European Journal of Operational Research 207 (2010) 165–173

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European Journal of Operational Research

journal homepage: www.elsevier .com/locate /e jor

Production, Manufacturing and Logistics

Manufacturer cooperation in supplier development under risk

Srinivas Talluri a,*, Ram Narasimhan a, Wenming Chung b

a Department of Supply Chain Management, Eli Broad Graduate School of Management, Michigan State University, N370 Business Complex, East Lansing, MI 48824, United Statesb Information and Decision Sciences Department, College of Business Administration, Room 202, University of Texas at El Paso, United States

a r t i c l e i n f o

Article history:Received 15 May 2009Accepted 26 March 2010Available online 30 March 2010

Keywords:Supplier developmentSupply chain managementRisk managementManufacturer–supplier relationshipsQuadratic programming

0377-2217/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.ejor.2010.03.041

* Corresponding author. Tel.: +1 15173536381; faxE-mail addresses: talluri@msu.edu (S. Talluri), narasi

wchung2@utep.edu (W. Chung).

a b s t r a c t

Supplier development involves efforts undertaken by manufacturing firms to improve their suppliers’capabilities and performance. These improvement efforts can be targeted at a variety of areas such asquality management, product development, and cost reduction. Since supplier development requiresinvestments on the part of the manufacturer, it is important to optimally allocate investment dollarsamong multiple suppliers to minimize risk while maintaining an acceptable level of return. This paperpresents a set of optimization models that address this issue. We consider two scenarios: single-manu-facturer and multiple suppliers (SMMS) and two-manufacturer and multiple suppliers (TMMS). In theSMMS case, we suggest optimal investments in various suppliers by effectively considering risk andreturn. The TMMS case investigates whether manufacturers with differing capabilities could gain riskreduction benefits from cooperating with each other in supplier development. Through illustrative appli-cations, we identify conditions in which both cooperation and non-cooperation are beneficial for manu-facturers. Under conditions of cooperation, we propose optimal investments for manufacturers to achievehigh levels of risk reduction benefits.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

Manufacturing firms are incurring procurement costs associ-ated with raw materials and components in excess of 50–60% ofthe firm’s total revenue and this trend is expected to continue[9,25]. This phenomenon is resulting in increased dependency ofmanufacturing firms on their suppliers [16,25]. Since a firm’s sup-plier performance has a significant impact on many of its productdimensions, such as cost, quality and on-time delivery [19], manu-facturing firms are placing increasing emphasis on effectivelyworking with suppliers by sharing demand information, produc-tion schedules, and technical expertise [29]. However, it can be ar-gued that manufacturing firms would need to involve themselvesin suppliers’ operations to a greater extent when suppliers’ futurecapabilities will likely fail to meet their changing needs and expec-tations [16,17,20]. Activities undertaken by a manufacturing firmto improve its suppliers’ capabilities and performance falls underthe rubric of supplier development [14,15]. Supplier developmentinitiative can potentially lead to identifying suppliers for strategicpartnerships [4]. Supplier development is intended to improvesupplier process capability, delivery capability, product develop-ment capability, component quality and cost, which, in turn, lead

ll rights reserved.

: +1 15174321112.mh@msu.edu (R. Narasimhan),

to long-term benefits for the manufacturing firms [20]. Since sup-plier development requires firms to invest assets and resources insuppliers, it is a selective investment process [19,20].

Toyota, Honda, Nissan, Chrysler, Ford, General Motors, and Gen-eral Electric all have implemented supplier development programsto assist suppliers, which have resulted in quality improvementand cost reduction [6,10]. In essence, supplier development is astrategic initiative that requires long-term commitment from man-ufacturing firms to achieve desired outcomes. Due to its lack ofimmediate return, firms are often reluctant to invest in supplierdevelopment [19]. Additionally, when the relationship betweenthe manufacturing firm and a supplier is unsuccessful, the benefitsgained from supplier development may not be enough to offset theexpenses incurred [14]. Furthermore, the efficacy of supplier devel-opment programs depends on the existing capabilities of a supplierand the effectiveness with which the manufacturing firm canleverage these programs and investments. Thus, it is entirely pos-sible that returns from these investments may vary across multiplesuppliers, an indication of risk in terms of uncertain returns in sup-plier development investments.

Supplier development, however, provides an opportunity forcollaboration among multiple manufacturing firms. It is notuncommon for manufacturing firms in the same industry to usesimilar or the same components that are sourced from the sameset of suppliers. Examples from various industries include: electricmotors in washing machines (e.g., Whirlpool and GE), engines inautomobiles (e.g., Toyota and Pontiac), and PC boards in personal

166 S. Talluri et al. / European Journal of Operational Research 207 (2010) 165–173

computers (e.g., Dell and HP). However, the issue of manufacturingfirms cooperating in supplier development has never been studied.

This research investigates the supplier development problemfrom a long-term investment perspective to better understand itspotential benefits. Specifically, we consider supplier developmentinvestments in the context of multiple suppliers who supply differ-ent types of materials and components to a manufacturing firm.We develop an analytical model that is based on three key aspectsof investments in supplier development. First, the resources avail-able for supplier development are not unlimited and should beoptimally deployed. Second, we assert that supplier developmentis characterized by long-term, continual efforts, the benefits ofwhich can be more thoroughly understood by tracking the returnson a regular basis over the investment period. Third, manufactur-ing firms can be involved in supplier development individually orcollaboratively. When cooperating, firms share resources and ben-efits, as well as cost and risk.

