In this paper, we refer to Wang’s method for ranking DMUs but argue that his way of selecting the weights is not the appropriate one. Namely, in the cross-efficiency evaluation of DMUs, we always search for the weights which use minimum resources to increase the production. | Yugoslav Journal of Operations Research 28 (2018), Number 4, 521–538 DOI: ALLOCATION OF WEIGHTS USING SIMULTANEOUS OPTIMIZATION OF INPUTS AND OUTPUTS CONTRIBUTION IN CROSS-EFFICIENCY EVALUATION OF DEA Seyed Hadi NASSERI Department of Mathematics, University of Mazandaran, Babolsar, Iran nasseri@ Hamid KIAEI Department of Mathematics, University of Mazandaran, Babolsar, Iran kiaeitonekaboni@ Received: October 2017 / Accepted: August 2018 Abstract: Cross-efficiency evaluation, an extension of the data envelopment analysis (DEA), has found an appropriate function in ranking decision making units (DMU). However, DEA suffers from a potential flaw, that is, the existence of multiple optimal solutions. Different methods have been proposed to obtain a unique solution (based on a specific criterion). In this paper, we refer to Wang’s method for ranking DMUs but argue that his way of selecting the weights is not the appropriate one. Namely, in the cross-efficiency evaluation of DMUs, we always search for the weights which use minimum resources to increase the production. Therefore, we suggest that the selection of weights among the multiple weights should be determined by decreasing the contribution of inputs in the use of resources, and increasing the contribution of outputs in the production, which should overtly prevent the selection of zero solutions to the extent possible. To this end, some examples are given to illustrate differences and advantages of our method compared to those usually used. Keywords: Data Envelopment Analysis, Cross-efficiency, Contribution of Inputs and Outputs, Non-zero weights, Ranking. MSC: 90B50, 90C05. 522 . Nasseri and H. Kiaei / Allocation of Weights 1. INTRODUCTION Data envelopment analysis is a nonparametric method based on linear programming in relative efficiency evolution of a series of homogeneous decision making units (DMUs) with multiple input and outputs. The relative
