased on external decision variables (compatibilitycriteria), for selecting the ultimate combination ofe$cient candidates to participate in the formationof the VCN.

The following section provides a brief introduc-tion to the CCR model, which is utilized in ourdecision making process.

3. The CCR model

Productivity models have traditionally beenused to measure e$ciencies of systems. The CCRmodel is a fractional programming technique thatevaluates the relative e$ciencies of homogeneousdecision making units (DMUs) in the presence ofmultiple input and output measures. For a givenDMU, this model maximizes the output-to-inputratio. The CCR model and family of other DEAmodels have been used primarily to compare thee$ciencies of schools, hospitals, shops, bankbranches, airlines, plants, and other areas wherethere is a relatively homogeneous set of units. Usingthe notation of Doyle and Green [15], the generale$ciency measure that is used by DEA can best besummarized by Eq. (1).

Eks"

+yO

syvky

+xIsxukx

(1)

where Eks

is the cross-e$ciency of DMU s, usingthe weights of `targeta DMU k, where the targetDMU is the unit whose e$ciency is to be evaluated,O

sythe amount of output y produced by DMU s,

Isx

the amount for input x used by DMU s, vky

theweight assigned to output y by DMU k and u

kxthe

weight assigned to input x by DMU k.

The CCR model maximizes the e$ciency valueof a target DMU k, from among a reference set ofDMUs s, by selecting the optimal weights asso-ciated with the input and output measures. Themaximum e$ciencies are constrained to 1. Theformulation is represented in expression (2).

Maximize Ekk"

+yO

kyvky

+xIkx

ukx

subject to

Eks)1 ∀DMU s, (2)

ukx

, vky*0.

This non-linear programming formulation (2) isequivalent to the following linear programmingformulation (3):

Maximize Ekk"+

y

Okyvky

subject to

Eks)1 ∀DMU s,

+x

Ikx

ukx"1, (3)

ukx

, vky*0.

The transformation is completed by constrainingthe denominator of the objective function from (2)to a value of 1. This is represented by the constraint+

xIkx

ukx"1.

The optimal objective function value E*kk

of for-mulation (3) provides the e$ciency of DMU k. IfE*kk"1, then it means that no other DMU is more

e$cient than DMU k for its selected weights. Thatis, E*

kk"1 has DMU k on the optimal frontier and

is not dominated by any other DMU. If E*kk(1

then DMU k does not lie on the optimal frontierand there is at least one other DMU that is moree$cient for the optimal set of weights determinedby Eq. (3). Formulation (3) is executed s times, oncefor each DMU.

4. The decision framework for VCN design

Fig. 1 depicts the phases and decision makingprocess involved in the formation of a VCN. The

S. Talluri et al. /Int. J. Production Economics 62 (1999) 133}144 135

Fig. 1. The framework for VCN design.

decision makers in this framework may be com-prised of upper level management and executivesacting as brokers. These brokers act as agents inselecting e$cient and compatible partners. Formore information on broker-lead dynamic net-works, see [6,16].

In the event of an identi"ed market opportunityfor a product, and given various environmentalfactors, the brokers are expected to respond bycreating a VCN and delivering the product at lowcost, high quality, and small lead times. The stagesin Fig. 1 are meant to represent a typical series ofdevelopment and implementation stages thata VCN would go through. The second stage, whichis the focus of this paper, is the analysis and deci-sion stage of VCN formation. After this selection

stage, a set of partners is identi"ed. In the initialsteps of the next phase, formalization of the rela-tionships is an immediate goal. The next steps inthis process will include some initial start-up opera-tions, ramping up design, production, and pilotstudies as necessary; full-#edged operations to ac-tually manufacture the products; and "nally thedelivery of the products to the market. Of course,a number of cyclical relationships may exist withinthe implementation phases as re"nements and in-cremental improvements are made to the productsand processes. Additional issues related to whethernew partners are selected and join in the processmay depend on product life cycle issues encoun-tered by the product family. The "nal stage, notdetailed in the diagram, is dissolution. Some VCN


characteristics include the relative impermanencyof the relationships. The VCN must be prepared todissolve, and plan to do so, once its market is nolonger viable. We shall now detail the decisionmaking process for the analysis and selection ofthe VCN.

