Evaluating Groups of Decision Making Units in the Data Envelopment Analysis Based on Cooperative Games

Data Envelopment Analysis (DEA) is a non-parametric method for evaluating the efficiency of those Decision Making Units (DMUs) that have the same functionality and use multiple inputs to generate multiple outputs. DMUs may sometimes be divided into several groups according to a series of criteria, and it is intended to evaluate a group of similar DMUs. In this paper, each group was considered as a player in a cooperative game and a subset of groups was considered as a coalition. Assuming the Production Possibility Set is made up of the members of the coalition, a characteristic function was defined in terms of the sum of the efficiency of all units to determine the marginal effect of each group in different coalitions. The groups were then evaluated using the Shapley Value as a solution of the cooperative game. Some Examples were provided to describe and apply the method.