Integrating fuzzy goal programming and data envelopment analysis to incorporate preferred decision-maker targets in effi
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Integrating fuzzy goal programming and data envelopment analysis to incorporate preferred decision-maker targets in efficiency measurement Debora Di Caprio1,2 · Ali Ebrahimnejad3 · Mojtaba Ghiyasi4 · Francisco J. Santos-Arteaga5 Received: 11 November 2019 / Accepted: 20 July 2020 © Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 2020
Abstract Data envelopment analysis (DEA) is a nonparametric frontier assessment method used to evaluate the relative efficiency of similar decision-making units (DMUs). This method provides benchmarking information regarding the removal of inefficiency. In conventional DEA models, the view of the decision maker (DM) is ignored and the performance of each DMU is solely determined by the observations retrieved. The current paper exploits the structural similarity existing between DEA and multiple objective programming to define a model that incorporates the preferences of DMs in the evaluation process of DMUs. Given the potential unfeasibility of the input and output targets selected by the DM, the model defines an interactive procedure that considers minimum and maximum acceptable objective levels. Given the feasible levels located closer to the targets selected by the DM, a program improving upon the feasible allocations is designed so that the suggested benchmark approximates the requirements fixed by the DM as much as possible. A real-life case study is included to illustrate the efficacy and applicability of the proposed hybrid procedure. Keywords Data envelopment analysis · Fuzzy goal programming · Multiple objective linear programming · Subjective preferences · Target setting · Efficiency JEL Classification C610 · D810
1 Introduction Data envelopment analysis (DEA) was originally proposed by Charnes, Cooper and Rhodes (CCR) in 1978 to evaluate the relative efficiency of a set of decision-making
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Francisco J. Santos-Arteaga [email protected]
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units (DMUs). The main practical contribution of DEA resides in the provision of benchmarking information that can be used to improve the efficiency of the different DMUs. However, conventional DEA models do not incorporate the preferences of the decision maker (DM) in the evaluation process. That is, the performance of each DMU is assessed based on the input and output observations and the DM viewpoint has no role in the evaluations. Different methods were initially suggested to include the preferences of DMs in the performance evaluation of DMUs. For instance, Golany (1988) introduced the so-called target setting model, which allows DMs to select the preferred set of output levels given the input levels of a DMU. Charnes and Cooper (1990) adjusted the observed input and output weights to capture value judgments within a closed cone polyhedral. Restrictions on the set of weights were defined by Dyson and Thanassoulis (1988), while Thompson et al. (1990) incorporated an assurance region to the analysi
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