Chapter 2. Literature Review
2.2 Data Selection and Description
One major advantage is that DEA has emerged as the leading method for efficiency
evaluation in terms of both the number of research papers published and the number of applications to real world problems (Seiford, 1997; Gattoufi et al., 2004). Previous studies that used DEA to investigate the relative efficiency of the retail industry are now described as follows.
According to the former chapter mention about the requirements, we need to find an effective method to satisfy the requirements. Because of the attributes of requirements, DEA has been used extensively for benchmarking analysis ever since its introduction by Charnes et al. (1978). DEA has many desirable features (Charnes et al., 1994) which may explain why researchers are interested in using it to investigate the efficiency of converting multiple inputs into multiple outputs. The previous studies that have used DEA as related to retail industry field are now described as follows. Thomas et al. (1998) implemented DEA to probe the intra-comparative efficiency using 500 domestic retail outlets of a leading specialist retailer in U.S. This study showed that DEA not only helped make sense of the data in deriving an overall efficiency index, but also identified the best practice stores within the organization by focusing on the efficiency frontier. By using the DEA approach, Keh and Chu (2003) adopted a three–stage transformation process to assess the operating efficiency of 13 grocery stores in the U.S. for the years 1988 through 1997. The finding showed that there were increasing returns to scale in grocery retailing.
Barros and Alves (2003) implemented DEA to explore operating efficiency for a Portuguese retail store. This study showed competitiveness should be based on benchmarking the retail outlets which composed the chain. Barros and Alves (2004) estimated total productivity change for a Portuguese retail store chain with the DEA-Malmquist productivity index for the period 1999-2000. This study reported that there is room for improvement in the management of the stores. Barros (2005) utilized the stochastic frontier model (SFA) to assess the technical efficiency of a Portuguese hypermarket
retail chain. This study proposed a modification of management procedures in order to enable efficiency to be increased, based on a governance-environment framework. Chen et al. (2005) assessed 13 companies in the retail industry by using the super-efficiency DEA.
This analysis indicated that the EB companies performed better in some areas than their non-EB counterpart. Table 1 presents the characteristics of these main previous studies using DEA.
Table 1. Literature survey of the DEA model on the retail industry
Paper Model Units Inputs Outputs
Thomas, Barr, (3) location related costs, (4) internal processes.
(3) assurance of product delivery, (4).product information,
(1) number of full-time employees, (2) cost of labors,
(3) number of cash-out points, (4) stock,
47 retail outlets of the Portugal, 1999-2000.
(1) number of full-time employees, (2) cost of labors,
(3) number of cash-out points, (4) stock,
(5) other costs.
(1) sales,
(2) operational results.
Barros (2005) Stochastic Frontier Approach (SFA)
47 retail outlets of the Portugal, 2000.
(1) price of labour, (2) price of capital, (3) sales at constant price, (4) earnings before taxes, (5) population,
(6) number of competitors, (7) the rate of part-time workers, (8) average days of staff
absenteeism,
(9) the purchasing power in the area.
(1) operational cost.
Chen, Motiwalla, and Khan (2005)
Super-efficiency 10 companies of the retail industry of the U.S., 1997-2000.
(1) number of employees, (2) inventory cost, (3) total current assets, (4) cost of sales.
(1) revenue, (2) net income.
To summarize the above studies, few research studies about the retail industry have been conducted in emerging countries (such as Taiwan) while applications of DEA for the
evaluation of retail stores have been very limited in the military. The main interest of this study is to address the issues related to the performance benchmarking analysis and to illustrate the use of a context-dependent DEA for evaluating GWSM retail stores, which should provide additional managerial insights into GWSM. The important contributions of this study include: (1) to provide a milestone analysis based on DEA to investigate Taiwan and assist the MND in improving the operational management of GWSM; (2) to design a decision-making matrix to identify the position of the 31 retail stores, which help the manager and/or authorities to improve their operating efficiencies; and (3) to implement the context-dependent DEA to draw the GWSM retail stores’ benchmark-learning roadmap to improve the inefficient retail stores progressively and can identify the best retail store.
Chapter 3. Research Design
3.1 Data Selection and Description
GWSM is in charge of the supply of supplementary foods and products in the military and provides its service to the soldiers, veterans, and their dependents. From a system perspective, organizational activities refer to the conversion of inputs in various resources to output. Output is a concrete measurement that an organization has reached its objectives.
This study uses the production approach to design the performance model. The performance model measures the performance of retail stores in using four inputs to produce four outputs.
