An upper bound on the minimal total cost of the transportation problem with varying demands and supplies |
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| Affiliation: | 1. School of Science, Sichuan University of Science and Engineering, Zigong 643000, China;2. Department of Mathematics, Nanchang University, Nanchang 330031, China;3. Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing 100080, China;1. School of Management, University of Science and Technology of China, Hefei, Anhui Province 230026, PR China;2. Hefei University of Technology, Hefei, Anhui Province 230026, PR China;3. Schulich School of Business, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3;1. Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands;2. Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;1. Faculty of Science, Ningbo University, Ningbo 315211, PR China;2. School of Management Science and Engineering, Dongbei University of Finance and Economics, Dalian 116025, PR China;1. Quantitative Hedge Fund, Singapore;2. Faculty of Natural Science – Technology, Taybac University, Viet Nam;3. School of Information and Communication Technology, Hanoi University of Science and Technology, Viet Nam;1. Department of Production Network Planning, Daimler Trucks, DE-70546 Stuttgart, Germany;2. TUM School of Management, Technische Universität München, Arcisstrasse 21, DE-80333 Munich, Germany |
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| Abstract: | In general cases, to find the exact upper bound on the minimal total cost of the transportation problem with varying demands and supplies is an NP-hard problem. In literature, there are only two approaches with several shortcomings to solve the problem. In this paper, the problem is formulated as a bi-level programming model, and proven to be solvable in a polynomial time if the sum of the lower bounds for all the supplies is no less than the sum of the upper bounds for all the demands; and a heuristic algorithm named TPVDS-A based on genetic algorithm is developed as an efficient and robust solution method of the model. Computational experiments on benchmark and new randomly generated instances show that the TPVDS-A algorithm outperforms the two existing approaches. |
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| Keywords: | Genetic algorithms Transportation problem Transportation problem with varying demands and supplies Bounds on the minimal total cost Upper bound on the minimal total cost |
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