A bargaining game model for performance evaluation in network DEA considering shared inputs in the presence of undesirable outputs

Data Envelopment Analysis (DEA) is a non-parametric method for measuring the relative efficiency of peer decision-making units (DMUs), where the internal structures of DMUs are treated as a black box. Traditional DEA models do not pay attention to the internal structures and intermediate values. Network data envelopment analysis models addressed this shortcoming by considering intermediate measure. The results of two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The centralized model has been widely used to evaluate the efficiency of two-stage systems, but the allocation problem of shared inputs and undesirable outputs has not been considered.  The aim of this paper is to develop a method based on bargaining for evaluation in network DEA considering shared inputs and undesirable outputs. The two stages are considered as players to bargain for a better payoff, which is offered by DEA ratio efficiency score of DMUs. The efficiency model is developed as a cooperative game model. Finally, a numerical example is given to evaluate the proposed model.