Extending the bargaining approach to DEA target setting

Abstract

This paper extends the approach based on bargaining for computing DEA targets. Thus, for each inefficient Decision Making Unit (DMU), a bargaining problem is defined where the players are the input and output variables that can be improved. In the case of the output players, their utility is an increasing linear function of the corresponding variable. The utility of input players is a decreasing linear function of the input. The disagreement point corresponds to the input and output utilities of the DMU being projected. We show how various well-known bargaining solutions, such as Nash bargaining solution, lexicographic Kalai–Smorodinsky solution, lexicographic egalitarian solution and normalized utilitarian solution, lead to corresponding DEA bargaining models. Some properties of the DEA bargaining models are derived as a consequence of those of the corresponding bargaining solutions. The proposed approach is validated using a container shipping lines application.