Fixed cost allocation based on a data envelopment analysis aggressive game approach

Abstract

The literature on organizational strategy and production operations suggests that establishing a shared platform would be beneficial for addressing competition and mitigating risks. However, the creation of a common platform inevitably incurs expenditures and costs, prompting the natural question of how to equitably distribute the total fixed cost among all participating units. While the fixed cost allocation (FCA) problem has been explored in the context of data envelopment analysis (DEA), this paper addresses a distinct decentralized environment wherein there is no central decision-maker, and each individual decision-making unit (DMU) pursues a self-interested strategy to minimize its allocated cost share. In tackling the challenge of proposing an acceptable allocation plan within this decentralized setting, we initially improve the non-egoistic principle by considering the perspective of operational size. This improvement mandates that each DMU bears the maximum fixed cost per unit of operational size in its own allocation proposal. The improved non-egoistic principle implicitly addresses the platform constraint and fairness concerns, while each DMU remains committed to maximizing other DMUs’ cost shares and minimizing their own performance efficiency. Additionally, we introduce an aggressive game process to amalgamate all DMUs’ allocation proposals into the DEA efficiency analysis. A DEA aggressive game approach and its corresponding computational algorithm are developed to facilitate consensus and determine the final FCA plan. Mathematically, we prove that all average post-allocation efficiencies, incorporating fixed costs, converge to the same aggressive game cross-efficiency for each DMU in the iterative algorithm. To the best of our knowledge, this paper represents the first study that employs an aggressive strategy in the FCA problem to minimize efficiency scores, while existing literature predominantly focuses on maximizing or maintaining efficiency scores. Finally, we apply the proposed approach to a classical numerical example and an empirical study involving nine independent truck fleets to showcase its characteristics and efficacy.