Fixed cost allocation for two-stage systems with cooperative relationship using data envelopment analysis

Allocating fixed cost among a group of entities is becoming increasingly important in management. Numerous studies have addressed this issue in single-stage systems based on data envelopment analysis (DEA). However, these studies frequently ignored the internal structure of systems, and in many real applications, enterprises with multiple stage processes cooperate with one another. Taking this issue into account in the allocation process, we approach fixed-cost allocation issues of two-stage systems by considering a cooperative relationship among decision making units (DMUs). We integrate cooperative game theory and the DEA methodology to generate a unique and fair allocation plan. The results confirm that each DMU can maximize its relative efficiency to one by a series of optimal variables after the fixed cost allocation. Based on these results, a unique nucleolus solution can be generated through a feasible computation algorithm. Finally, we apply the proposed approach to a random dataset and an empirical commercial bank application in China.