dea - Int. Journal of Math. Analysis, Vol. 1, 2007, no. 5,...

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Int. Journal of Math. Analysis, Vol. 1, 2007, no. 5, 237 - 246 Non-Discretionary Factors and Imprecise Data in DEA F. Hosseinzadeh Lot±, 1 and G. R. Jahanshahloo Dept. of Math., Science and Research Branch Islamic Azad University, Tehran 14515-775, Iran M. Esmaeili Dept. of Math., Islamic Azad University, Shahrekord P.O. Box 166, Shahrekord, Iran Abstract Discretionary models of data envelopment analysis (DEA) assume that all inputs and outputs can be varied at the discretion of man- agement or other users. In any realistic situation, however, there may exist ”exogenously Fxed” or non-discretionary factors that are beyond the control of a DMU’s management, which also need to be considered. Also DEA requires that the data for all discretionary inputs and out- puts be known exactly. The aim of this paper is measuring the relative efficiency of decision making units with non-discretionary inputs and interval discretionary data. Keywords: DEA, Interval data, Non-Discretionary inputs, Efficiency 1 Introduction Data envelopment analysis (DEA) is a mathematical programming approach for measuring and evaluating the relative efficiency of peer decision making units (DMUs) with multiple inputs and multiple outputs (Cooper et al., 2000). Discretionary models of DEA assume that all data are discretionary, i.e., con- trolled by the management of each DMU and varied at its discretion. In real world situations, however, there may exist ”exogenously Fxed” or non- discretionary factors that are beyond the control of a DMU’s management, which also need to be considered. Banker and Morey (1996a) developed the Frst model for evaluating DEA efficiency with ”exogenously Fxed” inputs and 1 Corresponding author:±arhad Hosseinzadeh LotF, E-mail:hosseinzadeh [email protected]
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238 F. Hosseinzadeh Lotf et al. outputs in forms like ”age of store” in an analysis of a network of fast-food restaurants (See Ray 1991; also Roggiero 1996; Roggiero 1998; Mu˜ n iz, 2006). Some examples of non-discretionary factors in the DEA literature are the num- ber of competitors in the branches of a restaurant chain, snowfall or weather in evaluating the efficiency of maintenance units, soil characteristics and topogra- phy in diFerent farms, age of facilities in diFerent universities, the populations of wards in evaluating the relative efficiency of public libraries. On the other hand, DEA requires that the data for all discretionary inputs and outputs be known exactly. When some discretionary data are unknown decision vari- ables, such as interval data, ordinal data, and ratio bounded data, the DEA models become nonlinear programming problems, and this is called imprecise DEA (IDEA)(See Cooper et al. 1999; Entali et al., 2002; Zhu 2003; Zhu 2004; Despotis and Smirlis 2002). In this paper we introduce an approach for deal- ing with non-discretionary inputs and discretionary interval data in DEA. Our approach is to transform a non-linear DEA model to a linear programming equivalent, on the basis of the original data set, by applying transformations only to the variables. Upper and lower bounds for the relative efficiency scores
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dea - Int. Journal of Math. Analysis, Vol. 1, 2007, no. 5,...

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