Journal
OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE
Volume 85, Issue -, Pages 16-25Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.omega.2018.05.008
Keywords
Data envelopment analysis; Three-stage system; Resource sharing; Payoff allocation; Shapley value
Funding
- National Natural Science Foundation of China [71501189, 71501034, 71771041]
- Natural Science Foundation of Hunan Province [2017JJ3397]
- open project of Mobile Health Ministry of Education-China Mobile Joint Laboratory of Central South University
- State Key Program of National Natural Science of China [71631008, 71431006]
- Major Project for National Natural Science Foundation of China [71790615]
- International Post-doctoral Exchange Fellowship Program by the Office of China Post-doctoral Council
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Resource sharing exists not only among multiple entities but also among various stages of a single network structure system. Previous studies focused on how to allocate total given sharable resources to stages to maximize the efficiency of the network structure system, and a few discussed the fair allocation of potential gains obtained from resource sharing. In this study, we explore a new case in which the common inputs (or shared resources) of all stages are known. By constructing a game that regards each stage as a player, we integrate cooperative game theory with network data envelopment analysis (DEA) to explore the payoff allocation problem in a three-stage system. We build network DEA models to calculate the optimal profits of the system before and after resource sharing (i.e., pre- and post-collaboration optimal profits), and then apply the Shapley value method to allocate the increased profits of the system to its stages. Results indicate that the game among stages in a three-stage system is superadditive. A numerical example is provided to illustrate our method. (C) 2018 Elsevier Ltd. All rights reserved.
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