The four input factors are namely the number of full-time employees (in persons), operating expenses (in NT$), cost of products (in NT$), and area of the retail store (in square meters). The employee factor is composed of businessmen, administrators, guards, drivers, and affair employees. These employees keep retail stores operating normally. The cost regarding maintenance, marketing, and administration makes up a so-called operating expense factor which is a necessary input for maintaining operations. The cost of products is used to purchase product so as to provide supplementary foods and products to the soldiers, veterans, and their dependents. The area of the retail store refers to the total floor space used by the operational units of the retail store, measured in square feet. The service outputs are measured in terms of quantitative outputs (number of customers and net profit) and qualitative outputs (consumer-satisfaction index and facilities-satisfaction index) which are the result of a brief questionnaire set to guests after shopping (as in figure 3).
This study investigates thirty-one GWSM retail stores in Taiwan based on the retail stores’ operation data shown in the period 2003. Each of these retail stores is treated as a decision making unit (DMU) in the DEA analysis. The 31 retail stores of various
geographical dispersion are selected since they are in charge of the supply of supplementary foods and products. The performances of the retail stores are accessed based on the data obtained for the year 2003. The data are extracted from the annual report of the GWSM except for consumer-satisfaction index and the facilities-satisfaction index. The service-satisfaction index can divide into consumer-satisfaction index and the facilities-satisfaction index two parts. We traveled to the 31 GWSM stores and asked for one thousand one hundred and seventeen customers to fill in the Service-Satisfaction Questionnaire (as in appendix A) in two months. We combined consumer-satisfaction index and the facilities-satisfaction index and divided by two which can get the service-satisfaction index. Table 2 presents descriptive statistics for our dataset. In table 2, we can find the mean of net profit is negative that means the general GWSM stores have poor operation performance. This is another reason why we need to do this research for improving the GWSM stores efficiency. Because of the reorganization in MND, the circumstance and Data are dynamic for each year. We only can select the data from the recent published document;
otherwise it can not match the real situation. Input/output data are reported as the total number throughout the year and can be found in The Operating Report of General Welfare Service Ministry in Taiwan published by the GWSM in November 2004, the most recent published document.
Input Factors
1.the number of employees :
•businessmen,
•administrators,
•guards, drivers,
• affair employees
.
Output Factors
provide supplementary foods / product 4,area of the retail store:
total floor square feet
Figure 3. Managerial Performance Model
Table 2. Descriptive statistics for the 31 GWSM retail stores in Taiwan
Mean Minimum Maximum Std. Dev. Valid N
Input factors
Employees (persons) 34 26 47 5 31 Operating expenses (NT$) 10,908,379 5,733,262 17,990,931 3,659,243 31 Cost of products (NT$) 159,846,440 35,446,619 299,696,847 84,295,358 31 Square feet of retail store 1,509 185 3,826 884 31 Output factors
Customers (persons) 337,676 67,839 696,274 176,170 31 Net profit (NT$) -2,702,147 -8,169,347 2,887,210 2,621,810 31 Customer-satisfaction index (%) 88.06 77 97 6.17 31 Facilities-satisfaction index (%) 83.58 73 93 6.12 31
Table 3 shows the correlation matrix of inputs x and outputsi y . Notice that all the i correlation coefficients are positive. Therefore, these inputs and outputs hold ‘isotonicity’
relations, and thus these variables are justified to be included in the model. Cooper et al.
(2001) suggested that the number of retail stores should be at least triple to the number of
inputs and outputs considered. In this study the number of retail stores is 31, which is larger than triple the number of inputs (4)/outputs(4), or 31>3(4+4) = 24. It can conform to Golany & Roll experience rules the number of retail stores is larger than triple the number of inputs plus outputs. Consequently, the developed DEA model should hold high construct validity in this study.
Table 3. Correlation coefficients among inputs and outputs
Net profit Customers Customer-Satisfaction index
Facilities-Satisfaction index
0.1055 0.7813 0.0137 0.0170 Employees
p=0.572 p=0.000 p=0.942 p=0.928 0.3394 0.1994 0.0856 0.0112 Operating expenses
p=0.062 p=0.282 p=0.647 p=0.952 0.5978 .9659 0.3672 0.3623 Cost of products
p=0.000 p=0.000 p=0.042 p=0.045 0.0155 0.7746 0.0378 0.0124 Square feet of retail store
p=0.934 p=0.000 p=0.840 p=0.947
3.2 Methodology: Data Envelopment Analysis Model
3.2.1 Efficiency Measurement Concepts
DEA is known as a mathematical programming method for assessing the comparative efficiencies of a decision making unit (DMU). DEA is a non-parametric method that allows for an efficient measurement, without specifying either the production functional form or weights on different inputs and outputs. This methodology defines a non-parametric best practice frontier that can be used as a reference for efficiency measurement which can be found in Cooper et al. (2000).
