یک مطالعه درباره انتخاب مسیر الگوبرداری در تحلیل پوششی داده ها(DEA)

One of the existing DEA methods’ limitations noted in the literature lies in the process of benchmarking of reference targets for inefficient DMUs. Difficulties arising in this process can be summarized to three aspects. First, the reference target might be a hypothetical DMU that does not actually exist (it is difficult and indeed unrealistic to learn from such a DMU). Second, the reference set of an inefficient DMU often has multiple efficient DMUs making it difficult to benchmark multiple best-practice DMUs simultaneously. Third, it is quite impossible for an inefficient DMU to achieve its target’s efficiency in a single step, especially when the inefficient DMU is far from the efficient frontier. In order to overcome these difficulties, we propose, in place of the selection of benchmarked DMUs on the efficient frontier, a method of selecting effective benchmarking paths that direct an inefficient DMU to its target on the efficient frontier in an implementable and realistic way. The proposed method was designed based on the idea of the context-dependent DEA proposed by Seiford and Zhu (2003). It starts by clustering DMUs into several layers according to their efficiency scores, and then establishes a benchmarking path across the sequence of layers. Among the DMUs in the next layer, the most preferable one is selected as the next benchmark target, based on three criteria: attractiveness, progress, and infeasibility. We tested the proposed method by applying it to the evaluation of the relative efficiency of operations of 26 container terminals located in Asia.

DEA (Data Envelopment Analysis) is a non-parametric linear programming based technique for assessing the relative efficiencies of a homogeneous set of Decision Making Units (DMUs) having multiple inputs and outputs. DEA has been widely utilized as a tool for evaluating and improving the performance of manufacturing and service operations in many application areas including schools, hospitals, banks, and public organizations. It is now recognized as a general methodology for solving multi-criteria decision-making problems (Talluri, 2000). Many papers on DEA applications have been published: Grosskopf and Moutray (2001) (education programs), Shafer and Byrd (2000) (IT investments), Donthu, Hershberger, and Osmonbekov (2005) (marketing), Mcmullen and Frazier (1998) (assembly-line balancing), Sueyoshi, Ohnishi, and Kinase (1999) (baseball teams), Luo (2003) (banks), Chang (1998) (hospitals), and others, to name only a few. There are several reasons DEA has been so successfully applied: it is a non-parametric technique that does not require any assumptions on the production function defining the relationship between inputs and outputs; it can consider multiple inputs and outputs simultaneously; it distinguishes efficient DMUs from inefficient ones, and it provides a proper benchmarking plan for inefficient DMUs. In DEA, the efficiency score is defined as the ratio of the weighted sum of outputs to the weighted sum of inputs. DMUs having an efficiency score of 1 are considered efficient whereas a score of less than 1 implies that the pertinent DMU is inefficient. Each DMU gives weights, obtained by linear programming, to inputs and outputs in a way that maximizes its efficiency score. DEA, in addition to determining the relative efficiency score of a DMU, identifies a set of efficient units that can be utilized as benchmarks for that DMU’s improvement. It should be noted, however, that DEA is primarily a diagnostic tool and does not prescribe any reengineering strategies to make inefficient units efficient (Talluri, 2000). DEA has been applied in diverse areas, and has seen significant methodological advances as well. Ever since Charnes, Cooper, and Rhodes (1978) introduced the basic DEA model (the CCR model) as a new way to measure the efficiency of DMUs, a number of DEA variants have been developed: the BCC model (Banker, Charnes, & Cooper, 1984), which assumes a variable return to scale, the non-radial additive model (Charnes, Cooper, Golany, Seiford, & Stutz, 1985); the Banker and Morey (1986) model, which involves qualitative inputs and outputs, and the Roll and Golany (1989) model, in which input–output weights are restricted to certain ranges of values. The practical application of DEA requires that a range of procedural issues be examined and resolved, including those that relate to the homogeneity of units under assessment, the input/output set selected, the weights attributed to them, and the reference targets to benchmark. Among these, the present study focused on the benchmarking of reference targets for inefficient DMUs, the purpose of this paper being to suggest a new method by which inefficient DMUs can reach benchmark targets. Difficulties arising in benchmarking reference targets for an inefficient DMU can be summarized to three aspects. First, the reference target might be a hypothetical DMU that does not actually exist. The efficiency of an inefficient DMU is measured relative to an efficient DMU or a convex combination of DMUs on the efficient frontier, which serves as a target for improvement. However, the target, when given as a combination of efficient DMUs, is not an actually existing DMU, but a hypothetical one, and it is difficult, indeed unrealistic, to learn from a DMU that does not exist. Second, it is not easy to benchmark multiple best-practice DMUs in the reference set simultaneously. The efficient DMUs that have positive weights in the combination yielding the hypothetical target DMU comprise the reference set of an inefficient DMU. And when the reference set of an inefficient DMU has multiple efficient DMUs, the inefficient DMU has multiple targets to benchmark, which is an obviously confounding situation. Third, it is very likely to be practically infeasible for an inefficient DMU to achieve the target’s efficiency in a single step. That is, if the inefficient DMU is far from the efficient frontier, it will be impossible to reach the frontier in a single move, the more reasonable alternative being to make stepwise gradual improvements in getting to the target. In this paper, we propose an effective benchmarking path selection method that overcomes the DEA limitations discussed above by directing an inefficient DMU to its ultimate target in an implementable and realistic way. The proposed method was devised based on the idea of the context-dependent DEA proposed by Seiford and Zhu (2003). It starts by clustering DMUs into several layers according to their efficiency scores, and then establishes a benchmarking path across the sequence of layers. Among the DMUs in the next layer, the most preferable one is selected as the next benchmark target, based on three criteria: attractiveness, progress, and infeasibility. This paper is organized as follows. Section 2 provides a brief overview of DEA methodology and the benchmarking difficulties of present concern. Section 3 presents the proposed method and considers the application-prerequisite issues. Section 4 provides details of an empirical study on the proposed method, in which the relative efficiencies of 26 container terminals located in Asia were evaluated. Section 5 summarizes our work and suggests directions for future research.

