Showing papers by "Kaoru Tone published in 2001"

A Slacks-based Measure of Super-Efficiency in Data Envelopment Analysis

Abstract: In most models of Data Envelopment Analysis (DEA), the best performers have the full efficient status denoted by unity (or 100%), and, from experience, we know that usually plural Decision Making Units (DMUs) have this “efficient status”. To discriminate between these efficient DMUs is an interesting subject. This paper addresses this “super-efficiency” issue by using the slacks-based measure (SBM) of efficiency, which the author proposed in his previous paper [European Journal of Operational Research 130 (2001) 498]. The method differs from the traditional one based on the radial measure, e.g. Andersen and Petersen model, in that the former deals directly with slacks in inputs/outputs, while the latter does not take account of the existence of slacks. We will demonstrate the rationality of our approach by comparing it with the radial measure of super-efficiency. The proposed method will be particularly useful when the number of DMUs are small compared with the number of criteria employed for evaluation.

Sensitivity and Stability Analysis in DEA: Some Recent Developments

Abstract: This paper surveys recently developed analytical methods for studying the sensitivity of DEA results to variations in the data. The focus is on the stability of classification of DMUs (Decision Making Units) into efficient and inefficient performers. Early work on this topic concentrated on developing solution methods and algorithms for conducting such analyses after it was noted that standard approaches for conducting sensitivity analyses in linear programming could not be used in DEA. However, some of the recent work we cover has bypassed the need for such algorithms. Evolving from early work that was confined to studying data variations in only one input or output for only one DMU at a time, the newer methods described in this paper make it possible to determine ranges within which all data may be varied for any DMU before a reclassification from efficient to inefficient status (or vice versa) occurs. Other coverage involves recent extensions which include methods for determining ranges of data variation that can be allowed when all data are varied simultaneously for all DMUs. An initial section delimits the topics to be covered. A final section suggests topics for further research.

On Returns to Scale under Weight Restrictions in Data Envelopment Analysis

Abstract: Weextend the concept of returns to scale in Data Envelopment Analysis(DEA) to the weight restriction environments. By the additionof weight restrictions, the status of returns to scale, i.e., increasing, constant and decreasing may suffer a change. Wefirst define ``returns to scale'' under weight restrictions andpropose a method for identifying the status of returns to scale.Then, it is demonstrated that the region of the most productivescale size (MPSS) will usually be narrowed by this addition.For an inefficient decision making unit (DMU), a simple rulefor determining the status of returns to scale of its projectedDMU will be presented. An empirical study compares the resultsof the proposed method with those of the BCC model and demonstratesthe change in the MPSS for both models.