DEA-based fixed cost allocation in two-stage systems: Leader-follower and satisfaction degree bargaining game approaches. (July 2020)

• Record Type: Journal Article
• Authors: Chu, Junfei; Wu, Jie; Chu, Chengbin; Zhang, Tinglong
• Is Part Of: Omega. Volume 94(2020)
• Publication Date: 2020-07
• Subjects: Fixed cost allocation -- Data envelopment analysis -- Two-stage system -- Leader-follower game -- Bargaining game; Management -- Periodicals; 658.4005
• DOI: 10.1016/j.omega.2019.03.012
• Languages: English
• ISSNs: 0305-0483

Abstract

Highlights: This paper considers fixed-cost allocation in two-stage systems with data envelopment analysis. We prove all decision making units can be made efficient with a common weight evaluation. We propose game models by considering unions of the first stages and the second stages as players, respectively. We propose leader-follower approaches for situations with dominance between the two stages. When there is no dominance between stages, we propose a Nash bargaining approach with satisfaction degree as payoffs. A method is proposed to obtain the Nash equilibrium. Abstract: This paper proposes new fixed cost allocation approaches for allocating a fixed cost among decision-making units (DMUs) with two-stage structures under the framework of data envelopment analysis (DEA). Firstly, we give the set of possible fixed cost allocations, prove that all DMUs can be overall efficient when evaluated by a common set of weights after fixed cost allocation. Secondly, from a centralized point of view, we consider the competition between the DMUs' two stages in fixed cost allocation and regard these two kinds of stages as two unions. Then, we incorporate leader-follower models to propose a fixed cost allocation approach to handle the situation in which the two unions make decisions sequentially. Based on the result of these models, a concept of satisfaction degree of each union on a fixed cost allocation is presented. A satisfaction degree bargaining game model is then proposed to obtain a fixed cost allocation which is a bargaining equilibrium of the two unions. We show that the proposed approaches always obtain a fixed cost allocation that is proportionally invariant. Additionally, the satisfaction degree bargaining game approach automatically guarantees the uniqueness of the fixed cost allocation. These properties make the fixed cost allocation generated by our approaches more stable and more acceptable. Finally, a numerical example and an application of fixed cost allocation among bank branches are given to illustrate the proposed approach and to compare it with a benchmark approach among the current studies, respectively.