4.1. Initial phase of the analysis and decision process

This phase is initiated by the brokers identifyingthe business processes types required to ful"lla market need. This step is followed by the identi-"cation of potential candidates for each businessprocess type. The input/output (I/O) measures foreach business process type are also identi"ed withinthis stage. These I/O measures should be in align-ment with the objectives, goals, policies, and pro-cedures of the VCN. The inputs should encompassany resources utilized by the business processes,and the outputs should include a range of perfor-mance and activity measures [17]. Data on all ofthe identi"ed I/O measures is then collected, andthe CCR model is used to evaluate all potentialcandidates for each process type.

Those enterprises identi"ed as e$cient candi-dates, with a relative e$ciency score of 1, areconsidered for further analysis. The ine$cientcandidates are dropped from further considerationbecause they are ine!ective even with their bestpossible weighting scheme. Some of the e$cientcandidates identi"ed by the CCR model may not begood overall performers. They may achieve a rela-tive e$ciency score of 1 by indulging in an inappro-priate or unrealistic weighting structure. Thesetypes of DMUs heavily weigh few inputs and out-puts that are most bene"cial to themselves, andcompletely ignore other inputs and outputs. Thesetypes of candidates are determined to be ineligibleto participate in a VCN. To aid in the di!erenti-ation of such candidates from good overall per-formers, we utilize cross-evaluation measures inour research.

Cross-evaluations [18] provide information onhow well a candidate is performing with respect tothe optimal CCR weights of other candidates of thesame process type. The cross-e$ciency is de"nedby expression (1). This information can be e!ec-

tively represented and aggregated into a matrix. Anelement in the ith row and jth column of sucha matrix represents the cross-e$ciency score ofcandidate j when using the optimal CCR weights oftarget candidate i. A candidate is considered a goodoverall performer if it achieves several high e$cien-cies along its column in this matrix. The columnmeans can be computed as an index to e!ectivelydiscriminate between good overall performers andpoor performers. In addition, there may be ine$c-ient candidates with relative e$ciency scores closeto 1 that did not pass the initial "ltering process. Itis advisable to test such borderline candidates inthe cross-evaluation process because they may havehigh column means. If an ine$cient candidate witha high column mean occurs, the decision to drop orinclude such candidates from further analysis is leftto the decision maker. Usually, those candidatesthat result in high mean cross-e$ciency scores arethe ones indulging in good operating practices.These are the types of candidates that are desiredwhen forming a VCN.

The CCR model with the cross-evaluations, re-duces the complexity of the problem by minimizingthe number of combinations that are to be analyzedin the "nal phase of the analysis and decision pro-cess, the multi-criteria decision making (MCDM)phase. Also, the candidates considered in the nextphase of the analysis are e$cient in an overallsense, i.e., they are indulging in good overall practi-ces, which is a key for participating in a VCN.

4.2. The MCDM phase of the analysis and decisionprocess

An integer goal programming model is used toselect an e!ective combination of candidates toparticipate in the formation of a VCN. The combi-nations identi"ed in the earlier phase are evaluatedwith respect to compatibility criteria. Some ofthe compatibility issues addressed in the literatureconcerning the linkages among the participatingbusiness processes are: e!ective communicationnetworks, cultural compatibility, frequent interac-tions, trust, and goals in alignment with the visionof the enterprise [11,13]. By incorporating someof these factors into the decision making process,


selection of an e!ective combination of partners iscompleted, thereby insuring that the participatingcandidates are e$cient individually and as a group.In this research, we assume that the following goalshave been identi"ed by the brokers as important inthe formation of the VCN (this is just an exemplarygroup, other goals may be developed as well).

Goal 1: Minimizing the costs associated with therelationship formation. These may be technicalhardware and software costs, new equipment costs,new employee costs and other costs associated withthe formation of the linkage.

Goal 2: Minimizing the distances among the parti-cipating candidates. To maximize the frequency ofinteractions among participants, and in order torespond quickly to the changing needs of the cus-tomer, it would be preferable to have the participat-ing candidates geographically close to each other.This goal assists in improving the frequency ofinteractions and manages in maintaining lowertransportation costs.

Goal 3: Minimize the inception time of the <CN.The inception time is de"ned as the time taken fora VCN to be operational. To capture the marketopportunity at the earliest, it is necessary to haverelatively low inception times.

Goal 4: Maximize the cultural compatibilityamong the participating candidates. Culture is one ofthe most vital ingredients for a successful partner-ship. It in#uences the behavior, values, and goals ofthe employees. An empowered work force, TotalQuality Management, and concurrency are some ofthe critical attributes used in evaluating culture[20].

