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

Abstract

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.