Under conditions of risk, a manufacturing firm may decide howto optimally allocate its supplier development investments amongmultiple suppliers to minimize risk while maintaining an accept-able level of return. This paper presents a set of mathematicalmodels to address this problem. We consider two scenarios: sin-gle-manufacturer and multiple suppliers (SMMS) and two-manu-facturers and multiple suppliers (TMMS). In SMMS case, werecommend optimal investments in various suppliers by consider-ing risk and return associated with supplier development efforts,and TMMS scenario investigates whether manufacturers with dif-fering capabilities could gain risk reduction benefits from cooper-ating with each other in supplier development.

The development of this research relied heavily on a case com-pany, Wistron Corporation, a Taiwan-based company that employs20,000 workers worldwide. Wistron develops high-technologyproducts such as notebook and desktop computer systems, serversand storage systems, information appliances, and networking andcommunication systems. Customers rely heavily on Wistron’scapability to provide a variety of design related engineering ser-vices to match their product development requirements. In turn,supplier development efforts have been an important part of thenew product development processes at Wistron. These efforts haveranged from intensively integrated teamwork with its suppliers tofinancial investments in selected strategic partners. Suppliers thatwere involved in Wistron’s supplier development programs in thepast include Catcher Technology (casing), ENlight Corporation(casing), Apacer (memory, IC), Tyco Electronics (connector), High-Tek Corporation (cable), to name a few. The development of ourmodels and the corresponding numerical examples were moti-vated by Wistron’s supplier development efforts and results.

The rest of the paper is organized as follows. The next sectionreviews literature in the areas of supplier development and portfo-lio investment models and risk, which is followed by model devel-opment. We then discuss model results based on illustrative dataand present managerial implications and opportunities for futureresearch.

2. Literature review

2.1. Supplier development

The topic of supplier development has received considerableattention from researchers in the past two decades [3,12,14,15,17–20,27,31]. Supplier development may range from limitedinvolvement such as supplier qualification and supplier perfor-mance evaluation, to more intense efforts such as training sup-plier’s personnel and assistance with new product design [14]. Itis generally believed that success in supplier development will lead

to better performance for the suppliers and the buying firms[15,17,20,23,31].

Krause et al. [16] examined the impact of differences in atti-tude towards supplier development activities on supplier perfor-mance. They found that firms that actively and strategicallyinvolve themselves in supplier development reap greater long-term benefits. Krause et al. [17] found that direct involvementactivities, such as site visits and supplier personnel training, playa critical role in performance improvement. Carr and Kaynak [3]found that supplier development efforts are critical in improvingthe buying firm’s financial performance. Li et al. [20] found thatcooperation and trust are the most important elements in sup-plier development that enhance buyer’s performance. Krauseet al. [19] found evidence indicating that commitment in supplierdevelopment initiatives from the buying firm can lead to betterperformance. According to Krause et al. [19], performanceimprovements through supplier development are often only pos-sible when the buying firms commit to long-term relationshipwith key suppliers.

While there is significant amount of conceptual and empiricalwork in the area of supplier development, to the best of our knowl-edge there have not been any formal decision models proposed forassisting firms in making resource allocation decisions in supplierdevelopment initiatives. Specifically, supplier development re-quires the buying firm to invest limited human or capital assetsthat are dedicated to the suppliers involved [19,20,30]. Conse-quently, optimal allocation of available resources across multiplesuppliers is an important issue that needs to be understood morethoroughly. Chan and Kumar [4] studied the supplier selectionproblem in supplier development and proposed a Fuzzy extendedAnalytic Hierarchy Process (AHP) model to evaluate performanceof multiple suppliers. However, their use of supplier developmentand supplier selection synonymously indicates that Chan and Ku-mar’s model was more of a supplier selection model rather thana supplier development approach.

2.2. Portfolio optimization and risk

When a manufacturing firm decides to pursue supplier develop-ment efforts, it expects to benefit from such an investment interms of cost savings, improved quality, delivery performanceand profitability. These benefits can be viewed as the investmentreturns [19]. However, suppliers differ in their capabilities relatingto quality management and control, product and process design,and delivery and execution competence. As a result, for the sameinvestment of resources, the return from each supplier can vary,and in each case, it can be higher or lower than the firm’s expecta-tion. Furthermore, supplier development poses potential opportu-nistic behavior on the part of the supplier [30], which may lead tototal failure or termination of the relationship earlier than ex-pected. Thus, when viewed as an investment, the supplier develop-ment efforts lead to ‘‘uncertain” returns due to variation in supplierperformance and the presence of moral hazard. Analogous to riskin financial investments, we conceptualize uncertainty of returnsin supplier development as risk. Consequently, supplier develop-ment risk can be defined as the uncertainty of outcomes (i.e.,improvements in suppliers’ capabilities and performance) associ-ated with a firm’s supplier development efforts.

Allocation of supplier development investments among multi-ple suppliers can be viewed analogous to a portfolio selectionproblem. Specifically, given limited budget and resources and theuncertainty of returns from supplier development investments,the problem faced by a manufacturer is similar to constructingan optimal investment portfolio. Krause et al. [16] reported thatfirms involved in supplier development strategically apply portfo-lio analysis to deal with the task of selection and prioritizing. How-

S. Talluri et al. / European Journal of Operational Research 207 (2010) 165–173 167

ever, there are no existing decision models in the supplier develop-ment literature that have addressed this important issue.

Investment portfolio and risk assessment is an area that has re-ceived significant attention in the finance literature. Seminal workin this area was due to Dunn and Young [6] in proposing a modelfor portfolio assessment. This model has been applied to a varietyof investment decisions in the literature [7,11,13,22]. The mainidea of portfolio optimization is to select the best combination ofinvestments (for example, stocks) that meets budget constraintswhile minimizing risk.