Of the four goals mentioned above, the tangibleones (costs, distances and inception times) can bemeasured in quantitative units. The intangible one(culture) can be measured on a numerical scale of1 to 10 units, where 1 and 10 represent low and highcultural compatibility, respectively.

Goal programming (GP) was "rst introduced byCharnes and Cooper [21] for evaluating infeasiblelinear programming problems. The technique hasbeen expanded to deal with a variety of problems inareas such as "nance, marketing, production plann-ing, corporate planning, medicare planning, etc.; formore information on GP, see [19]. Although goalprogramming re#ects complex reality and allows

for multidimensionality of the objective function, ithas some limitations. Primarily, the decision makermust either set priorities to goals, which is di$cultto do, or assign weights to deviations which isusually a subjective exercise.

In this model formulation, we propose to deter-mine cardinal relationships among the compatibil-ity criteria by making the assumption of linearrelationships among them. Conversion factors canbe determined between cost ($) and the remainingthree goals; frequency of personal interactions(distance in miles used as a surrogate measure),inception time (days), and cultural compatibility(units). These conversion factors are used asweights in the objective function.

The conversion scale between cost ($) and dis-tance (miles) can be identi"ed by estimating the costincurred in covering a mile of distance. The rela-tionship between cost ($) and inception time (days)can be determined by estimating the cost of lostsales for each day of delay in the inception process.Finally, the association between cost ($) and cul-tural compatibility (units) can be determined byestimating the costs involved in empowering thework force (training programs) and implementingphilosophies such as Total Quality Management(TQM) to achieve a cultural compatibility of 10 (ona scale of 1}10).

Although the following binary GP formulation isproposed for three business process types and fourgoals, it is easily extensible to any number of pro-cesses and goals. The combination of enterprisesand organizations that minimizes the sum of theweighted deviations from the `besta goal compati-bility measure is selected as the VCN.

Minimize4+t/1

wtvt

subject to

+i

+j

+k

xijk"1,

+i

+j

+k

cijk

xijk!v

1"c

.*/,

+i

+j

+k

dijk

xijk!v

2"d

.*/,


+i

+j

+k

tijk

xijk!v

3"t

.*/,

+i

+j

+k

cijk

xijk#v

4"k

.!9,

xijk"0 or 1,

vt*0,

wherea is the total number of e$cient candidates of

business process type A.b is the total number of e$cient candidates of

business process type B.c is the total number of e$cient candidates of

business process type C.i"1 through a.j"1 through b.k"1 through c.xijk"1; implies that the combination of ith e$-

cient candidate of process type A, jth e$cient can-didate of process type B and kth e$cient candidateof process type C was selected for the VCN.

cijk

is the cost associated with the formation ofcombination ijk.

dijk

is the distance associated with combinationijk.

kijk

is the cultural compatibility unit for combi-nation ijk.

tijk

is the estimated inception time associatedwith combination ijk.

c.*/

is the cost bound derived from the minimumcost combination.

d.*/

is the distance bound derived from the min-imum distance combination.

t.*/

is the time bound derived from the minimuminception time combination.

k.!9

is the cultural bound derived from the max-imum cultural compatibility combination.

wt

is the weight derived from the conversionfactor for deviations from the goal target t.

vtis the deviation from the `besta goal compati-

bility measure for the goal target t.The solution to the integer goal programming

model identi"es an e!ective combination of e$-cient candidates to participate in the formation ofa VCN. The two stages of the analysis and decisionprocess, using hypothetical data, is illustrated in thefollowing sections.

5. Illustrative example

The following example illustrates the decisionprocess involving the formation of a VCN that isconsidering relationships to form an organizationcomprised of two processes, a supply process anda manufacturing process. In this example, sevensuppliers and seven manufacturers are consideredfor the analysis. Phase 1 of the analysis identi"esthe e$cient suppliers and manufacturers, andPhase 2 selects an e!ective supplier}manufacturercombination.

The supplier and manufacturer I/O measuresconsidered in Phase 1 of the analysis are:

Supplier inputs

1. Average operating costs/period (AOC) } Theseare the costs associated with equipment pur-chasing and maintenance, holding costs, ordercosts and other operating costs.

2. Number of employees (EMP) } The total num-ber of employees involved in the supply process.

Supplier outputs

1. Product quality (PQ) } The quality level of thesupplied product expressed as a percentage.

2. On-time deliveries/period (OTD) } The percent-age of on-time deliveries by the supplier.

Manufacturer inputs

1. Average operating costs/period (AOC) } Costsassociated with the manufacturing process suchas equipment costs, maintenance costs, orderprocessing costs, holding costs, etc.

