Value chain performance measurement: a simple DEA analysis using intermediate measures.
The paper develops a simple way to measure value chain performance by considering the presence of intermediate measures. An application study is presented to show the usefulness of the model. The proposed method can serve as a tentative solution for measuring the efficiency of the value chain systems.

Keywords: Value chain, data envelopment analysis, performance

Article Type:
Mathematical optimization (Measurement)
Wong, Wai Peng
Wong, Kuan Yew
Pub Date:
Name: Review of Business Research Publisher: International Academy of Business and Economics Audience: Academic Format: Magazine/Journal Subject: Business, international Copyright: COPYRIGHT 2010 International Academy of Business and Economics ISSN: 1546-2609
Date: Jan, 2010 Source Volume: 10 Source Issue: 1
Geographic Scope: Malaysia Geographic Code: 9MALA Malaysia
Accession Number:
Full Text:

Performance measurement of value chains is a complex task as it needs to take into considerations the existence of multiple measures that characterize the performance of each member in the chain as well as the existence of intermediate measures between them. Wong and Wong (2007 and 2008) highlighted that Data Envelopment Analysis (DEA) is a powerful tool for measuring value chain efficiency. The reason is that it can handle multiple inputs and outputs and it does not require prior unrealistic assumptions on the variables which are inherent in typical supply chain optimization models (i.e. known demand rate, lead time etc).

DEA's vitality, real-world relevance, diffusion and global acceptance are clearly evident, as supported from such literature studies as Seiford (1996) and Gattoufi et al. (2004a and 2004b). There are number of DEA studies on value chain efficiency (Fare and Grosskopf, 2000; Golany et al., 2006, Liang et al., 2006); yet, most of them tend to focus on a single chain member. This can be partly due to the lack of DEA models for the entire value chain or multi-stage systems. Note that DEA cannot be directly applied to the problem of evaluating the entire value chain efficiency because the value chain cannot be simply viewed as a simple input-output system as conceptualized in DEA.

One similarity of the recent models for addressing chain effect or multilayer system is that they take into consideration the presence of intermediate measures; their differences lie in their mechanic system design. The issue of intermediate measures was initially addressed by Banker and Morey (1986) in a service industry which operates in a single layer. The model separates the inputs/outputs into two groups, i.e., discretionary and non-discretionary; non-discretionary inputs/outputs are exogenously fixed inputs/outputs that are not controllable and their values are predetermined.

The current paper draws on previous Banker's model and extends the model construction for value chain. We analyze its dual formulation and explain how it suits the value chain setting. This paper contributes to the existing value chain (multistage system) literature by providing an alternative model to measure value chain or multistage efficiency. This model is simple, easy to understand and widely accepted. Though, this model may not have addressed all the concerns in value chain or multistage system, it can still serve as a tentative solution for measuring the efficiency of these systems.

In the following section, we will review Banker's model by analyzing its dual formulation and then provide the insight on how it can address the value chain or multistage efficiency. Then we present an application study to show the usefulness of the model.


In a value chain, the best practice of one channel does not mean that it fits the other channel. The impact from the performance of one member may affect the performance of another member. Therefore, in order to better characterize value chain system, we use the concept of 'discount, which is to remove the impact of the performance improvement of one member that affects the efficiency status of the other.

From the basic DEA model (Charnes et al., 1978) in fractional (ratio) form, let's denote IS as the set of intermediate inputs, DS as the set of direct inputs, R as the set of outputs, [] as the tth intermediate input of DMU j and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] as the tth intermediate input for observed DMU [j.sub.0]. Note that DS [union] IS = S.


where [u.sub.r] and [v.sub.s] are the weights for the output r and input s respectively and [v.sub.t] is the weight for the intermediate variables. Note that the weight for the intermediate variables may be zero, but for the direct variables, the weights must always be positive. The intermediate term represents the performance of one chain member (e.g. the upstream channel) that feeds into other chain member (e.g. the downstream channel). By subtracting the intermediate terms from the model, it is analogous to 'discounting' the impact of one's performance that affects the other. Note that, by removing the indirect factor, the efficiency obtained in this model will be the best case efficiency. Model (1) can be further transformed into its equivalent linear form as shown in Model (2) (the dual model) as below.

Dual model


Given Model (2), a possible way to evaluate the entire value chain efficiency, is to estimate the efficiency, Q as the normalized (weighted) efficiency of all the members or stages. That is,

[OMEGA]* = [summation over (i[member of]I)] [w.sub.i][[OMEGA].sup.*.sub.i]/ [summation over (i[member of]I)] [w.sub.i] (3)

where Q* is the optimal efficiency score of the value chain, I is the set of members in the chain, [[OMEGA].sup.*.sub.i], i e I, is the optimal efficiency score for a specific chain member (channel) and [w.sub.i] is the weight reflecting the extent of each channel contributing to the evaluation of the entire value chain efficiency. These weights can be estimated using various methods such as AHP (Analytic Hierarchical Process), Delphi method and pareto analysis (Clemen and Reilly, 2001; Kirkwood, 1997). In this research, we consider all channels (stages) have equal contribution to the value chain (multistage) system performance.


To illustrate our proposed approach, we model a value chain setting based on the global value chain system of the multinational semiconductor corporations. There are three channels in the proposed setting, e.g., supplier, manufacturer and retailer. We use the supply chain operations reference (SCOR) to determine the value chain performance metrics. The metrics used are the financial and operational measures. Table 1 shows the categorization of the metrics.

Readers can refer to Wong and Wong (2007) for detail definition of the measures. We evaluate a total of 10 DMUs i.e. value chains. The results are analyzed using Excel and its linear optimization solver.

