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The split-demand one-commodity pickup-and-delivery travelling salesman problem

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  • Salazar-González, Juan-José
  • Santos-Hernández, Beatriz

Abstract

This paper introduces a new vehicle routing problem transferring one commodity between customers with a capacitated vehicle that can visit a customer more than once, although a maximum number of visits must be respected. It generalizes the capacitated vehicle routing problem with split demands and some other variants recently addressed in the literature. We model the problem with a single commodity flow formulation and design a branch-and-cut approach to solve it. We make use of Benders Decomposition to project out the flow variables from the formulation. Inequalities to strengthen the linear programming relaxation are also presented and separated within the approach. Extensive computational results illustrate the performance of the approach on benchmark instances from the literature.

Suggested Citation

  • Salazar-González, Juan-José & Santos-Hernández, Beatriz, 2015. "The split-demand one-commodity pickup-and-delivery travelling salesman problem," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 58-73.
    • Handle: RePEc:eee:transb:v:75:y:2015:i:c:p:58-73
    DOI: 10.1016/j.trb.2015.02.014
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    1. J. M. Belenguer & M. C. Martinez & E. Mota, 2000. "A Lower Bound for the Split Delivery Vehicle Routing Problem," Operations Research, INFORMS, vol. 48(5), pages 801-810, October.
    2. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Rejoinder on: Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 45-47, July.
    3. Jin, Mingzhou & Liu, Kai & Bowden, Royce O., 2007. "A two-stage algorithm with valid inequalities for the split delivery vehicle routing problem," International Journal of Production Economics, Elsevier, vol. 105(1), pages 228-242, January.
    4. Claudia Archetti & Martin W. P. Savelsbergh & M. Grazia Speranza, 2006. "Worst-Case Analysis for Split Delivery Vehicle Routing Problems," Transportation Science, INFORMS, vol. 40(2), pages 226-234, May.
    5. H.L.M. Kerivin & M. Lacroix & A.R. Mahjoub & A. Quilliot, 2008. "The splittable pickup and delivery problem with reloads," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 2(2), pages 112-133.
    6. Irnich, S. & Schneider, M. & Vigo, D., 2014. "Four Variants of the Vehicle Routing Problem," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 63514, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    7. H. L. M. Kerivin & M. Lacroix & A. R. Mahjoub, 2012. "Models for the single-vehicle preemptive pickup and delivery problem," Journal of Combinatorial Optimization, Springer, vol. 23(2), pages 196-223, February.
    8. Gulczynski, Damon & Golden, Bruce & Wasil, Edward, 2010. "The split delivery vehicle routing problem with minimum delivery amounts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(5), pages 612-626, September.
    9. Mosheiov, Gur, 1994. "The Travelling Salesman Problem with pick-up and delivery," European Journal of Operational Research, Elsevier, vol. 79(2), pages 299-310, December.
    10. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-31, July.
    11. Matteo Fischetti & Juan José Salazar González & Paolo Toth, 1997. "A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem," Operations Research, INFORMS, vol. 45(3), pages 378-394, June.
    12. Lee, Chi-Guhn & Epelman, Marina A. & White III, Chelsea C. & Bozer, Yavuz A., 2006. "A shortest path approach to the multiple-vehicle routing problem with split pick-ups," Transportation Research Part B: Methodological, Elsevier, vol. 40(4), pages 265-284, May.
    13. Maciek Nowak & Özlem Ergun & Chelsea C. White, 2008. "Pickup and Delivery with Split Loads," Transportation Science, INFORMS, vol. 42(1), pages 32-43, February.
    14. Dell'Amico, Mauro & Hadjicostantinou, Eleni & Iori, Manuel & Novellani, Stefano, 2014. "The bike sharing rebalancing problem: Mathematical formulations and benchmark instances," Omega, Elsevier, vol. 45(C), pages 7-19.
    15. Leandro C. Coelho & Jean-François Cordeau & Gilbert Laporte, 2014. "Thirty Years of Inventory Routing," Transportation Science, INFORMS, vol. 48(1), pages 1-19, February.
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    1. Fan, Tijun & Pan, Qianlan & Pan, Fei & Zhou, Wei & Chen, Jingyi, 2020. "Intelligent logistics integration of internal and external transportation with separation mode," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 133(C).
    2. Xu, Dongyang & Li, Kunpeng & Zou, Xuxia & Liu, Ling, 2017. "An unpaired pickup and delivery vehicle routing problem with multi-visit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 218-247.

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