Constructing a Benchmark-Learning Roadmap

After identifying the efficient , the role it plays in being benchmarked by other inefficient is also important. Previously, various efforts have been devoted to develop methods without priority information to identify the benchmark in DEA. One way to accomplish such a task is to count the number of times a particular efficient DMU acts as a reference DMU (Smith and Mayston, 1987). Andersen and Petersen (1993) presented the procedure referred to as the super-efficiency CCR model for ranking efficient units. Their basic idea is to compare the under evaluation with all other in the sample, i.e., the itself is excluded. Seiford and Zhu (1999) offered a super-efficiency BCC

DMU DMUs

DMU DMUs

DMU

model in which increasing, constant, and decreasing returns to scale are allowed. The model is based on a reference technology constructed from all other DMUs. Li and Reeves (1999) proposed a multiple criteria approach that is called Multiple Criteria DEA, which focuses on solving two key problems: a lack of discrimination and inappropriate weighting schemes.

To identify the inputs/outputs that are most important or to distinguish those efficient

which can be treated as benchmarks, the reference-share measure (Zhu 2000) is defined as a ranking measure by combining the factor-specific measure and BCC model. Tone (2002) wrote a super-efficiency model using the slacks-based measure of efficiency. The detail description for above methodologies can check in appendix A. To summarize the above previous studies, the benchmarks derived from the proposed methods above can possibly become unimitable or unattainable goals for the inefficient immediately. A series of step-by-step benchmarks (or called ‘a benchmark-learning roadmap’) for an inefficient retail store to learn and gradually improve its operating efficiency seems to be more realistic and reasonable.

DMUs

DMUs

In this section the context-dependent DEA, by incorporating stratification DEA, attractiveness measure, and progress measure, can draw the GWSM retail stores’

benchmark-learning roadmap to improve the inefficient retail stores progressively and can identify the best retail store. By using stratification DEA model, Eq. (3), we can get the first-level best-practice frontier when l=1. When l=2, Eq. (3) gives the second-level best-practice frontier. Then, the third-level frontier when l=3, and so on. Before continued to explain, it needs to make a definition for attractive and progress. Progress meaning the second level or third level needs to catch up the first or second level learning curve distance, in another word, it real means is falling behind degree from level two or three to level one.

Attractive meaning the first level which takes the lead level two or level three degree, that is to say, level two or level three needs do their efforts to come up with level one or level three needs to improve it’s performance to catch up with level two’s performance. (as in Figure 6)

In this research, the three levels of efficient frontiers are reported in Table 6.

According to Morita, Hirokawa, and Zhu (2005), the benchmark targets of the inefficient retail stores on level 3 should take retail stores on level 2 as initial targets to improve efficiency in the first stage. In the second stage, after retail stores on level 3 achieve the second-level efficient frontier, these on level 3 can use the first-level efficient frontier as secondary benchmarks for improvement and so on to proceed stage by stage. We call this composition of learning tracks for retail stores in different levels as a ‘benchmark-learning roadmap.’ Note that as pointed out in Chen, Morita, and Zhu (2005), the levels obtained using Eq. (3) do not necessarily follow the order of the TE scores. For instance, five retail stores (Beijhong, Miaoli, Pinglin, Tainan01, and Taoyuan01) on the third-level have a larger TE score than does Chiayi on the second-level.

Level 1 Level 2 Level 3 Attractive Progress

0

‧

Level 3

Level 2

Level 1

X2

/

X1

/

1.916

1.467

Figure 6. Context-DEA Figure: Attractive and Progress Measurement Values

Table 6. Levels of efficient frontiers

First-Level Second-Level Third-Level DMU No. DMU Name TE DMU No. DMU Name TE DMU No. DMU Name TE

2 Keelung 1 1 Neiyi 0.820 4 Beijhong 0.725 3 Beibei 1 5 Beisi 0.967 15 Miaoli 0.846 8 Sioulang 1 6 Beidong 0.877 17 Pinglin 0.771 9 Banciao 1 7 Beinan 0.925 20 Tainan01 0.684 13 Hsinchu 1 10 Shuanghe 0.882 22 Gaosyong 0.596 16 Taichung 1 12 Taoyuan02 0.794 30 Taitung 0.572 19 Hsinying 1 14 Guangfu 0.980 31 Ilan 0.614 23 Zuoying 1 18 Chiayi 0.682 11 Taoyuan01 0.731 24 Kaohsiung 1 21 Tainan02 0.745

25 Fongshan 1 28 Hualian 0.982 26 Dailiao 1

27 Pingtung 1 29 Meilun 1

We now turn to the attractiveness measure and the progress measure (Eqs. 4 and 5) of the 31 retail stores when different efficient frontiers are chosen as evaluation contexts.

