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European Journal of Operational Research xxx (2008) xxx–xxx www.elsevier.com/locate/ejor

Invited Review

Data envelopment analysis (DEA) – Thirty years on
Wade D. Cook a,*, Larry M. Seiford b
a

Department of Operations Management and Information Systems, Schulich School of Business, York University, Toronto, Ontario, CanadaM3J 1P3 b Industrial and Operations Engineering, College of Engineering, University of Michigan, Ann Arbor, MI, United States Received 19 January 2008; accepted 22 January 2008

Abstract This paper provides a sketch of some of the major research thrusts in data envelopment analysis (DEA) over the three decades since the appearance of the seminal work of Charnes et al. (1978) [Charnes, A.,Cooper, W.W., Rhodes, E.L., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444]. The focus herein is primarily on methodological developments, and in no manner does the paper address the many excellent applications that have appeared during that period. Specifically, attention is primarily paid to (1) the various models for measuring efficiency, (2)approaches to incorporating restrictions on multipliers, (3) considerations regarding the status of variables, and (4) modeling of data variation. Ó 2008 Elsevier B.V. All rights reserved.
Keywords: DEA; Models; Multiplier restrictions; Data variation

1. Introduction Efficiency measurement has been a subject of tremendous interest as organizations have struggled to improve productivity. Reasonsfor this focus were best stated fifty years ago by Farrell (1957) in his classic paper on the measurement of productive efficiency. ‘‘The problem of measuring the productive efficiency of an industry is important to both the economic theorist and the economic policy maker. If the theoretical arguments as to the relative efficiency of different economic systems are to be subjected to empirical testing, itis essential to be able to make some actual measurements of efficiency. Equally, if economic planning is to concern itself with particular industries, it is important to know how far a given industry can be expected to increase its output by simply increasing its efficiency, without absorbing further resources.” Farrell further stated that the primary reason that all attempts to solve the problem hadfailed, was due to a failure to combine the measurements of the multiple inputs
*

Corresponding author. Tel.: +1 416 736 2100/33573. E-mail address: wcook@schulich.yorku.ca (W.D. Cook).

into any satisfactory measure of efficiency. These inadequate approaches included forming an average productivity for a single input (ignoring all other inputs), and constructing an index of efficiency in which aweighted average of inputs is compared with output. Responding to these inadequacies of separate indices of labor productivity, capital productivity, etc., Farrell proposed an activity analysis approach that could more adequately deal with the problem. His measures were intended to be applicable to any productive organization; in other words, ‘‘from a workshop to a whole economy.” Unfortunately,he confined his numerical examples and discussion to single output situations, although he was able to formulate a multiple output case. Twenty years after Farrell’s seminal work, and building on those ideas, Charnes et al. (1978), responding to the need for satisfactory procedures to assess the relative efficiencies of multi-input multi-output production units, introduced a powerful methodologywhich has subsequently been titled data envelopment analysis (DEA). The original idea behind DEA was to provide a methodology whereby, within a set of comparable decision making units (DMUs), those exhibiting best practice could be identified, and would form an efficient frontier.

0377-2217/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2008.01.032

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