Imprecise Data Envelopment Analysis: Concepts, Methods, and Interpretations
DEA has proven to be a useful tool for assessing efficiency or productivity of organizations. While DEA assumes exact input and output data, the development of imprecise DEA (IDEA) broadens the scope of applications to efficiency evaluations involving imp
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Imprecise Data Envelopment Analysis: Concepts, Methods, and Interpretations K. Sam Park
Abstract DEA has proven to be a useful tool for assessing efficiency or productivity of organizations. While DEA assumes exact input and output data, the development of imprecise DEA (IDEA) broadens the scope of applications to efficiency evaluations involving imprecise information which implies various forms of ordinal and bounded data often occurring in practice. The primary purpose of this article is to review what has been developed so far, including the body of concepts and methods that go by the name of IDEA. This review comprises (a) why we look at imprecise data and how to elicit imprecise information, (b) how to calculate the efficiency measures, and (c) how we can interpret the resulting efficiency. Special emphasis will be placed on how to deal with strict inequality types of imprecise data, such as strict orders and strict bounds, rather than weak inequalities. A general approach to these strict imprecise data is presented, in order to arrive at efficiency scores. This approach first constructs a nonlinear program, transform it into a linear programming equivalent, and finally solve it via a two-stage method. Keywords Imprecise data envelopment analysis
Fuzzy sets Fuzzy DEA
1 Introduction This article is concerned with the use of imprecise data in data envelopment analysis (DEA). Imprecise data implies that some data are known only to the extent that the true values lie within prescribed bounds while other data are known only in terms of ordinal relations. [1, 2] showed how DEA could be extended to treat ordinal data. To deal with all aspects of imprecise data in DEA, [3] proposed
K. S. Park (&) Business School, Korea University, Anam-5 Ga, Seongbuk, Seoul 136-701, Korea e-mail: [email protected]
A. Emrouznejad and M. Tavana (eds.), Performance Measurement with Fuzzy Data Envelopment Analysis, Studies in Fuzziness and Soft Computing 309, DOI: 10.1007/978-3-642-41372-8_2, Springer-Verlag Berlin Heidelberg 2014
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a body of concepts and methods that go by the name of imprecise data envelopment analysis (IDEA). There have since been a number of refinements, extensions, and applications [4–11]. These studies have also developed different methods for solving a nonlinear IDEA problem because some inputs and outputs are unknown decision variables with values to be determined in the model. Although the computational algorithms are different, they result in the same efficiency scores and, hence, the same efficiency classifications into efficient and inefficient groups. Still further extensions of the IDEA approach have been made. [12] treated interval or bounded data in DEA and showed how the upper and lower bounds of efficiency could be achieved in order to accomplish more detailed classifications of efficiency performance, a three-group efficiency classification rather than the customary two-group partition. Later, [13] developed an extended method to handle ordinal as well as interval data a
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