Efficiency decomposition in a three-stage network structure: Cooperative DEA, Nash bargaining game models and conic relaxations

¹ Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
² Department of Applied Mathematics, Faculty of Mathematical Sciences, and Center of Excellence for Mathematical Modeling, Optimization and Combinatorial Computing (MMOCC), University of Guilan, Rasht, Iran

^* Corresponding author: salahim@guilan.ac.ir; salahi.maziar@gmail.com

Received: 1 November 2019
Accepted: 21 November 2021

Abstract

In this paper, for evaluating the efficiency in a three-stage DEA structure we use the additive and the multiplicative cooperative models that comply with the cooperation paradigm in the organizations, where for improving efficiency of system, stages cooperate together. Since the overall efficiency from the cooperative models may not be unique and consequently the stages’ efficiencies, then we combine them with the Nash bargaining game approach that besides maximizing efficiency scores for stages and the whole system, provides a unique and fair efficiency decomposition. Second order programming relaxation of the proposed nonlinear models are given in contrast to the parametric linear models in the literature. Finally, the effectiveness of the proposed models are illustrated with two numerical examples.