While risk is an important aspect of this paper, our focus is not onthe development of a (new) risk measure. Rather, we seek to studythe supplier development problem by applying the concept offinancial investment under risk. Markowitz [21,22] assessed riskby calculating variance of the investment portfolio. However,Markowitz’s portfolio model is suited only for the case of ellipticdistribution such as Normal or t-distribution with finite variance[28]. While the distribution of the returns of supplier developmentinvestments can be elliptic or non-elliptic, to simplify our analysis,we assume that the distribution of the returns is normal, and thus, iselliptic. With this assumption, the adoption of variance as the mea-sure of risk is appropriate when applying Markowitz’s portfoliomodel [5,7,28]. Recent studies suggest that an appropriate risk mea-sure should be ‘‘coherent” (see [2] for the definition of coherent).Among the various coherent risk measures, the Conditional value-at-risk (CVaR) has received tremendous attention due to its attrac-tive computation properties [1,24,28]. Specifically, Reed and Walsh[25] pointed out that the optimal portfolio solutions may be thesame using either variance or CVaR as the risk measures under cer-tain conditions. The readers can refer to the use of CVaR and otherrisk measures in Konno and Yamazaki [13],Vermeulen [29], Jiaand Dyer [7], Grootveld and Hallerback [8], Rockafellar and Uryasev[26], Szegö [28], Ahmed et al. [1], Natarajan et al. [24].

Given the setting and characteristics of the supplier develop-ment problem under risk, we utilize Markowitz’s portfolio selec-tion model to assist manufacturing firms in optimally allocatingsupplier development dollars among multiple suppliers. We firstdiscuss the SMMS model and subsequently extended it to TMMSand cooperative supplier development case.

3. Model development

3.1. SMMS model

Fig. 1 depicts the case where a single manufacturer engages insupplier development efforts with multiple suppliers. The manu-

j

n

jj Rx∑

=1

Supplier 1

Manufacturer

1x

2x

3x

4x

…..

Supplier 4

Supplier 3

Supplier 2

Single manufacturerMultiple suppliers

Manufacturer investment portfolio

jR

jx : amount manufacturer invests in supplier j

: rate of return from investing in supplier j

Fig. 1. Single-manufacturer and multiple-supplier case.

facturer has limited amount of budget (resources) for supplierdevelopment efforts that needs to be optimally allocated to multi-ple suppliers. Thus, the amount invested in a supplier is dependenton the amounts invested in other suppliers. In addition, investmentreturns vary among suppliers depending on their capabilities andexecution competence. The goal of the manufacturer is to allocateinvestment amounts so that a target return is achieved at mini-mum risk. Risk is affected by variability of returns from suppliersand the amounts invested. Note that the unit of analysis is at thefirm level. The supplier development program may involve in sin-gle or multiple products with a supplier. The investment return is,therefore, an overall return.

The Markowitz’s model recast as a supplier development deci-sion model for the single-manufacturer, multiple-supplier case isshown below:

Minimize VarXn

j¼1

xjRj

!ð1Þ

Subject To :Xn

j¼1

xj ¼ X; ð2Þ

Xn

j¼1

rjxj P qX; ð3Þ

lj 6 xj 6 lj; 8j ¼ 1 � n; ð4Þ

where n is the number of suppliers; xj is the amount manufacturerinvests in supplier j; lj is the maximum amount that can be in-vested in supplier j; lj is the minimum amount that needs to be in-vested in supplier j; X is the total budget; Rj is the random variablerepresenting the ‘‘rate of return” from investing in supplier j; rj isthe expected value of Rj; and q is the minimum overall expectedrate of return required by manufacturer.

The objective function is the variance of the supplier develop-ment investment portfolio, which can also be expressed asPn

i¼1

Pnj¼1xixjrij, where rij is covariance of returns for investments

in suppliers i and j. Note that covariance exists between Ri and Rj

because both suppliers benefit from the manufacturer’s capabili-ties and common efforts in terms of initiation and implementationof improvement programs. Expression (2) is the budget constraint.Expression (3) is the return expectation constraint, which statesthat the manufacturer’s overall expected return must exceed a tar-get level of return ðqXÞ. Finally, expression (4) restricts the maxi-mum and minimum amounts that the manufacturer can invest inany supplier. Specifically, when there are several suppliers thatthe manufacturer can invest in as part of supplier development,this constraint prevents investing all of the available resources ina single supplier.

As discussed previously, resources that a manufacturer investsin supplier development include assets, funds, staff and timeamong others. These can be transformed into monetary terms,the sum of which is expressed as the budget limit X. Therefore,implicitly budget means more than ‘‘cash” in our model. It is acomposite parameter that represents the value of resources inmonetary terms. Moreover, the benefits from supplier develop-ment will eventually impact a firm’s financial performance [3].As such, the investment returns are financial gains experiencedby the manufacturer from specific performance improvements.

To solve the current quadratic problem, we followed Hossain etal.’s [11] approach in calculating the covariances ðrijÞ as shown be-low: Assume ri is known for all i ¼ 1; . . . ;n. Let rit be the ‘‘realized”or actual return from investment in supplier i in period t. So, bydefinition, rij can be estimated as:

rij ¼1T

XT

t¼1

ðrit � riÞðrjt � rjÞ:

'1x

'3x

'2x

Supplier 1

Manufacturer 1

1x

2x

3x

4x

Supplier 3

Supplier 2

Manufacturer 2'4x

j

n

jj Rx∑

=1

'

1

'j

n

jj Rx∑

=

Two manufacturersMultiple suppliers

Manufacturer 1 investment portfolio

Manufacturer 2 investment portfolio

168 S. Talluri et al. / European Journal of Operational Research 207 (2010) 165–173

Therefore, the objective function becomes:

VarXn

j¼1

xjRj

!¼Xn

i¼1

Xn

j¼1

xixjrij

ffiXn

i¼1

Xn

j¼1

xixj1T

XT

t¼1

ðrit � riÞðrjt � rjÞ" #

¼ 1T

XT

t¼1

Xn

i¼1

Xn

j¼1

xixjðrit � riÞðrjt � rjÞ" #

¼ 1T

XT

t¼1

Xn

j¼1

ðrjt � rjÞxj

" #2

:

…..