2. Number of employees (EMP) } The number ofemployees involved in the manufacturing pro-cess.

Manufacturer outputs

1. Product options (PO) } The number of productoptions provided by the manufacturer.

2. Overall quality level (OQL) } The overall qual-ity level of all the product options expressed asa percentage.

3. Average throughput rate (ATR) } The averagenumber of units produced per unit time.


These inputs and outputs, whose values areshown in Tables 2 and 3, respectively, are notintended to be exhaustive, they simply providesome general measures to consider when evaluatingthe performance of the supply and manufacturingprocesses. Other performance measures such aswork-in-process (WIP) levels, utilization ratios,and di!erent types of #exibility measures can beincorporated into these models, depending on whatperformance measures the competitive environ-ment considers the òrder winnersa.

5.1. Phase 1 results and discussion

Of the seven suppliers considered, the CCRmodel identi"ed suppliers 2, 4, and 7 to be e$cientwith a relative e$ciency score of 1. The relativee$ciency scores of suppliers 1, 3, 5, and 6 are 0.83,0.73, 0.66, and 0.55, respectively. These suppliersare not considered for further analysis becausegiven the choice of their best possible weightingscheme they exhibited low relative e$ciency scores.These results are shown in Table 1.

The relatively e$cient suppliers (2, 4, and 7) arefurther investigated to examine whether they aregood overall performs. The matrix shown inTable 2, indicates that supplier 2 exhibited fairlyhigh cross-e$ciency scores of 1 and 0.87 withthe optimal CCR weights of suppliers 4 and 7,respectively. The cross-e$ciency mean score forsupplier 2 is 0.96 (column mean). Supplier 7 also

Table 1Input/output values and relative e$ciency scores of supplyorganizations

Supplier Inputs Outputs Relativee!. (h)

AOC ($) EMP (d) PQ (%) OTD (%)

1 50 000 30 0.95 0.80 0.832 45 000 20 0.99 0.95 1.003 60 000 35 1.00 0.75 0.734 40 000 30 0.95 0.83 1.005 65 000 45 0.96 0.90 0.666 80 000 40 0.98 0.90 0.557 50 000 18 0.98 0.98 1.00

Table 2Supplier cross-evaluations

S2 S4 S7

Target S2 1.00 0.77 1.00Target S4 1.00 1.00 0.91Target S7 0.87 0.50 1.00Mean score 0.96 0.76 0.97

exhibited high e$ciency scores of 1 and 0.91 withthe optimal weights of suppliers 2 and 4, respective-ly. The mean score for supplier 7 is 0.97. Supplier4 exhibited low e$ciency scores of 0.77 and 0.50with the optimal weights of suppliers 2 and 7,respectively. The mean score for supplier 4 is 0.76,which is signi"cantly low compared to the meanscores of suppliers 2 and 7. Thus, supplier 4 isa poor overall performer. Consequently, suppliers2 and 7 are not only considered to be relativelye$cient based on the CCR model results but also as`competitivelya e$cient when compared to otherrelatively e$cient suppliers. Supplier 4 is droppedout of further analysis, and suppliers 2 and 7 areconsidered for the next phase of the analysis.

Of the seven manufacturers considered, manu-facturers 1, 3, 4 and 6, shown in Table 3, wereidenti"ed by the CCR model to be e$cient withrelative e$ciency scores of 1. Manufacturers 2,5 and 7 were identi"ed to be ine$cient with relativee$ciency scores of 0.69, 0.81, and 0.82, respectively.These manufacturers are not considered for furtheranalysis for the same reason provided in the sup-plier analysis.

The relatively e$cient manufacturers are furtheranalyzed using the cross-evaluations shown inTable 4. It is evident from the matrix that manufac-turer 3 exhibited low relative e$ciency scores of0.71, 0.25, 0.82 with the optimal weights of manu-facturers 1, 4, and 6, respectively. Manufacturer 6also exhibited low relative e$ciency scores of 0.54,0.77, and 0.40 with the optimal weights of 1, 3, and4, respectively. The mean cross-e$ciency scores formanufacturers 3 and 6 are 0.69 and 0.68, respective-ly. These manufacturers are identi"ed as poor over-all performers, and are not considered for furtheranalysis. Manufacturer 1 exhibited fairly highrelative e$ciency scores of 0.95, 0.71, and 1 with