Table 7 gives the results. The number of the right of each score indicates the ranking position by the attractiveness measure and progress measure ((1) represent the top-rank position). As regards to the attractiveness measure, when the second-level is chosen as the evaluation context, Hsinying in first-level is the best retail store because it has the largest attractiveness score of 5.196. The retail stores in first-level can be ranked by using attractiveness measure in the order of Hsinying Meilun, Dailiao, Hsinchu, Keelung, Taichung, Pingtung, Kaohsiung, Beibei, Zuoying, Fongshan, Sioulang, and Banciao retail stores.

Results also show that 11 out of the 13 retail stores on the first level are located on the north and south regions, indicating that retail stores located on north and south regions are more competitive. When the third-level is chosen as the evaluation context, Hsinying is still the best retail store, as followed by Meilun retail store. The findings show that Hsinying retail

store is the most attractive retail store, i.e. global leader, no matter which evaluation context is chosen.

As regards to the progress measurement, when the first-level is chosen as the evaluation context, Taitung retail store is the worst retail store in the third-level because it has the largest progress score of 1.750. The retail stores in third-level can be ranked by using progress measure. When the second-level is chosen as the evaluation context, Taitung is still the worst retail store in the third-level. The findings show that Taitung retail store is the worst retail store, no matter which evaluation context is chosen. Note that the ranking position is change for Dailiao, Hsinchu, Keelung, Taichung, Pingtung, Kaohsiung, Beibei, Zuoying, Fongshan, Sioulang, and Banciao retail stores in first-level when evaluation context is changed. This demonstrates that the performance of retail stores can be dependent on the evaluation background (Zhu, 2003).

Table 7. Attractive and progress scores for the retail stores in different evaluation context

Evaluation Context Evaluation Context Evaluation Context

Second-Level Third-Level First-Level Third-Level First-Level Second-Level

First-Level DMU

1st-Degree^a 2nd-Degree^a

Second-Level

1. ^aThis represents attractive.

2. ^bThis represents progress.

3. First level is the best performance then the second level, the third level represents the worst performance.

4. Ranks are given in parenthesis.

According to Seiford and Zhu (2003), for retail stores that are not located on the first or last level of efficient frontier, we can characterize their performance by their attractiveness and progress scores. Each retail store in the second-level is classified into a zone by examining (1) whether the attractiveness score is greater than or less than 1.80, (2) whether the progresses score is greater than or smaller than 1.25. In Figure 7 the attractiveness and progress scores give a two-by-two matrix to classify the retail stores in the second-level. A good performer shows high attractiveness and low progress and, a wrong performer shows low attractiveness and high progress. A high progress indicates that the retail store needs to improve its outputs substantially, and a high attractive indicates that the retail store have better competitive advantage than the other ones. Retail stores have been split subjectively into four groups plotted respectively in the zones of LH, HH, HL, and LL. The retail stores in each group are summarized as follows.

Zone LH: Those retail stores enjoy low progress and high attractiveness scores. Five retail stores are included here: Neiyi, Beisi, Beidong, Shuanghe, and Guangfu retail stores.

The findings show that the retail stores located on Zone LH have better competitive advantage than the other ones in the second-level.

Zone HH: The retail store experiences a higher progress and attractiveness scores.

Chiayi retail store is included. It is suggested that Chiayi retail store should place more emphasis on activities of improving its outputs substantially.

Zone HL: The retail store experiences a higher progress and lower attractiveness scores.

Taoyuan02 and Tainan02 retail stores are included. It is suggested that Taoyuan02 and Tainan02 retail stores should put forth efforts on learning more capabilities for effective outcomes such as enhancing the activities of operational management and relocating the resources between inputs and outputs. Further, these retail stores must draw up a short-term or middle-term plan to enhance its’ competitive advantage.

Zone LL: Those retail stores which have a lower progress and lower attractiveness scores. Two retail stores are included here: Beinan and Hualian retail stores. It is suggested that these retail stores must make up a short-term or middle-term plan to enhance its’ competitive advantage for moving up into the Zone LH.

Neiyi

Figure 7. Attractiveness/progress score for the retail stores in the second-level