Chance-constrained data envelopment analysis modeling with random-rough data^★

¹ School of Mathematics Science, University of Tabriz, Tabriz, Iran
Rashed.shiraz@gmail.com
² Business Systems and Analytics Department, Distinguished Chair of Business Analytics, La Salle University, Philadelphia, PA 19141, USA
³ Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, 33098 Paderborn, Germany
⁴ Department of Mathematics and Statistics, York University, Toronto, M3J 1P3, Canada
dicaper@mathstat.yorku.ca
⁵ Polo Tecnologico IISS G. Galilei, Via Cadorna 14, 39100, Bolzano, Italy
debora.dicaprio@istruzione.it

^a Corresponding author: tavana@lasalle.edu; http://tavana.us/

Received: 16 June 2016
Accepted: 6 December 2016

Abstract

Data envelopment analysis (DEA) is a useful management tool for measuring the relative efficiency of decision making units (DMUs) which consumes multiple inputs to produce multiple outputs. Although precise input and output data are fundamentally indispensable in classical DEA models, real-world problems often involve random and/or rough input and output data. We present a chance-constrained DEA model with random and rough (random-rough) input and output data and propose a deterministic equivalent model with quadratic constraints to solve the model. The main contributions of this paper are fourfold: (3.1) we propose a DEA model for problems characterized by random-rough variables; (3.2) we transform the proposed chance-constrained model with random-rough variables into a deterministic equivalent non-linear form that could be simplified as a deterministic model with quadratic constraints; (3.3) we perform sensitivity analysis to investigate the stability and robustness of the proposed model; and (3.4) we use a numerical example to demonstrate the feasibility and richness of the obtained solutions.