Allocating a fixed cost based on a DEA-game cross efficiency approach

In many real managerial applications, an issue of considerable importance is allocating a total fixed cost across a set of competing decision making units (DMUs). The fixed cost allocation problem has also become one of the most important applications of the data envelopment analysis (DEA) methodology. In this paper, we will approach the fixed cost allocation problem by explicitly considering both competition and cooperation relationships among DMUs. To this end, we integrate cooperative game theory and the cross efficiency method to develop a DEA-game cross efficiency approach to generate a unique and fair allocation plan. With the proposed approach, each DMU is considered as a player and a super-additive characteristic function is defined for coalitions of DMUs. Then, the Shapley value is calculated for each DMU and accordingly associated common weights are optimized to determine the final allocation plan. Since the cross efficiency method considers peer appraisal and the cooperative game theory allows for equitable negotiations, all DMUs are supposed to reach a consensus on the equitable allocation scheme through our novel approach. From this perspective, our proposed approach is promising and attractive for allocating a fixed cost in large organizations. Finally, the DEA-game cross efficiency approach is demonstrated with a numerical example derived from previous literature and the results are compared to some existing methods. Additionally, we apply the proposed approach to an empirical application concerning city commercial bank activities in China.