Coordinated production target setting for production–pollutant control systems: A DEA two-stage bargaining game approach

Setting a production target for a two-stage production–pollutant control system can provide guidance for the system to achieve efficient performance in its future production. The existing studies have succeeded in targeting but have missed the consideration of coordination between the adjustments for the two stages’ input and output metrics. In this article, we propose an approach to address this problem using a non-parametric method: data envelopment analysis. First, we use the leader–follower analysis from game theory to propose slacks-based measure models for production target setting in situations where a dominance relationship exists between the two stages of the systems. Based on the results generated by the leader–follower models, we define each stage’s dissatisfaction degree with the set targets. Further, considering the coordination between the adjustments of the two stages’ inputs and outputs, we incorporate the bargaining game theory to propose a model which can generate the set of coordinated adjustments that is a bargaining solution taking account of both the dissatisfaction degrees of the two stages. The properties of the solution generated by the bargaining model feature fairness, which makes the target setting result coordinated between each system’s two stages. Finally, the proposed approaches are applied and tested in an empirical study of 30 provincial regions in China.