Controlling Factor Weights in Data Envelopment Analysis YAAKOV ROLL Professor of Industrial Engineering Faculty of Industrial Engineering and Management Technion Haifa, Israel WADE D. COOK Professor of Management Science Faculty of Administrative Studies York University Toronto, Canada M3J IP3 BOAZ GOLANY Assistant Professor of Industrial Engineering Faculty of Industrial Engineering and Management Technion Haifa, Israel Abstract: Data Envelopment Analysis (DEA) is a mathematical programming approach to assessing relative ef- ficiencies within a group of Decision Making Units (DMUs). An important outcome of such an analysis is a set of virtual multipliers or weights accorded to each (input or output) factor taken into account. These sets of weights are, typically, different for each of the participating DMUs. A version of the DEA model is offered where bounds are imposed on weights, thus reducing the variation in the importance accorded to the same factor by the various DMUs. Techniques for locating appropriate bounds are suggested and the notion of a common set of weights is examined. Possible interpretations to differences in efficiency ratings obtained with the various models developed are discussed. • DEA is a systematic approach for measuring relative ef- ficiencies within a group of DMUs, which utilize several inputs to produce a set of outputs. Developed by Charnes, Cooper and Rhodes (CCR) [5], it extends the classical en- gineering approach to non-engineering environments such as not-for-profit or public sector organizations. Comparisons of DEA to other efficiency measurement approaches have been carried out by Charnes et al. [7] and Bowlin et al. [1]. For recent applications and theory on DEA see Chames et al. [2], [4], [6] and [7]. Supported under NSERC grant IIA8966 and Ontario Ministry of Trans- portation Contract 1/26108. This research was also supported by the E. and J. Bishop Fund through the Technion Vice President for Research office. Received May 1988; revised January and May 1989. Handled by the De- partment of Applied Optimization. The relative efficiency of a DMU within the DEA frame- work is defined as the ratio of weighted outputs to weighted inputs, where the model selects weights for each DMU that reflect its standing in the most favorable light. Since the DEA approach has been proposed, it has received consid- erable attention from both researchers and practitioners (see the bibliographical list in Seiford [12]). The model has been applied to such organizations as airforce maintenance units, school districts, hospitals, etc. A detailed account of a typical application, citing the rel- evant inputs and outputs, and discussing the meaning of ef- ficiency, is given in Charnes et al. [6]. In this 1981 study, the authors set out to evaluate the level of efficiency of each of a large set of school districts. Each district constitutes a DMU. The output measures used to appraise the perform- ance of the DMUs included, among other things, a math score (M) and a reading score (R). Inputs or influence fac- tors included the number of teachers (T) available in the 2 0740-817X/911$3.00x.OO © 1991 "ilE" Volume 23, Number 1, lIE Transactions, March 1991