The input-oriented technical efficiency implies “by how much can input quantities be proportionally reduced without changing the output quantities produced?” The efficiency frontier presents that each DMU minimizes its inputs, keeping the output level constant.
DMUs on the frontier are efficient, while DMUs inside the frontier are inefficient. Consider the case of a single input x and a single output . In Figure 4, the constant returns to scale (CRS) frontier is a simple ray (ray 0C) through the origin that envelops the data. The efficient DMU at point C lies on this frontier and its technical efficiency (TE) score equals one. The other four DMU stores (B, E, D, F) operating inside the frontier are inefficient.
The TE score for the DMU operating at point E is defined by y
PQ PE . However, the CRS assumption is only appropriate when all DMU stores are operating at an optimal scale.
Many realistic factors, such as imperfect competition, financial constraints, etc., may cause a DMU not to operate at optimal scale. Thus, there is also a variable returns to scale (VRS) DEA model. In Figure 4, the VRS frontier is the piecewise linear frontier ABCD. This general form envelops the data more closely. The DMUs at B, C, and D lying on this frontier are efficient with a score of one. The relative inefficient DMU E is given by a pure technical efficiency (PTE) score (PR PE ). The TE is decomposed into PTE and scale efficiency (SE). The SE can be estimated by dividing PTE into TE.
To investigate the current operating region to scale inefficient DMU stores, this may be determined by running an additional DEA problem with non-increasing returns to scale (NIRS) imposed. This may be determined by running an additional DEA problem with non-increasing returns to scale (NIRS) imposed. The NIRS DEA frontier is also plotted in Figure 4. The nature of the scale inefficiencies (i.e. due to increasing or decreasing returns to scale) for a particular DMU can be determined by seeing whether the NIRS TE score is equal to the VRS TE score. If they are unequal (as will be the case for the point E in Figure
4), then increasing returns to scale (IRS) exist for the DMU. If they are equal (as is the case for point F in Figure 4), then decreasing returns to scale (DRS) apply.
Figure 4. Graphical Illustration of Measuring Technical Efficiency (Input-Oriented DEA Using a Single Input to Produce a Single Output)
3.2.2 Multiplier Model of the CCR/BCC Model
DEA is a mathematical model that measures the relative efficiency of decision-making units with multiple inputs and outputs but with no obvious production function to aggregate the data in its entirety. Relative efficiency is defined as the ratio of total weighted output to total weighted input. By comparing n units with outputs denoted by s y , ro r= … , 1, ,s and m inputs denoted by x , ,io i= …,m, the efficiency measure ho for the target
( ) is
DMUo
1, , o= … n
1
where the weights, and , are non-negative. A second set of constraints requires that the same weights, when applied to all DMUs, do not provide any unit with efficiency greater than one. This condition appears in the following set of constraints:
ur vi
The efficiency ratio ranges from zero to one, with the target being considered relatively efficient if it receives a score of one. Thus, each unit will choose weights so as to maximize self-efficiency, given the constraints. The result of the DEA is the determination of the hyper planes that define an envelope surface or Pareto frontier. DMUs that lie on the surface determine the envelope and are deemed efficient, whilst those that do not are deemed inefficient. The formulation described above can be translated into a linear program, which can be solved relatively easily and a complete DEA solves linear programs, one for each DMU.
Eq. (1), often referred to as the CCR model (Charnes et al., 1978), assumes that the production function exhibits constant returns to scale. The BCC model (Banker et al., 1984) adds an additional constant variable, uo, in order to permit variable returns to scale:
1
It should be noted that the results of the CCR input-minimized or output-maximized formulations are the same, which is not the case in the BCC model. Thus, in the output-oriented BCC model, the formulation maximizes the outputs given the inputs and vice versa.
3.2.3 The Dual Program of the CCR/BCC Model
If a DMU proves to be inefficient, a combination of other efficient units can produce either greater output for the same composite of inputs; use fewer inputs to produce the same composite of outputs or some combination of the two. A hypothetical decision making unit can be composed as an aggregate of the efficient units, referred to as the efficient reference set for inefficient . The solution to the dual problem of the linear program directly computes the multipliers required to compile efficient units. The pure technical efficiency (PTE) of the target ( ) in the BCC model can be computed as a solution to the following linear programming (LP) problem.
