Title: Multi objective constrained optimisation of data envelopment analysis by differential evolution

Authors: Narravula Ankaiah; Vadlamani Ravi

Addresses: Center of Excellence in CRM and Analytics, Institute for Development and Research in Banking Technology (IDRBT), Castle Hills Road #1, Masab Tank, Hyderabad-500 057 (AP), India ' Center of Excellence in CRM and Analytics, Institute for Development and Research in Banking Technology (IDRBT), Castle Hills Road #1, Masab Tank, Hyderabad-500 057 (AP), India

Abstract: Traditional data envelopment analysis (DEA) has serious shortcomings: 1) linear programming is run as many times as the number of decision making units (DMUs) resulting in no common set of weights for them; 2) maximising efficiency, a nonlinear optimisation problem, is approximated by a linear programming problem (LPP); 3) the efficiencies obtained by DEA are only relative. Hence, we propose multi objective DEA (MODEA) solved by differential evolution. Here, we maximise the efficiencies of all the DMUs simultaneously. We developed two variants of the MODEA using: 1) scalar optimisation; 2) Max-Min approach. The effectiveness of the proposed methods is demonstrated on eight datasets taken from literature. We also applied NSGA-II to solve the nonlinear optimisation problem in the strict multi objective sense. It was found that MODEA1, MODEA2 and NSGA-II are comparable, as evidenced by Spearman's rank correlation coefficient test. However, MODEA1, MODEA2, and NSGA-II yielded better discrimination among the DMUs compared to the traditional DEA.

Keywords: data envelopment analysis; DEA; differential evolution; multiobjective optimisation; absolute efficiency; fractional programming; nonlinear programming; constrained optimisation; NSGA-II; genetic algorithms; nonlinear optimisation; decision making units; DMUs.

DOI: 10.1504/IJIDS.2015.074131

International Journal of Information and Decision Sciences, 2015 Vol.7 No.4, pp.334 - 357

Available online: 12 Jan 2016 *

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