This research developed a method of selecting effective benchmarking paths on which inefficient DMUs can reach their ultimate targets on the efficient frontier in a more practically feasible way. The proposed method starts by clustering DMUs into several layers according to their efficiency scores, after which it establishes a benchmarking path across the sequence of layers. Among the DMUs in the next layer, the most preferable one is selected as the next benchmark target according to the criteria of attractiveness, progress, and infeasibility. The proposed method was designed to tackle the limitations of the conventional DEA-based benchmarking. To that end, the first salient point is that benchmarking paths constructed by the proposed method are composed of a series of DMUs, each of which is selected from a sequence of layers of DMUs resulting from the stratification procedure. This kind of gradual improvement schedule helps inefficient DMUs to avoid the practical infeasibility of achieving the target’s efficiency in a single step, especially when they are far from the efficient frontier. The second point to consider is that the proposed method, when establishing benchmarking paths, selects existing DMUs from a sequence of layers of DMUs, thereby avoiding any confusion that might otherwise result from benchmarking DMUs that do not actually exist. Thirdly, by selecting a single DMU as a target for subsequent improvement instead of multiple ones, the proposed method overcomes the practical difficulties of referring to multiple benchmarks, which is often the case in the conventional DEA-based benchmarking. Furthermore, the selection of benchmark targets is based on a composite index of three criteria, including attractiveness, progress, and infeasibility, which makes the resultant benchmarking paths more effective, efficient, and practically feasible. We should note that, when establishing benchmarking paths, it might be possible to find, rather than the best path at each level, the overall best path. Roughly speaking, defining xkp as the binary decision variable that is assigned the value 1 when DMU p is selected as a target for DMU k, and 0 otherwise, we can build a 0–1 integer mathematical programming model to find the overall optimal benchmarking path that maximizes the sum of Skpxkp. This will be our future research topic. Finally, we have to admit that the container terminal experiment referred to in Section 4 was not a full-scale application, but rather a partial-scale study utilized just to illustrate the proposed method. Various considerations needing to be taken into account for a fully justifiable DEA application were simplified or ignored.