Supplier 4

jR

jx : amount manufacturer 1 invests in supplier j

: rate of return from investing in supplier j for manufacturer 1

'jx : amount manufacturer 2 invests in supplier j

'jR : rate of return from investing in supplier j for manufacturer 1

Fig. 2. Two-manufacturer and multiple-supplier case.

3.2. TMMS model

In this section, we extend the single-manufacturer model to thetwo-manufacturer case. When two manufacturing firms target thesame supplier in their supplier development efforts, they maychoose to cooperate or not cooperate. The benefit of not cooperat-ing is that firms may develop unique components with featuresthat can help differentiate their products from those of their com-petitors. However, firms still need to bear all of the risk associatedwith supplier development and may need a higher level of budgetto achieve the same returns. In contrast, by cooperatively investingin the same component supplier, the development efforts for bothcompanies can decrease and the resources can be shared. Highervolume can further reduce the cost of the component througheconomies of scale. While cooperation may result in greater homo-geneity of their products, firms still have room to create differenti-ation on other features of their products. For example, a Dell PCmay look different from an HP PC, even if they purchased the main-boards from the same supplier. It is useful to note that cooperativebuying schemes using ‘buying councils’ have been adopted in sev-eral industries such as the automotive industry. The above discus-sion alludes to the possibility of a synergy between cooperativebuying and cooperative supplier development. In our TMMS mod-el, we assume that through cooperation a manufacturing firm canenjoy the benefit of the other firm’s investment, whereas in a non-cooperative situation a manufacturing firm’s benefit will primarilybe derived from its own investment. Similarly, the two cooperativemanufacturers will face the same level of ‘‘shared” risk.

In the two-manufacturer model, a manufacturer’s investment ina supplier not only depends on its investments in other suppliers butalso depends on the other manufacturer’s investments in the samesupplier and the rest of the suppliers. In other words, covarianceof investment returns exists within the investment portfolio of eachmanufacturer, as well as across the two portfolios from both manu-facturers. The TMMS model can be described as shown in Fig. 2 andrepresented by the risk minimization model shown below.

Minimize VarXn

j¼1

xjRj þXn

j¼1

x0jR0j

!ð5Þ

Subject To :Xn

j¼1

xj ¼ X; ð6Þ

Xn

j¼1

x0j ¼ X0; ð7Þ

Xn

j¼1

max½rj; r0j�ðxj þ x0jÞP max½qðX þ X 0Þ;q0ðX þ X0Þ�;

ð8Þlj 6 xj 6 lj ;8j ¼ 1 � n; ð9Þl0j 6 x0j 6 l0j ;8j ¼ 1 � n: ð10Þ

The objective function in expression (5) minimizes the total vari-ance of the investment portfolios of both manufacturers; super-script ‘‘prime” is to represent manufacturer 2. Thus, the objectivefunction value represents the risk level faced by the two manufac-turers. Expressions (6) and (7) are the budget constraints for eachmanufacturer. Expression (8) requires that each manufacturer’soverall expectation of return be met. Note that the left-hand-sideof (8) contains the term max ðrj; r0jÞ. This reflects the higher levelof benefit (return) realized by both manufacturers because of coop-eration. We allow the two manufacturers to have their own overallexpectations because it is reasonable to assume that the better-per-forming manufacturer should have a higher overall expectationthan the other manufacturer. Accordingly in expression (8), totalexpected benefit (TEB) for a manufacturer is computed by the prod-uct of total investment dollars and the higher of the expected re-turns of the two manufacturers from each supplier. Finally,expressions (9) and (10) are the investment amount constraintswhich prevent the manufacturers from over investing in any spe-cific supplier. While there may be legal issues involved in suchcooperative decisions, our research considers that all legal aspectsof cooperation between two firms are satisfied and thus, are notwithin the scope of this study.

To solve TMMS, we would need COVðR0i;R0jÞ;COVðRi;RjÞ and

COVðRi;R0jÞ as parameters in the model. In Appendix A, we show

how this nonlinear model can be solved by replacing the objective

function with 1T

PTt¼1

Pnj¼1½xjðrjt � rjÞ þ x0jðr0jt � r0jÞ�

h i2. Note that ex-

pected return is assumed to be known in our model. In situationswhere the manufacturing firms do not know what the exact distri-bution of investment return is, they can utilize the average histori-cal rate of return �rj for approximating the expected return rj andT � 1 for T. This will convert the objective function into a statisti-cally unbiased estimation of variance based on historical data. Thelinearized version of the model is shown in Appendix B. Finally, thismodel can be extended to the n-manufacturer–m-suppliers case asshown in Appendix C. In situations where the number of suppliersand manufacturers is significantly large, linearization of the objec-tive function can be utilized in solving the optimization model.

4. Numerical experiments and results

To utilize our models, firms need to estimate the costs of sup-plier development in selecting an appropriate total budget. Basedon our discussions with the staff at Wistron Corporation, we con-clude that while an exact monetary budget for supplier develop-ment may be difficult to obtain, it is feasible for firms to obtain a

0

10000

20000

30000

40000

50000

60000

0.15 0.17 0.19 0.21 0.23 0.25 0.27

$

supplier1

supplier2

supplier3

supplier4

ρ

Fig. 3. Supplier allocation vs. overall expected return (q) with investment limits.

