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Allocating the fixed cost based on data envelopment analysis in view of the Shapley value
Author(s) -
Meng Fanyong,
Wu Li,
Chu Junfei
Publication year - 2020
Publication title -
expert systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.365
H-Index - 38
eISSN - 1468-0394
pISSN - 0266-4720
DOI - 10.1111/exsy.12539
Subject(s) - shapley value , computer science , data envelopment analysis , cooperative game theory , cost allocation , mathematical optimization , premise , process (computing) , resource allocation , value (mathematics) , fixed cost , monotonic function , operations research , game theory , mathematical economics , mathematics , economics , microeconomics , computer network , linguistics , philosophy , mathematical analysis , accounting , machine learning , operating system
This paper considers fixed cost allocation in view of cooperative game theory and proposes an approach based on data envelopment analysis while incorporating the perspectives of coalition efficiency and the Shapley value. To do this, we first build two models to evaluate coalition efficiencies before and after cost allocation, and we prove that all coalitions can be efficient after fixed cost allocation. Then, following the premise that each coalition makes itself efficient without reducing the efficiencies of other decision‐making units' preallocation efficiency, we propose a model that determines the acceptable range of each coalition's allocated fixed cost. Furthermore, a model is constructed to determine the final cost allocation based on three principles: efficiency, monotonicity, and similarity. Moreover, the Shapley value is employed to obtain the cost allocated to each decision‐making unit (DMU). The proposed approach considers the relationships among DMUs across their forming coalitions to determine their interaction types and then generates a fixed cost allocation result that possesses the features of the Shapley value. This process makes the fixed cost allocation more acceptable. Finally, a simple numerical example and an empirical case are provided to illustrate the calculation process of the proposed approach and compare our approach with the traditional methods.