Measuring Performance of a Three-Stage Network Structure Using Data Envelopment Analysis and Nash Bargaining Game: A Supply Chain Application

The issue of efficiency analysis of network and multi-stage systems, as one of the most interesting fields in data envelopment analysis (DEA), has attracted much attention in recent years. A pure serial three-stage (PSTS) process is a specific kind of network in which all the outputs of the first stage are used as the only inputs in the second stage and in addition, all the outputs of the second stage are applied as the only inputs in the third stage. In this paper, a new three-stage DEA model is developed using the concept of three-player Nash bargaining game for PSTS processes. In this model, all of the stages cooperate together to improve the overall efficiency of main decision-making unit (DMU). In contrast to the centralized DEA models, the proposed model of this study provides a unique and fair decomposition of the overall efficiency among all three stages and eliminates probable confusion of centralized models for decomposing the overall efficiency score. Some theoretical aspects of proposed model, including convexity and compactness of feasible region, are discussed. Since the proposed bargaining model is a nonlinear mathematical programming, a heuristic linearization approach is also provided. A numerical example and a real-life case study in supply chain are provided to check the efficacy and applicability of the proposed model. The results of proposed model on both numerical example and real case study are compared with those of existing centralized DEA models in the literature. The comparison reveals the efficacy and suitability of proposed model while the pitfalls of centralized DEA model are also resolved. A comprehensive sensitivity analysis is also conducted on the breakdown point associated with each stage.