Finding the nucleolus of the vehicle routing game with time windows |
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| Affiliation: | 1. Korea Institute of Industrial Technology, Cheonan, Chungnam 31056, Republic of Korea;2. Department of Industrial and Management Engineering, Pohang University of Science and Technology, Pohang, Gyeongbuk 37673, Republic of Korea;3. WM Logistics, 5910 Farm to Market Road 1488, Magnolia, TX 77354, USA;1. Mathematical Sciences and Business School, University of Southampton, Southampton SO17 1BJ, United Kingdom;2. School of Business, University of Southampton, Southampton SO17 1BJ, United Kingdom |
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| Abstract: | Computing the nucleolus is recognized as an equitable solution to cooperative n person cost games, such as a vehicle routing game (VRG). Computing the nucleolus of a VRG, however, has been limited to small-sized benchmark instances with no more than 25 players, because of the computation time required to solve the NP-hard separation problem. To reduce computation time, we develop an enumerative algorithm that computes the nucleolus of the VRG with time windows (VRGTW) in the case of the non-empty core. Numerical simulations demonstrate the ability of the proposed algorithm to compute the nucleolus of benchmark instances with up to 100 players. |
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