A cross-bargaining game approach for direction selection in the directional distance function

As one of the most useful performance and productivity evaluation tools, the directional distance function (DDF) has received substantial attention and research. One of the key concerns to address in DDF measurement is selecting the direction along which to measure the distance from an inefficient decision making unit (DMU) to the production frontier. The least distance approach helps the inefficient DMUs find their own most preferred directions that maximize their own efficiency scores with least effort, but some DMUs may not accept the results because of the inconsistent evaluation basis. To overcome this limitation, we propose a peer-evaluation mode to evaluate the performance of the DMUs. We give a cross-directional evaluation approach and further provide a cross-bargaining game approach. In the cross-directional evaluation approach, each inefficient DMU is evaluated using both its own preferred projection direction and the other DMUs’ most preferred projection directions. However, the resulting average cross-directional efficiencies are not Pareto-optimal, so we develop a cross-bargaining game approach to improve the cross-directional efficiency approach even further. In the cross-bargaining game, each pair of inefficient DMUs is treated as two players who will obtain a common projection direction by bargaining with each other. The use of cross-bargaining negotiated projection directions and the Pareto-optimality of the DMUs’ final average cross-bargaining-directional efficiencies make the evaluation results more acceptable to all inefficient DMUs. Finally, an empirical example of 28 international airlines is applied to illustrate the practicality and superiority of our cross-bargaining game approach.