S. Talluri et al. / European Journal of Operational Research 207 (2010) 165–173 169

reasonable estimation. For example, investment costs associatedwith factors such as tooling, facility, and training can be obtainedfrom the existing accounting systems without much difficulty.Other costs relating to employee involvement in supplier’s opera-tions (time value, traveling expense, on-site technical support)can also be calculated. As for the benefits, cost reduction can betransformed into percentage of savings. Quality improvement canbe assessed through the quality assurance system in terms of num-ber of rejects, returns, repairs, and each of these measures can betranslated into cost (reduction) terms. Similarly, delivery perfor-mance can be expressed in terms of on-time delivery rate, numberof delays, number of line breakdowns and its costs, and stock-outfrequency and costs. While we could not acquire data due to con-fidentiality issues, we assert that it is worth the efforts for manu-facturers to collect such data, due to the managerial insights thatthe portfolio investment models can provide. Our analysis in thispaper mainly focuses on investigating the relationships amongkey variables in our models by using synthetic data.

4.1. Results for SMMS case

We consider a randomly generated dataset with predefined dis-tributions to demonstrate the application of our models. In thisexperiment, there are four candidate suppliers for a manufacturerto consider for supplier development investments. The total avail-able budget for the next period is assumed to be $100,000. Histor-ical supplier development return data is assumed to be availablefor the past ten periods. These historical return data are randomlygenerated from four Normal distributions, N(0.15, 0.0225),N(0.2,0.04), N(0.25, 0.0625), and N(0.3, 0.09), for suppliers 1, 2, 3and 4, respectively. Therefore, the average return from the foursuppliers, with equal investments, will be about 0.225. The unitof investment return is dollar per dollar invested. Note that coeffi-cient of variation (CV) for all return distributions are set equal (to1) so that the effect of CV can be controlled. The detailed data aresummarized in Table 1.

Fig. 3 shows investments across the four suppliers at differentlevels of q when investment is restricted to a maximum of$50,000 for each supplier. It is evident from Fig. 3 that at low levelsof q the manufacturer needs to consider investing more in suppli-ers 1 and 2 and to a lesser degree in suppliers 3 and 4. As the q va-lue increases the manufacturer must consider investing more insuppliers 3 and 4 and less in suppliers 1 and 2. The managerialimplication is that when high overall expected return is risky toachieve or is infeasible, the manufacturer may lower the expecta-tion or adjust the investment allocation based on the analysis fromFig. 3. An alternative way to meet higher expectation is to cooper-ate with another manufacturer in supplier development, which wedemonstrate and discuss next.

4.2. Results for TMMS case

We randomly generated the historical rates of return for manu-facturer 2 from suppliers 1, 2, 3, and 4 with Normal distributions,

Table 1Expected returns and historical actual returns by supplier.

Actual returns P1 P2 P3 P4 P5

Supplier 1 0.1725 0.1248 0.1706 0.1882 0.1229

Supplier 2 0.2098 0.2053 0.2014 0.1815 0.2151

Supplier 3 0.1132 0.2169 0.2103 0.2438 0.2549

Supplier 4 0.2893 0.2385 0.2131 0.1262 0.2080

Unit: $/per dollar invested.Expected return: rj .

N(0.2,0.04), N(0.25, 0.0625), and N(0.3, 0.09), and N(0.35, 0.1225),respectively, with all CVs controlled at 1 (see Table 2). Manufac-turer 2’s budget is also assumed to be $100,000. Data in Table 1are used for manufacturer 1. When the investment dollars areequally distributed among the four suppliers, the average rate ofreturn for manufacturer 2 is 0.275. As such, we intend to differen-tiate manufacturer 2 as having better capability in implementingsupplier development initiatives than manufacturer 1 for everycandidate supplier. Manufacturer 2 can be superior in many as-pects, such as better execution capability, efficiency, technicaldevelopment capability, problem-solving capability, and cost con-trol capability. All these factors can result in higher returns fromsupplier development.

Fig. 4 compares the case of cooperation and non-cooperationbetween the two manufacturers. It is evident from this figure thatwhen manufacturer 1’s expectations of returns increase given thatmanufacturer 2’s is held constant at 0.275, cooperating with man-ufacturer 2 is always beneficial to manufacturer 1 because the TEB/risk ratio is higher. High TEB to risk ratio indicates high benefit perunit of risk, which is preferred by manufacturers. Similarly, whenmanufacturer 2’s expectations of returns increases given that man-ufacturer 1’s is held constant at 0.225, cooperating with manufac-turer 1 will result in a higher TEB to risk ratio for the most part.However, it is important to note that the benefit derived fromcooperating with manufacturer 1 decreases for manufacturer 2for low values of expected returns. Specifically, when q is below0.2, manufacturer 2 should choose not to cooperate with manufac-turer 1. In the next few experiments, we investigated the situationsin which it may not be advantageous for manufacturer 2, to coop-erate with manufacturer 1, and vice versa.

First, we examined the impact of various levels of expected re-turns on the TEB/risk ratio from manufacturer 1’s perspective as

P6 P7 P8 P9 P10 rj

0.1482 0.1521 0.1380 0.1301 0.1295 0.1500

0.2140 0.2512 0.2611 0.2126 0.2586 0.2000

0.2655 0.2272 0.2059 0.2188 0.1846 0.2500

0.4015 0.3539 0.2041 0.2612 0.3659 0.3000

Table 2Manufacturer 2’s expected returns and historical actual returns by supplier.

