一种AHP/DEA方法对决策单元进行排名外文翻译资料

Intl. Trans. in Op. Res. 7 (2000) 109plusmn;124

An AHP/DEA methodology for ranking decision making units

Zilla Sinuany-Stern*, Abraham Mehrez, Yossi Hadad

Department of Industrial Engineering and Management, Ben-Gurion University, P.O. Box 653, Beer-Sheva, Israel

Received 24 March 1999; received in revised form 30 November 1999; accepted 15 December 1999

Abstract

This paper presents a two-stage model for fully ranking organizational units where each unit has multiple inputs and outputs. In the first stage, the Data Envelopment Analysis (DEA) is run for each pair of units separately. In the second stage, the pairwise evaluation matrix generated in the first stage is utilized to rank scale the units via the Analytical Hierarchical Process (AHP). The consistency of this AHP/DEA evaluation can be tested statistically. Its goodness of fit with the DEA classification (to ebull;cient/inebull;cient) can also be tested using non-parametric tests. Both DEA and AHP are commonly used in practice. Both have limitations. The hybrid model AHP/DEA takes the best of both models, by avoiding the pitfalls of each. The nonaxiomatic utility theory limitations of AHP are irrelevant here: since we are working with given inputs and outputs of units, no subjective assessment of a decision maker evaluation is involved. AHP/DEA ranking does not replace the DEA classification model, rather it furthers the analysis by providing full ranking in the DEA context for all units, ebull;cient and inebull;cient. 7 2000 IFORS. Published by Elsevier Science Ltd. All rights reserved.

Keywords: Data envelopment analysis (DEA); Analytical hierarchical process (AHP); Multi-criteria decision analysis (MCDA); Decision theory; Ranking; Scaling; Eciency

1. Introduction

In this paper, we deal with the problem of fully ranking organizational units in the DEA context (see Charnes et al., 1978). In the DEA, for each organizational unit, based on its given

multiple inputs and outputs (for a certain period), the units are classified into two dichotomic groups: ebull;cient and inebull;cient. Since 1978, DEA has developed in many directions and in numerous applications, as summarized by Seiford (1996) who cites almost a thousand publications.

Many researchers (e.g., Belton and Vickers, 1993) highlight the relationship between DEA and Multi-Criteria Decision Analysis (MCDA): ``Indeed in common with many approaches to multiple criteria analysis, DEA incorporates a process of assigning weights to criteria (see also other references, Belton, 1992; Cook et al., 1990, 1992; Doyle and Green, 1993; Stewart, 1994, 1996). Ranking is very common in MCDA literature, especially when we have a discrete list of elements or alternatives with single or multiple criteria which we wish to evaluate and compare or select. Various approaches are suggested in the literature for fully ranking elements, ranging from the utility theory approach (see Keeney and Rai a, 1976; Keeney, 1982; Sinuany-Stern and Mehrez, 1987; Fishburn, 1988), to the AHP developed by Saaty (1980).

The pareto optimum concept on which DEA is founded is well accepted by various disciplines such as economics, MCDA and statistics. It is often also called `admissible solution, `dominant solution or even `ebull;cient frontier. Nevertheless, the pareto principle has its own drawbacks. To clarify this statement, if we consider the following two vector solutions: (20, 50, 10) and (20¹⁰, 50¹⁰, 10 yuml; edagger; when e is very small, then, in formal terms, according to the pareto optimum principle, these two vectors are ebull;cient solutions in relation to each other. However, every decision maker will obviously prefer the second solution, (most MCDA ranking methods will point to the second solution as a better one). This example well clarifies the limitation of the DEA.

MCDA ranks elements on the basis of single or multiple criteria, where each contributes positively to the overall evaluations. The evaluations are often carried out subjectively by the decision maker. However, DEA deals with classifying the elements (units) into two categories, ebull;cient and inebull;cient, based on two sets of multiple criteria: multiple inputs contributing negatively to the overall evaluation and multiple outputs contributing positively to the overall evaluation. The original DEA does not perform full ranking, it merely provides classification into two dichotomic groups: ebull;cient and inebull;cient. It does not rank them ETH; all ebull;cient units are equally good (receiving ebull;ciency 1) in the pareto sense. Nevertheless, during the last decade, there have been attempts to fully rank units in the context of DEA. Cook and Kress (1990), Cook et al. (1992), and Green et al. (1996) utilize subjective decision analysis approaches. Norman and Stoker (1991) suggest a stepwise approach, utilizing the sum of selected simple ratios between pairs of inputs and outputs. Ganley and Cubbin (1992) develop common weights for all the units by maximizing their sum of ebull;ciency ratios. Sinuany-Stern et al. (1994) utilize the linear discriminant analysis for ranking units, based on the pregiven DEA dichotomic classification. Friedman and Sinuany-Stern (1997) utilize the canonical correlation analysis (CCA/DEA) to fully rank the units based on common weights. Sinuany-Stern and Friedman (1998a, 1998b) develop the discriminant analysis of ratios (DR/DEA), rather than the traditional linear discriminant analysis. Oral et al. (1991) use the cross ebull;ciency matrix in order to select Ramp;D projects. Sinuany-Stern and Friedman (1998a, 1998b) use the cross ebull;ciency matrix to rank units.

As highlighted by Friedman and Sinuany-Stern (1998), each method has its limitations. Some are based on subjective data and others are limited to part of the units, yet none provides an ultimately good model for fully ranking units in the DEA context. Our current paper is another attempt to fully

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