Table 3Input/output values and relative e$ciency scores of manufacturer organizations

Manufacturer Inputs Outputs RelativeE!. (h)

AOC ($) EMP (d) PO (d) ATR (units/sec) OQL (%)

1 90 000 37 6 0.067 0.99 1.002 120000 55 4 0.056 0.95 0.693 110000 35 2 0.045 0.99 1.004 95 000 35 8 0.050 0.97 1.005 110000 50 7 0.040 0.96 0.806 70 000 43 4 0.042 0.93 1.007 84 000 52 2 0.033 0.92 0.82

Table 4Manufacturer cross-evaluations

M1 M3 M4 M6

Target M1 1.00 0.71 0.79 0.54Target M3 0.95 1.00 0.98 0.77Target M4 0.71 0.25 1.00 0.40Target M6 1.00 0.82 1.00 1.00Mean score 0.91 0.69 0.94 0.68

the optimal weights of manufacturers 3, 4, and 6,respectively. Manufacturer 4 also exhibited highrelative e$ciency scores of 0.79, 0.98 and 1 withthe optimal weights of manufacturers 1, 3, and6 respectively. The mean cross-e$ciency scoresfor manufacturers 1 and 4 are 0.914 and 0.943,respectively. These two manufacturers are theones identi"ed as both relatively e$cient based onthe CCR model results and `competitivelya e$-cient when compared to other relatively e$cientmanufacturers.

Based on these results, the combinations S2}M1,S2}M4, S7}M1, and S7}M4 are considered for thenext phase, where `Sa stands for supplier and `Mastands for manufacturer.

5.2. Phase 2 results and discussion

This phase identi"es an e!ective supplier}manufacturer combination from the four possible

Table 5Supplier}manufacturer combination compatibility criteria

Combination Cost Distance Culture Time($) (miles) (d)

M2}S1 8000 500 8 30M2}S4 7000 800 3 15M7}S1 4000 1000 7 22M7}S4 5000 700 6 20

combinations resulting from Phase 1. Table 5shows the hypothetical data on the evaluating cri-teria used in the model. The integer goal program-ming model is solved by using the followingconversion factors.

5.2.1. Conversion factor between cost ($) anddistance (miles)

Consider the supplier}manufacturer combina-tion that is 500 miles apart. The cost for coveringthis distance is assumed to be $200. So the conver-sion factor between cost and distance is $0.4 permile per interaction. If the estimated number ofinteractions during the life of VCN is 20 then thetotal cost/mile is $8. Thus, deviation v

2is given

a weight of 8. Because of the highly variable costingstructures used in the transportation industry thiscost/mile would obviously vary for the four combi-nations. However, for the purpose of this examplewe assume this factor to be the same for all fourcombinations.


5.2.2. Conversion factor between cost ($) andinception time (days)

To derive this conversion factor, the expectedsales ($) of the VCN must be estimated and thisvalue should be divided by the estimated VCN lifespan. This ratio provides a dollar "gure of sales perday. For example, assume total sales are estimatedto be $180 000 for an estimated VCN life span of180 days. The ratio provides a conversion factor of$1000/day, which is considered to be the cost of lostsales for every day of delay in the inception processof the VCN. The value 1000 is used as the weightfor the deviation v

3.

5.2.3. Conversion factor between cost ($) andcultural compatibility (units)

The cultural compatibility of combinations isgiven a score of 1}10 based on the values of em-ployees, motivation to partner, and commitment topartnership. The costs associated in achievinga score of 10 units are estimated. These costs in-clude empowering the work force with trainingprograms, implementation of philosophies such asTotal Quality Management (TQM) and other pro-jects that improve the cultural compatibility of theparticipating business processes. For this example,if these costs are assumed to be $20 000 for a scoreof 10 units. Thus, the conversion factor is $2000 perunit of cultural compatibility. A weight of 2000 isused for the deviation v

4. Although an extensive

estimation process is required in deriving the con-version factors in a real world problem, they aremore objective than some of the other methodsutilized in solving GP problems.

The integer goal programming problem shownbelow was solved by using a commercial softwarepackage. The conversion factors derived above areused as weights to the deviations in the objectivefunction.

