Journal
MATHEMATICAL AND COMPUTER MODELLING
Volume 54, Issue 11-12, Pages 2827-2838Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.mcm.2011.07.003
Keywords
Data envelopment analysis; Fuzzy data; Interval data; Overall profit efficiency; Profit Malmquist productivity index
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Although crisp data are fundamentally indispensable for determining the profit Malmquist productivity index (MPI), the observed values in real-world problems are often imprecise or vague. These imprecise or vague data can be suitably characterized with fuzzy and interval methods. In this paper, we reformulate the conventional profit MPI problem as an imprecise data envelopment analysis (DEA) problem, and propose two novel methods for measuring the overall profit MPI when the inputs, outputs, and price vectors are fuzzy or vary in intervals. We develop a fuzzy version of the conventional MPI model by using a ranking method, and solve the model with a commercial off-the-shelf DEA software package. In addition, we define an interval for the overall profit MPI of each decision-making unit (DMU) and divide the DMUs into six groups according to the intervals obtained for their overall profit efficiency and MPIs. We also present two numerical examples to demonstrate the applicability of the two proposed models and exhibit the efficacy of the procedures and algorithms. (C) 2011 Elsevier Ltd. All rights reserved.
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