Approximation results for min‐max path cover problems in vehicle routing |
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Authors: | Zhou Xu Liang Xu Chung‐Lun Li |
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Affiliation: | 1. Department of Logistics and Maritime Studies, Faculty of Business, The Hong Kong Polytechnic University, Hung 2. Hom, 3. Kowloon, Hong Kong |
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Abstract: | This article studies a min‐max path cover problem, which is to determine a set of paths for k capacitated vehicles to service all the customers in a given weighted graph so that the largest path cost is minimized. The problem has wide applications in vehicle routing, especially when the minimization of the latest service completion time is a critical performance measure. We have analyzed four typical variants of this problem, where the vehicles have either unlimited or limited capacities, and they start from either a given depot or any depot of a given depot set. We have developed approximation algorithms for these four variants, which achieve approximation ratios of max{3 ‐ 2/k,2}, 5, max{5 ‐ 2/k,4}, and 7, respectively. We have also analyzed the approximation hardness of these variants by showing that, unless P = NP , it is impossible for them to achieve approximation ratios less than 4/3, 3/2, 3/2, and 2, respectively. We have further extended the techniques and results developed for this problem to other min‐max vehicle routing problems.© 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010 |
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Keywords: | approximation algorithms approximation hardness min‐max path cover vehicle routing |
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