Allocating the fixed cost: an approach based on data envelopment analysis and cooperative game
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Allocating the fixed cost among a set of users in a fair way is an important issue both in management and economic research. Recently, Du et al. (Eur J Oper Res 235(1): 206–214, 2014) proposed a novel approach for allocating the fixed cost based on the game cross-efficiency method by taking the game relations among users in efficiency evaluation. This paper proves that the novel approach of Du et al. (Eur J Oper Res 235(1): 206–214, 2014) is equivalent to the efficiency maximization approach of Li et al. (Omega 41(1): 55–60, 2013), and may exist multiple optimal cost allocation plans. Taking into account the game relations in the allocation process, this paper proposes a cooperative game approach, and uses the nucleolus as a solution to the proposed cooperative game. The proposed approach in this paper is illustrated with a dataset from the prior literature and a real dataset of a steel and iron enterprise in China.
KeywordsData envelopment analysis (DEA) Fixed cost allocation Cooperative game Nucleolus
The authors would like to thank the Editor of Annals of Operations Research and two anonymous reviewers for their kind work and valuable comments. We would also acknowledge helpful comments from Professor Joe Zhu. This research was financially supported by the National Natural Science Foundation of China (Grant Nos. 71271196 and 71671172), the Youth Innovation Promotion Association of Chinese Academy of Sciences (CX2040160004), and Science Funds for Creative Research Groups of University of Science and Technology of China (No. WK2040160008). Professor Xie would like to thank the GreatWall Scholar Training Program of Beijing Municipality (CIT&TCD 20180305) and Social Science Foundation of Beijing (16JDGLC005).
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