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Capacitated vehicle routing problem on line with unsplittable demands

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Abstract

In this paper we study the capacitated vehicle routing problem. An instance of capacitated vehicle routing problem consists of a set of vertices with demands in a metric space, a specified depot, and a capacity bound C. The objective is to find a set of tours originating at the depot that cover all the demands, such that the capacity of each tour does not exceed C and the sum of the tour lengths is minimized. For the case that the metric space is a line and the demands are unsplittable, we provide a \(\frac{5}{3}\)-approximation algorithm. An instance is given to show that the bound is tight.

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References

  • Altinkemer K, Gavish B (1990) Heuristics for delivery problems with constant error guarantees. Transp Sci 24:294–297

    Article  Google Scholar 

  • Asano T, Katoh N, Kawashima K (2001) A new approximation algorithm for the capacitated vehicle routing problem on a tree. J Comb Optim 5(2):213–231

    Article  MathSciNet  Google Scholar 

  • Becker A (2018) A tight 4/3 approximation for capacitated vehicle routing in trees. Leibniz Int Proc Inform 116(1):3

    MathSciNet  MATH  Google Scholar 

  • Dósa G, Sgall J (2013) First Fit bin packing: a tight analysis. In: Proceedings of the \(30\)th symposium on theoretical aspects of computer science, Kiel

  • Dósa G, Tan ZY, Tuza Z, Yan YJ, Lányi CS (2014) Improve bounds for batch scheduling with nonidentical job sizes. Naval Res Logist 61(5):351–358

    Article  MathSciNet  Google Scholar 

  • Haimovich M (1985) Bounds and heuristics for capacitated routing problems. Math Oper Res 10(4):527–542

    Article  MathSciNet  Google Scholar 

  • Hamaguchi S, Katoh N (1998) A capacitated vehicle routing problem on a tree. In: International symposium on algorithms and computation, pp 399–407

  • Labbé M, Laporte G, Mercure H (1991) Capacitated vehicle routing on trees. Oper Res 39(4):616–622

    Article  Google Scholar 

  • Laporte G, Nobert Y (1983) A branch and bound algorithm for the capacitated vehicle routing problem. OR Spektrum 5:77–85

    Article  Google Scholar 

  • Zhang GC, Cai XQ, Lee CY, Wong CK (2001) Minimizing makespan on a single batch processing machine with nonidentical job sizes. Naval Res Logist 48(3):226–240

    Article  MathSciNet  Google Scholar 

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Acknowledgements

Dedicated to Professor Minyi Yue on the Occasion of His 100th Birthday. This work is supported by National Natural Science Foundation of China (NSFCs: Nos. 11871213 and 71431004 ).

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  1. School of Science, East China University of Science and Technology, Shanghai, China

    Yuanxiao Wu & Xiwen Lu

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  1. Yuanxiao Wu
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  2. Xiwen Lu
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Correspondence to Xiwen Lu.

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Wu, Y., Lu, X. Capacitated vehicle routing problem on line with unsplittable demands. J Comb Optim 44, 1953–1963 (2022). https://doi.org/10.1007/s10878-020-00565-5

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  • DOI: https://doi.org/10.1007/s10878-020-00565-5

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