Actual returns P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 rj

Supplier 1 0.2301 0.1911 0.2237 0.2163 0.1606 0.2421 0.2283 0.1553 0.2783 0.2331 0.2000

Supplier 2 0.2578 0.3305 0.2412 0.2137 0.2860 0.3473 0.2654 0.2584 0.2522 0.2211 0.2500

Supplier 3 0.3918 0.2606 0.3446 0.3401 0.1493 0.3325 0.4027 0.1415 0.2428 0.2583 0.3000

Supplier 4 0.4882 0.3894 0.3991 0.5917 0.3724 0.3304 0.3304 0.1658 0.2380 0.3422 0.3500

Unit: $/per dollar invested.

0

2

4

6

8

10

12

14

16

18

20

0.15 0.17 0.19 0.21 0.23 0.25 0.27 0.29

TEB

/Ris

k

cooperationmanufacturer 1(non-coop.)manufacturer 2(non-coop.)

ρ

Fig. 4. Cooperation vs. non-cooperation: TEB/risk vs. q.

170 S. Talluri et al. / European Journal of Operational Research 207 (2010) 165–173

shown in Fig. 5. The current expected returns for manufacturer 2are (0.2, 0.25, 0.3, and 0.35). The expected return (ER) ratio indi-cates the increase or decrease of expected returns from these baselevel values at which the ER ratio is 1. For example, an ER ratio of1.2 for manufacturer 2 indicates that expected returns have in-creased from the current levels of (0.2, 0.25, 0.3, and 0.35) to targetlevels of (0.24, 0.3, 0.36, and 0.42). These targets can be viewed as

0

5

10

15

20

25

30

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5

cooperation

non-cooperation

TEB

/ Ris

k

Manufacturer 2 ER Ratio

Fig. 5. Cooperation vs. non-cooperation for manufacturer 1: TEB/risk vs. manufac-turer 2 ER ratio.

what manufacturer 2 is expecting in the form of returns from sup-plier development initiatives. Note that the data, the actual perfor-mance, in Tables 1 and 2 is left unchanged when varying the ERratio. Thus, when ER ratio is higher than 1, it indicates that the ac-tual performance is lower than expected.

In this analysis, manufacturer 2’s ER ratio was varied whilemanufacturer 1’s ER ratio was set at 1.0 and q at 0.225. It is evidentthat it is not always beneficial for manufacturer 1 to cooperatewith the manufacturer 2. When the ER ratio of manufacturer 2 isP1.42, manufacturer 1 should choose not to cooperate with man-ufacturer 2, because manufacturer 2 is relatively under-performingwhen compared to their expectations. Also, manufacturer 1 shouldbe wary of cooperating with manufacturer 2 when the ER ratio formanufacturer 2 is 60.92. The superior performance of manufac-turer 2 in the past could be a result of an unexpected or accidentaloccurrence given that manufacturer 2 has low expected returns,and that the performance of manufacturer 2 may not continue tobe high in future periods. Finally, so long as the ER ratio of manu-facturer 2 is P0.82 and 61.42, manufacturer 2 can be consideredto be a stable and a good performer, and manufacturer 1 will ben-efit from cooperating with manufacturer 2. This analysis providesvaluable information to manufacturer 1 in terms of conditions un-der which cooperation with manufacturer 2 would prove to bebeneficial.

Fig. 6 provides similar analysis and strategies that must be pur-sued by manufacturer 2. In this case, manufacturer 1’s ER ratio wasvaried while manufacturer 2’s ER ratio was set at 1 and q at 0.275.Interestingly, while manufacturer 2 is a better-performing manu-facturer, our analysis indicates that manufacturer 2 is likely to ben-efit from cooperating with manufacturer 1, unless manufacturer 1is highly under-performing or over-performing. Nonetheless, the

0

2

4

6

8

10

12

14

16

18

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5Manufacturer 1 ER Ratio

TEB/

Ris

k

cooperationnon-cooperation

Fig. 6. Cooperation vs. non-cooperation for manufacturer 2: TEB/risk vs. manufac-turer 1 ER ratio.

0

5

10

15

20

25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Shar

ed T

EB /

Ris

k

% of total investment from manufacturer 1

Fig. 7. Shared TEB/risk vs. percentage of total investment from manufacturer 1.

S. Talluri et al. / European Journal of Operational Research 207 (2010) 165–173 171

benefit of cooperation decreases as the ER ratio increases or de-creases from 1.

Finally, we investigated the conditions of ideal allocation ofinvestment dollars from both manufacturers, based on the ex-pected returns and historical achievement shown in Tables 1 and2. Fig. 7 depicts the results of this analysis. It is evident that havingmanufacturer 1 bear 80% of the total investment dollars will resultin the highest benefit/risk ratio for both manufacturers. Note thatmanufacturer 1 is the ‘‘inferior” manufacturer in our illustrationand it is reasonable that they invest more resources while manu-facturer 2 can contribute more in the form of technical expertise,execution capability and better competency. The ideal investmentpercentages between manufacturers 1 and 2 are 80% and 20%,respectively, for the illustrative case. Any deviation from this 80%level will result in declining values of benefit to risk ratio.

5. Managerial implications

The single-manufacturer case can assist managers in optimallyallocating resources to various suppliers in the supplier develop-ment process. Thus, the proposed models have high practical rele-vance for the decision-makers in this area. However, the moreinteresting, two-manufacturer case has a number of useful mana-gerial implications.

When both manufacturers’ historical performance is close totheir expectation, they should always seek to cooperate with eachother. Through cooperation, both manufacturers will be able toacquire the same level of benefits at lower risk. Also, when amanufacturer’s past investment returns are commensurate withtheir expected returns they will always be a good candidate forcooperation in supplier development. Based on our analysis, coop-erating with such a manufacturer can enhance the benefit perunit of risk.

