Title: A data envelopment analysis model with discretionary and non-discretionary factors in fuzzy environments

Authors: Saber Saati, Adel Hatami-Marbini, Madjid Tavana

Addresses: Department of Mathematics, Tehran-North Branch, Islamic Azad University, P.O. Box 19585-936, Tehran, Iran. ' Louvain School of Management, Center of Operations Research and Econometrics (CORE), Universite Catholique de Louvain, 34 Voie du Roman Pays, B-1348 Louvain-la-Neuve, Belgium. ' Management Information Systems, Lindback Distinguished Chair of Information Systems, La Salle University, Philadelphia, PA 19141, USA

Abstract: Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision-making units (DMUs) that use multiple inputs to produce multiple outputs. The standard DEA models assume that all inputs and outputs are crisp and can be changed at the discretion of management. While crisp input and output data are fundamentally indispensable in the standard DEA evaluation process, input and output data in real-world problems are often imprecise or ambiguous. In addition, real-world problems may also include non-discretionary factors that are beyond the control of a DMU|s management. Fuzzy logic and fuzzy sets are widely used to represent ambiguous, uncertain or imprecise data in DEA by formalising the inaccuracies inherent in human decision-making. In this paper, we show that considering bounded factors in DEA models results in a disregard to the concept of relative efficiency since the efficiency of the DMUs are calculated by comparing the DMUs with their lower and/or upper bounds. In addition, we present a fuzzy DEA model with discretionary and non discretionary factors in both the input and output-oriented CCR models. A numerical example is used to demonstrate the applicability and the efficacy of the proposed models.

Keywords: Malmquist DEA; data envelopment analysis; non-discretionary factors; discretionary factors; bounded factors; fuzzy programming; relative efficiency; decision making units; multiple inputs; multiple outputs; crisp data; input data; output data; real-world problems; fuzzy logic; fuzzy sets; mathematical programming; ambiguous data; uncertain data; imprecise data; CCR model; Abraham Charnes; William Cooper; Edward Rhodes; productivity; quality management.

DOI: 10.1504/IJPQM.2011.041097

International Journal of Productivity and Quality Management, 2011 Vol.8 No.1, pp.45 - 63

Published online: 07 Jul 2011 *

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