Title: Optimistic and pessimistic performance and congestion analysis in fuzzy data envelopment analysis
Authors: Mohamad Khodabakhshi; Madjid Tavana; Fatemeh Baghbani Abootaleb
Addresses: Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Tehran, Iran ' Business Systems and Analytics Department, Lindback Distinguished Chair of Information Systems and Decision Sciences, La Salle University, Philadelphia, PA 19141, USA; Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, D-33098 Paderborn, Germany ' Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
Abstract: The notion of input congestion in data envelopment analysis (DEA) is analogous to the 'law of diminishing returns' in the classical economic theory of production which states that if a single input is increased while other inputs are held constant, the marginal product of the variable input diminishes. Congestion has been an under-researched topic in economic theory especially when there is a need for augmenting inputs to serve important objectives besides output maximisation. We propose a fuzzy DEA model and represent the imprecise and ambiguous input and output data with fuzzy numbers. We solve the model with an α-cut approach and obtain the value of input congestion for the optimistic and pessimistic cases. The fundamental idea in this paper is to transform the fuzzy DEA model into a crisp linear programming model using the α-cut approach. Two auxiliary crisp models are solved to obtain optimistic and pessimistic values of congestion for evaluating the decision-making units (DMUs). We use a numerical example from the literature to demonstrate the applicability of the proposed method and exhibit the efficacy of the procedures and algorithms.
Keywords: data envelopment analysis; fuzzy DEA; input congestion; fuzzy inputs; fuzzy outputs; alpha-cut approach; optimistic congestion; pessimistic congestion; grey system theory; crisp modelling; linear programming; decision making units; DMUs; DMU evaluation.
International Journal of Logistics Systems and Management, 2016 Vol.24 No.1, pp.1 - 17
Received: 06 Jan 2015
Accepted: 11 Jan 2015
Published online: 31 Mar 2016 *