When considering cooperation in supplier development, amanufacturer should not only examine the other manufacturer’sefficiency of past investment performance, but also their level ofcompetence in achieving the expected returns. If the other manu-facturer is competent to a lesser extent, the manufacturer shouldnot consider cooperation even if the other manufacturer didachieve higher returns in the past. One way to estimate the othermanufacturer’s competence is by comparing the manufacturer toother firms of the same size with similar capability and identify-ing how its investment returns in supplier development differs.

Firms may possibly obtain this type of information by participat-ing in benchmarking through an independent benchmarking ser-vice provider (e.g., Center for Advanced Purchasing Studies –CAPS).

We anticipated that in situations where both manufacturers donot meet their expected performance, the high performing manu-facturer should choose not to cooperate with the low performingmanufacturer and instead should either invest in supplier develop-ment on their own or seek opportunities to cooperate with othermanufacturers. In contrast, the low performing manufacturershould try to cooperate with the high performing manufacturerby offering certain incentives. Interestingly, our numerical exam-ple results suggest the opposite, that is, the high performing man-ufacturer is recommended to seek cooperation while the lowperforming manufacturer should not cooperate when the expectedreturn is low. After a careful examination of the data, we found thatthe additional financial funds from the low performing manufac-turer will allow an increase of the total expected return that isattractive to the high performing manufacturer for cooperation.Through cooperation in supplier development, the additionalfinancial resources from the low performing manufacturer allowthe high performing manufacturer to achieve higher benefits. Inour experiment, the ratio is 4 to 1 between the low and high per-forming manufacturer, respectively. Therefore, the ideal strategyfor the high manufacturer is to cooperate with other manufactur-ers and then utilize their investment dollars to create higherbenefits.

Through collaborative supplier development partnership, firmscan team up to leverage their resources, capability, and purchasingpower to achieve competitive advantage. Similar to the concept ofconsortia buying, firms can form a supplier development consor-tium, seeking competent, efficient, and capable firms for partner-ship and screen firms with questionable historical performanceand poor competence.

Finally, it is worth noting that manufacturing firms should bewary of other firms’ opportunistic behavior. Specifically, a low per-forming firm may secretly enjoy the benefits of a supplier’s im-proved performance that is mainly due to the high performingfirm’s supplier development capabilities without contributingmuch in terms of effort or resources. Although such behavior andlegal aspects of supplier development are not incorporated in ourmodels, we deem them as important factors that require carefulevaluation in the decision process of supplier development.

6. Conclusions

Supplier development is a long-term, resource-consuming busi-ness activity that requires commitment from both manufacturingfirms and suppliers. It requires manufacturing firms to invest sig-nificant amounts of resources in suppliers. Considering the limitedresources available, how to best allocate investments in multiplesuppliers that produce different types of materials or componentsis a critical issue faced by manufacturing firms.

This study makes two main contributions. First, we propose thatsupplier development is analogous to a portfolio investment deci-sion when multiple suppliers are involved. We present howMarkowitz’s portfolio investment model can be used to help firmsoptimally allocate their available resources while maintaining ex-pected benefits. Second, we investigate the issue of collaborativesupplier development and identify conditions in which coopera-tion and non-cooperation are beneficial for manufacturing firms.Our approach enables two collaborative firms to decide the alloca-tion of contributions considering their past performance in sup-plier development initiatives. Our paper is the first to present ananalytical approach to addresses the issue of ‘‘risk” in deciding

172 S. Talluri et al. / European Journal of Operational Research 207 (2010) 165–173

the optimal allocation of available resources for the supplier devel-opment program. It also provides a novel method to assess thebenefits of cooperating with other firms in supplier developmentefforts.

Availability of historical data regarding returns from supplierdevelopment efforts is a key to the application of models proposedin this paper. In situations, where such data are not readily avail-able, firms must estimate these returns by identifying cost reduc-tions and improvements that resulted from supplier developmentefforts of the past. Also, our models may not be appropriate forselecting new candidate suppliers for supplier development be-cause of lack of historical data and interactions with the buyingfirm. Finally, the issue of competing manufacturers when they bothinvest in supplier development in the same suppliers withoutcooperating with each other or being involved in partial coopera-tion needs to be addressed. Can one manufacturer ‘‘steal” the ben-efits from the other manufacturer’s supplier development efforts?How can manufacturers prevent this from happening? Is collabora-tion still a good strategy in such a circumstance? We leave theseissues for exploration as extensions of the models developed in thispaper.

Appendix A

By definition

VarXn

j¼1

xjRj þXn

j¼1

x0jR0j

!¼ Var

Xn

j¼1

xjRj

!þ Var

Xn

j¼1

x0jR0j

!

þ 2CovXn

j¼1

xjRj;Xn

j¼1

x0jR0j

!: ðA1Þ

Assuming ri known for all i ¼ 1; . . . ;n, then we have

VarXn

j¼1

xjRj

!¼ 1

T

XT

t¼1

Xn

j¼1

xjðrjt � rjÞ" #2

; ðA2Þ

VarXn

j¼1

x0jR0j

!¼ 1

T

XT

t¼1

Xn

j¼1

x0jðr0jt � r0jÞ" #2

: ðA3Þ

Also, the covariance term in Eq. (A1) can be approximated asfollows:

CovXn

j¼1

xjRj;Xn

j¼1

x0jR0j

!

¼ EXn

j¼1

xjRj � EXn

j¼1

xjRj

!" # Xn

j¼1

x0jR0j � E

Xn

j¼1

x0jR0j

!" #

¼ EXn

j¼1

xjRj �Xn

j¼1

x0jR0j

" #� E

Xn

j¼1

xjRj

!� E

Xn

j¼1

x0jR0j

!

