Allocating a fixed cost across decision making units with explicitly considering efficiency rankings

Fixed cost allocation (FCA) is one of the most important applications of the data envelopment analysis (DEA). Numerous studies on this problem have appeared in the literature in the last two decades; however, almost all of them are based on either efficiency invariance or efficiency maximization, both of which focus mainly on efficiency scores. It is notable that the efficiency score is more an intermediate indicator and the corresponding efficiency ranking is actually the main focus. Motivated by this observation, this paper aims to propose a new approach for allocating the fixed cost across decision making units (DMUs) based on efficiency ranking. To this end, the efficiency ranking intervals are explicitly determined by taking allocated costs and feasible weights into account. The results indicate that each DMU can be ranked at any position ranging from the best one to the worst n, and there are fixed cost allocation schemes that can determine the best efficiency ranking of one for each individual DMU simultaneously under a set of common weights. Furthermore, we define a new comprehensive satisfaction degree based on the interval of the upper and lower bounds of the allocated costs. Then, we generate the final allocation scheme using an iterative procedure to maximize the satisfaction degree across all DMUs. Finally, the proposed approach is applied to a classic numerical example from prior literature and an empirical study from the real world to illustrate its usefulness and efficacy.