We compare the efficiency obtained through our model with the basic DEA model. Thee basic DEA model is applied separately on each stage and the value chain efficiency is obtained by taking the average. We found that the value chain efficiency from Model (1) is always less than or equal to the value chain efficiency from the basic DEA model. The reduction of the value chain efficiency score is due to the removal of the impact from the indirect (intermediate) measures. This also denotes that there are potential savings that can realized from the value chain if we characterized it using intermediate measures (i.e. Model 1). A summarized results analysis is shown in Table 2.


This paper provides an alternative model to evaluate value chain efficiency. Though, it may not have addressed all the concerns in value chain system, it can serve as a tentative solution for measuring the efficiency of the systems. This model can be further enhanced by analyzing how different settings of weights affect the overall value chain. In addition, future research can also look into how to adapt the model in uncertain environment, e.g., by utilizing the Monte Carlo method. Lastly, this paper serves as an exposition to the awareness about potential of simple conventional models to address more complex problems.


Banker, R.D., Morey, R.C., "Efficiency analysis for exogenously fixed inputs and outputs", Operations Research, Vol.34(4), 1986, 513-521.

Charnes, A., Cooper, W.W., Rhodes, E., "Measuring the inefficiency of Decision Making Units", European Journal of Operational Research, Vol. 2(6), 1978, 429-444.

Fare, R., Grosskopf, S., "Network DEA", Socio-Economic Planning Sciences, Vol.34(1), 2000, 35-49.

Gattoufi, S., Oral, M., Kumar, A., Reisman, A., "Epistemology of data envelopment analysis and comparison with other fields of OR/MS for relevance to applications", Socio-Economic Planning Sciences, Vol.38(2/3), 2004, 123-140.

Gattoufi, S., Oral, M., Reisman, A., "Data Envelopment Analysis literature: a bibliography update (1996-2001)", Socio-Economic Planning Sciences, Vol.38(2/3), 2004, 122-159.

Golany, B., Hackman, S.T., Passy, U., "An Efficiency Measurement Framework for Multi-Stage Production Systems", Annals of Operations Research, Vol.145(1), 2006, 51-68.

Kirkwood, C.W., Strategic Decision Making: multiobjective decsion analysis with spreadsheets, Duxbury, California, 1997.

Clemen, R.T., Reilly, T., Making hard decisions with DecisionTools, Duxbury Thomson Learning, U.S., 2001.

Liang, L.F. Yang, Cook, W.D., Zhu, J., "DEA models for supply chain efficiency evaluation", Annals of Operations Research, Vol.145(1), 2006, 35-49.

Seiford, L.M., "Data envelopment analysis: the evolution of the state of the art (1978-1995)", Journal of Productivity Analysis, Vol.7(2/3), 1996, 99-137.

Wong, W.P., Wong, K.Y., "Supply chain performance measurement system using DEA modeling", Industrial Management & Data Systems, Vol. 107(3), 2007, 361-381.

Wong, W.P., Wong, K.Y., "A review on benchmarking of supply chain performance measures", Benchmarking: an International Journal, Vol.15(1), 2008, 25-51.


Dr. Wai Peng Wong earned her Ph.D at the National University of Singapore in 2009. Currently, she is a senior lecturer at the School of Management, Universiti Sains Malaysia, Penang, Malaysia.

Dr. vKuan Yew Wong earned his Ph.D from Birmingham University, UK in 2005. He is currently a senior faculty member at the Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, Skudai, Malaysia.

Wai Peng Wong, Universiti Sains Malaysia, Malaysia

Kuan Yew Wong, Universiti Teknologi, Malaysia
Table 1: Metrics categorization

Direct Inputs     Cost (including labor , variable,
                  and capital components) ($)

Intermediates     Fill rate (%), on-time delivery
                  (%), cycle time (days)

Direct output     Revenue ($)

Table 2: Value chain efficiency

                         Basic DEA model

               Stage1                       Stage
DMU    ([[theta].sup.*.sub.1])    2 ([[theta].sup.*.sub.2])

1               1.000                       0.865
2               0.883                       1.000
3               0.875                       0.880
4               0.524                       1.000
5               0.743                       1.000
6               0.501                       1.000
7               0.554                       1.000
8               0.600                       0.974
9               1.000                       1.000
10              1.000                       0.822

                         Basic DEA model

                Stage                      Average
DMU   3 ([[theta].sup.*.sub.3])       ([[theta].sup.*])

1               0.988                       0.951
2               1.000                       0.961
3               1.000                       0.918
4               1.000                       0.841
5               1.000                       0.914
6               1.000                       0.834
7               1.000                       0.851
8               1.000                       0.858
9               0.876                       0.959
10              1.000                       0.941

                 DEA supply chain model (Model 1)

               Stage1                       Stage
DMU    ([[theta].sup.*.sub.1])    2 ([[theta].sup.*.sub.2])

1               0.944                       0.428
2               0.874                       1.000
3               0.771                       0.491
4               0.516                       1.000
5               0.729                       1.000
6               0.497                       1.000
7               0.551                       1.000
8               0.597                       0.815
9               0.722                       0.978
10              1.000                       0.410

                 DEA supply chain model (Model 1)

               Stage 3                      Chain
DMU   3 ([[theta].sup.*.sub.3])       ([[theta].sup.*])

1               0.839                       0.737
2               1.000                       0.958
3               0.811                       0.691
4               1.000                       0.839
5               0.688                       0.806
6               1.000                       0.832
7               0.953                       0.835
8               0.985                       0.799
9               0.603                       0.768
10              1.000                       0.803

Note: ([[theta].sup.*.sub.i]), i = {1, 2, 3} refers
to the efficiency score obtained using basic model
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