DMUo
In the case of an efficient DMU, all dual variables will equal zero except for λo and
θo, which reflect the ’s efficiency, both of which will equal one. If is inefficient,
DMUo DMUo
θo will equal the ratio solution of the primal problem. The remaining variables, λj, if positive, represent the multiples by which ’s inputs and outputs should be multiplied in order to compute the composite efficient DMU. If
DMUo
1 1
n j= λj =
∑
is droppedfrom Eq.(3), then the technology is said to exhibit constant returns to scale (CRS). The technical efficiency (TE) of the target DMUo is defined as TE = θo under the input-oriented CRS model (Charnes et al., 1978).
3.2.4 The Slack-Adjusted CCR/BCC Model
In the slack-adjusted DEA models, see for example model (3), a weakly efficient DMU will now be evaluated as inefficient, due to the presence of input and output oriented slacks
and , respectively. The pure technical efficiency (PTE) of the target
( ) in the BCC model can be computed as a solution to the following linear programming (LP) problem. smaller than one, then is technically inefficient. The solution value of
s− s+ DMUo
DMUo λj
indicates whether DMUj serves as a role model or peer for DMUo. If λj = , then 0 is not a peer. However, if
DMUj λj > , say 0 λj =0.4, then is a peer DMU
with a 40 percent weight placed on deriving the target efficient output and input levels for . For an inefficient , we have the expression in Eq. (5).
DMUj
DMUo DMUo
1 can be improved and become efficient by deleting its excess input and augmenting the shortfall output as follows:
(
,This operation is called BCC-projection.
If is dropped from Eq.(4), then the technology is said to exhibit constant
returns to scale (CRS). The technical efficiency (TE) of the target is defined as
=
TE θo under the input-oriented CRS model (Charnes et al., 1978). The scale efficiency (SE) for the target DMUo is then obtained as.
/
SE=TE PTE. (7)
The represents the proportion of inputs that can be further reduced after pure technical inefficiency is eliminated if scale adjustments are possible. It has a value of less than or equal to one. If the target has a value equal to one, then it is operating at the constant returns to scale size. If is less than one, then the target is scale inefficient and there is potential input savings through the adjustment of its operational scale.
Whether the scale inefficient should be either downsizing or expanding depends on its current operating scale.
SE
DMUo
SE DMUo
DMUo
3.2.5 Returns to Scale
There are at least three different basic methods of testing a DMU's returns to scale (RTS) nature which have appeared in the DEA literature. Banker (1984) shows that the CCR model can be employed to test for DMUs' RTS using the concept of most productive scale size (MPSS), i.e. the sum of the CCR optimal lambda values can determine the RTS classification. This method is called the CCR RTS method. Banker et al. (1984) report that a new free BCC dual variable ( ) estimates RTS by allowing variable returns to scale (VRS) for the CCR model, i.e. the sign of determines the RTS. We call this method the BCC RTS method. Finally, Färe et al. (1985) provide the scale efficiency index method for the determination of RTS using DEA. These three RTS methods, in fact, are equivalent but different presentations (Banker et al., 1996; Färe et al., 1994; Zhu et al., 1995).
uo
uo
The three basic RTS methods have been widely employed in real world situations (Byrnes et al., 1984; Charnes et al., 1989; Zhu, 1996a). However, it has been noted that the CCR and BCC RTS methods may fail when DEA models have alternate optima, i.e. the original CCR and BCC RTS methods assume unique optimal solutions to the DEA formulations. In contrast to the CCR and BCC RTS methods, the scale efficiency index method does not require information on the primal and dual variables and, in particular, is robust even when there exist multiple optima. Since it may be impossible or at least unreasonable to generate all possible multiple optima in many real world applications, a number of modifications or extensions of the original CCR and BCC methods have been developed to deal with multiple optima.
Banker and Thrall (1992) generalize the BCC RTS method by exploring all alternate optima in the BCC dual model, i.e. RTS in their extended technique is measured by intervals for uo. Banker et al. (1995) further modified the technique to avoid the need for examining
all alternate optima. Using the same technique, Banker et al. (1996) introduce a modification to the CCR RTS method by determining the maximum and minimum values of
1 n
j= λj
∑
in the CCR model in order to reach a decision. On the other hand, by the scale efficiency index method, Zhu and Shen (1995) suggest a remedy for the CCR RTS method under possible multiple optima.According to the recent result of Zhu and Shen (1995), one can easily estimate the returns to scale (RTS) by the CCR and BCC scores and
∑
nj=1λj in any optimal solution to the CCR model without exploring all possible multiple optimal solutions. That is, if CCR score is equal to the BCC score, then CRS (constant return to scale) prevails; otherwise, if the CCR and BCC scores are not equal, then1 1
n j= λj <