1. INTRODUCTION
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.
2. DEA SUPPLY CHAIN 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, [x.sub.tj] 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.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
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
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
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.
3. APPLICATION STUDY
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.
4. CONCLUSION
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.
REFERENCES:
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
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AUTHOR PROFILES:
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