Journal of Industrial and Management Optimization (JIMO)

An interactive MOLP method for solving output-oriented DEA problems with undesirable factors

Pages: 1089 - 1110, Volume 11, Issue 4, October 2015      doi:10.3934/jimo.2015.11.1089

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Ali Ebrahimnejad - Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr 47651-61964, Iran (email)
Madjid Tavana - Business Systems and Analytics Department, Lindback Distinguished Chair of Information Systems and Decision Sciences, La Salle University, Philadelphia, PA 19141, United States, Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, D-33098 Paderborn, Germany (email)
Seyed Mehdi Mansourzadeh - Department of Mathematics, University of Mazandaran, Babolsar 47416-95447, Iran (email)

Abstract: Data Envelopment Analysis (DEA) and Multiple Objective Linear Programming (MOLP) are widely used for performance assessment in organizations. Although DEA and MOLP are similar in structure, DEA is used to assess and analyze past performance and MOLP is used to predict future performance. Several equivalence models between output-oriented DEA models and MOLP models have been proposed in the literature. However these models are not applicable to performance evaluation problems with undesirable outputs. We propose an interactive method for solving output-oriented DEA models with undesirable outputs. We show that the output-oriented BCC model of Seiford and Zhu [47] can be equivalently stated as the maximization of the minimum of several objectives over the production possibility set, which in turn is a scalarization of a multi-objective linear program. We then employ the well-known Zionts-Wallenius procedure to solve the multi-objective optimization problem. We present an example to demonstrate the applicability of the proposed method and exhibit the efficacy of the procedures and algorithms.

Keywords:  Data envelopment analysis, undesirable output, multiple objective linear programming, min-ordering optimization problem.
Mathematics Subject Classification:  Primary: 90C05, 68M20; Secondary: 90C29.

Received: April 2014;      Revised: July 2014;      Available Online: March 2015.