Minimize Z"v1#8v

2#1000v

3#2000v

4

subject to:

x21#x

24#x

71#x

74"1,

8000x21#7000x

24#4000x

71#5000x

74!v

1

"4000,

500x21#800x

24#1000x

71#700x

74!v

2"500,

30x21#15x

24#22x

71#20x

74!v

3"15,

8x21#3x

24#7x

71#6x

74#v

4"8,

x21"0 or 1,

x24"0 or 1,

x71"0 or 1,

x74"0 or 1,

v1, v

2, v

3, v

4*0.

The solution to the above problem was found tobe the combination S7}M4. This combination re-sulted in the minimum value for the objective func-tion (11 600). The basis variables in the solution arex74"1, v

1"1000, v

2"200, v

3"5, and v

4"2.

Thus, Supplier 7 and Manufacturer 4 are selectedfor participating in the VCN. In addition, postoptimality (sensitivity) analysis in Table 6 indicatesthat the current solution (S7}M4) remains optimalfor the following coe$cient ranges of the devi-ations:

3.34)w2)45,

300)w3)1760,

733.34)w4)3400.

For a value of w2

greater than 45 the moste!ective combination can be shown to be S2}M1,and for a value less than 3.34 the combinationS7}M1 should be selected. An increase of w

3over

1760 results in S2}M4 becoming the best combina-tion, and a decrease to below 300 results in S7}M1becoming the best combination. Likewise, a valueof w

4greater than 3400 results in S7}M1 becoming

Table 6Objective function coe$cient ranges in which the basis is un-changed

Variable Currentcoe!.

Allowableincrease

Allowabledecrease

v2

8 37 4.66v3

1000 760 700.00v4

2000 1400 1266.66


the most e!ective combination, and a value lessthan 733.34 results in S2}M4 becoming the bestchoice. This type of post optimality analysis, allowsthe decision maker forming the VCN to havea much better feel for the strength of the "nalselection. Also, these ranges indicate as to which ofthe estimated weights are most sensitive. This in-formation can be used by the decision makers inimproving the estimation process, as required.

6. Limitations

There are certain concerns that may arise froman actual application of this methodology. Onemajor concern deals with the initial "ltering pro-cess. If initial data is "ltered in an optimizationprocedure, then the solution to the problem may besub-optimal. This is also true for the proposedanalysis. In the initial screening process, some unitsthat are dropped out of the analysis due to ine$c-iency may in fact have better compatibility charac-teristics when analyzed in the subsequent phase. Toalleviate the severity of this problem, the borderlinecandidates could be considered in the cross-evalu-ations for possible inclusion in Phase 2 of theanalysis. The cuto! point for inclusion of thesecandidates in Phase 2 of the analysis is a subjectivedecision, which depends on the objectives, policies,and procedures of the VCN. A decision maker mustmake an astute decision in selecting such a cuto!point.

Another issue is that the actual determination ofwhich input and output factors to consider may bea substantially di$cult endeavor. The broker hasmuch responsibility in this area and must be wellaware of the market forces and other environ-mental factors to make sure that factors selected inthe evaluation process will meet the objectives ofthe VCN and the market.

7. Conclusions

E$cient VCNs are envisioned as the solution tomeet the constantly changing needs of the customerat low cost, high quality, small lead times and highvariety. Some of the critical issues in the formation

of the VCNs are addressed in this paper. A quantit-ative model is proposed to aid the decision makingprocess in the formation of an e$cient VCN. TheCCR model is utilized to identify the e$cient busi-ness processes, and a MCDM model is utilized toselect an e!ective combination of the e$cient busi-ness processes.

Further extensions such as restricting weights inthe initial "ltering process can be very e!ective indi!erentiating between good overall performersand poor performers. These weight restrictionsmust be in alignment with the objectives, policiesand procedures of the VCN. To make the initial"ltering process more robust, other I/O measuressuch as availability of advanced technologies and#exibility of the processes need to be incorporatedinto the evaluation process.

While the analysis in this paper is performedfrom the standpoint of brokers, it can also beperformed from the standpoint of a lead businessprocess. In such a situation, before becominginvolved in the formation of a VCN, the leadbusiness process must evaluate its e$ciencyrelative to other similar business processesand implement process improvement techniques tobecome e$cient, if necessary.

In the formation of the VCNs, there are otherissues to be considered such as VCN workers divid-ing their loyalty and responsibility between thisnew venture and their parent corporation, whichmay not be feasible in some types of networks. Also,the possibility of losing con"dential informationthrough the alliance channels is a key deterrent tothe e!ectiveness of these VCNs. In spite of all theseand other problems, many companies around theworld are becoming involved in such networks tocapture a speci"c market opportunity.

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