Title: A multiplier form of slacks-based measure model in stochastic data envelopment analysis

Authors: Mohammad Hossein Tavassoli; Ali Asghar Foroughi

Addresses: Department of Mathematics, University of Qom, Qom 3716146611, Iran ' Department of Mathematics, University of Qom, Qom 3716146611, Iran

Abstract: Data envelopment analysis (DEA) is a mathematical approach based on linear programming, which evaluates the rational efficiency of decision-making units (DMUs) with multiple inputs and outputs. In conventional DEA, the data values are considered to be deterministic. However, the data might be non-deterministic in nature, and DMUs evaluation within DEA may be sensitive to imprecise data. An approach to deal with imprecise data is considering stochastic data within DEA. In this paper, chance constrained programming (CCP) concept is applied to develop slacks-based measure (SBM) multiplier model within stochastic DEA. The deterministic equivalent of this stochastic model is transformed into a nonlinear and then to a quadratic program. The objective function value and also the weighted output-input ratio, determined by using the optimal solution of the developed model, is used to evaluate DMUs. Two real data of the Chinese textile industry and Iranian provincial gas companies are used to assess the performance of the developed approach.

Keywords: data envelopment analysis; DEA; slacks-based measure; SBM; stochastic DEA; chance constrained programming; CCP; multiplier form.

DOI: 10.1504/IJMDM.2022.124409

International Journal of Management and Decision Making, 2022 Vol.21 No.3, pp.243 - 261

Received: 07 Jan 2021
Accepted: 13 Jun 2021
Published online: 26 Jul 2022 *

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