¼ E½ðx1R1 þ x2R2 þ � � � þ xnRnÞðx01R01 þ x02R02 þ � � � þ x0nR0nÞ�� ðx1r1 þ x2r2 þ � � � þ xnrnÞðx01r01 þ x02r02 þ � � � þ x0nr0nÞ

¼Xn

i¼1

Xn

j¼1

xix0j½EðRiR0jÞ � rir0j� ¼

Xn

i¼1

Xn

j¼1

xix0jr0ij

¼Xn

i¼1

Xn

j¼1

xix0j1T

XT

t¼1

ðrit � riÞðr0jt � r0jÞ" #

¼ 1T

XT

t¼1

Xn

i¼1

Xn

j¼1

xix0jðrit � riÞðr0jt � r0jÞ" #

: ðA4Þ

So,

VarXn

j¼1

xjRj þXn

j¼1

x0jR0j

!

¼ 1T

XT

t¼1

Xn

j¼1

xjðrjt � rjÞ" #2

þXn

j¼1

x0jðr0jt � r0jÞ" #2

24

þ2Xn

i¼1

Xn

j¼1

xix0jðrit � riÞðr0jt � r0jÞ#

¼ 1T

XT

t¼1

Xn

j¼1

xjðrjt � rjÞ þXn

j¼1

x0jðr0jt � r0jÞ" #2

¼ 1T

XT

t¼1

Xn

j¼1

½xjðrjt � rjÞ þ x0jðr0jt � r0jÞ�" #2

: ðA5Þ

Appendix B

It can be shown that minimizing 1T

PTt¼1

Pnj¼1½xjðrjt � rjÞþ

hx0jðr0jt � r0jÞ��

2 is equivalent to minimizing 1T

PTt¼1

Pnj¼1½xjðrjt � rjÞþ

���x0jðr0jt � r0jÞ�j. Let ajt ¼ rjt � rj and a0jt ¼ r0jt � r0j. The TMMS model canthen be expressed as follows:

Minimize1T

XT

t¼1

yt

Subject To : yt þXn

j¼1

ðajtxj þ a0jtx0jÞP 0 8t ¼ 1 � T;

yt �Xn

j¼1

ðajtxj þ a0jtx0jÞP 0 8t ¼ 1 � T;

Xn

j¼1

xj ¼ X;

Xn

j¼1

x0j ¼ X 0;

Xn

j¼1

maxðrj; r0jÞðxj þ x0jÞP qðX þ X0Þ;

Xn

j¼1

maxðrj; r0jÞðxj þ x0jÞP q0ðX þ X 0Þ;

0 6 xj 6 lj 8j ¼ 1 � n;

0 6 x0j 6 l0j 8j ¼ 1 � n:

Appendix C

The m-manufacturer–n-supplier model:

Minimize VarXm

i¼1

Xn

j¼1

xijR

ij

!

Subject To :Xn

j¼1

xij ¼ Xi; 8i ¼ 1 � m;

Xn

j¼1

Maxi0¼1�m

ðri0

j ÞXm

i0¼1

xi0

j

!" #P qi

Xm

i¼1

Xi; 8i ¼ 1 � m;

lij 6 xij 6 li

j; 8i ¼ 1 � m:

Linearization:By definition, Var

Pmi¼1

Pnj¼1xi

jRij

� �¼Pm

i¼1VarPn

j¼1xijR

ij

� �þ 2

Pmi¼1Pm

i0¼iCOVPn

j¼1xijR

ij;Pn

j¼1xi0j Ri0

j

� �.

From (A2), VarPn

j¼1xijR

ij

� �¼ 1

T

PTt¼1

Pnj¼1ðri

jt � rijÞxi

j

h i2; 8i ¼ 1 �

m.

S. Talluri et al. / European Journal of Operational Research 207 (2010) 165–173 173

From (A4),

COVXn

j¼1

xijR

ij;Xn

j¼1

xi0

j Ri0

j

!¼ COV

Xn

j¼1

xijR

ij;Xn

j0¼1

xi0

j0Ri0

j0

0@

1A

¼ 1T

XT

t¼1

Xn

j¼1

Xn

j0¼1

xijx

i0

j0 ðrijt � ri

jÞðri0

j0t � ri0

j0 Þ

24

35:

So VarPm

i¼1

Pnj¼1xi

jRij

� �¼ 1

T

PTt¼1

Pmi¼1

Pnj¼1ðri

jt � rijÞxi

j

� �2þ

�2Pm

i¼1

Pmi0¼i

Pnj¼1

Pnj0¼1xi

jxi0

j0 ðrijt � ri

jÞðri0

j0t� ri0

j0 Þ� ¼1T

PTt¼1

Pmi¼1

Pnj¼1ðri

jt � rijÞxi

j

h i2.

Similarly, it can be shown that minimizing 1T

PTt¼1

Pmi¼1

�Pn

j¼1ðrijt � ri

jÞxij�

2 is equivalent to minimizing 1T

PTt¼1

Pmi¼1

Pnj¼1

���ðri

jt � rijÞxi

jj. Let aijt ¼ ri

jt � rij. Thus, the m-manufacturer–n-supplier

problem can be re-formulated as:

Minimize1T

XT

t¼1

yt

Subject To : yt þXm

i¼1

Xn

j¼1

aijtx

ij P 0; 8t ¼ 1 � T;

yt �Xm

i¼1

Xn

j¼1

aijtx

ij P 0; 8t ¼ 1 � T;

Xn

j¼1

xij ¼ Xi; 8i ¼ 1 � m;

Xn

j¼1

Maxi0¼1�m

ðri0

j ÞXm

i0¼1

xi0

j

!" #P qi

Xm

i¼1

Xi; 8i ¼ 1 � m;

lij 6 xij 6 li

j; 8i ¼ 1 � m:

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