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Enhanced Branch-Cut-and-Price algorithm for heterogeneous fleet vehicle routing problems

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  • Pessoa, Artur
  • Sadykov, Ruslan
  • Uchoa, Eduardo

Abstract

This paper considers a family of Vehicle Routing Problem (VRP) variants that generalize the classical Capacitated VRP by taking into account the possibility that vehicles differ by capacity, costs, depot allocation, or even by the subset of customers that they can visit. This work proposes a Branch-Cut-and-Price algorithm that adapts advanced features found in the best performing exact algorithms for homogeneous fleet VRPs. The original contributions include: (i) the use of Extended Capacity Cuts, defined over a pseudo-polynomially large extended formulation, together with Rank-1 Cuts, defined over the Set Partitioning Formulation; (ii) the concept of vehicle-type dependent memory for Rank-1 Cuts; and (iii) a new family of lifted Extended Capacity Cuts that takes advantage of the vehicle-type dependent route enumeration. The algorithm was extensively tested in instances of the literature and was shown to be significantly better than previous exact algorithms, finding optimal solutions for many instances with up to 200 customers and also for some larger instances. A new set of benchmark instances is also proposed.

Suggested Citation

  • Pessoa, Artur & Sadykov, Ruslan & Uchoa, Eduardo, 2018. "Enhanced Branch-Cut-and-Price algorithm for heterogeneous fleet vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 270(2), pages 530-543.
    • Handle: RePEc:eee:ejores:v:270:y:2018:i:2:p:530-543
    DOI: 10.1016/j.ejor.2018.04.009
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    References listed on IDEAS

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    1. Subramanian, Anand & Penna, Puca Huachi Vaz & Uchoa, Eduardo & Ochi, Luiz Satoru, 2012. "A hybrid algorithm for the Heterogeneous Fleet Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 221(2), pages 285-295.
    2. Mads Jepsen & Bjørn Petersen & Simon Spoorendonk & David Pisinger, 2008. "Subset-Row Inequalities Applied to the Vehicle-Routing Problem with Time Windows," Operations Research, INFORMS, vol. 56(2), pages 497-511, April.
    3. Uchoa, Eduardo & Pecin, Diego & Pessoa, Artur & Poggi, Marcus & Vidal, Thibaut & Subramanian, Anand, 2017. "New benchmark instances for the Capacitated Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 257(3), pages 845-858.
    4. Roberto Baldacci & Aristide Mingozzi & Roberto Roberti, 2011. "New Route Relaxation and Pricing Strategies for the Vehicle Routing Problem," Operations Research, INFORMS, vol. 59(5), pages 1269-1283, October.
    5. Diego Pecin & Claudio Contardo & Guy Desaulniers & Eduardo Uchoa, 2017. "New Enhancements for the Exact Solution of the Vehicle Routing Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 489-502, August.
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    Cited by:

    1. Diego Pecin & Eduardo Uchoa, 2019. "Comparative Analysis of Capacitated Arc Routing Formulations for Designing a New Branch-Cut-and-Price Algorithm," Transportation Science, INFORMS, vol. 53(6), pages 1673-1694, November.
    2. Vidal, Thibaut & Laporte, Gilbert & Matl, Piotr, 2020. "A concise guide to existing and emerging vehicle routing problem variants," European Journal of Operational Research, Elsevier, vol. 286(2), pages 401-416.
    3. Michael Khachay & Yuri Ogorodnikov & Daniel Khachay, 2021. "Efficient approximation of the metric CVRP in spaces of fixed doubling dimension," Journal of Global Optimization, Springer, vol. 80(3), pages 679-710, July.
    4. Anirudh Subramanyam & Panagiotis P. Repoussis & Chrysanthos E. Gounaris, 2020. "Robust Optimization of a Broad Class of Heterogeneous Vehicle Routing Problems Under Demand Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 661-681, July.
    5. Artur Pessoa & Ruslan Sadykov & Eduardo Uchoa, 2021. "Solving Bin Packing Problems Using VRPSolver Models," SN Operations Research Forum, Springer, vol. 2(2), pages 1-25, June.
    6. Yu, Yang & Wang, Sihan & Wang, Junwei & Huang, Min, 2019. "A branch-and-price algorithm for the heterogeneous fleet green vehicle routing problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 511-527.
    7. Jost, Christian & Jungwirth, Alexander & Kolisch, Rainer & Schiffels, Sebastian, 2022. "Consistent vehicle routing with pickup decisions - Insights from sport academy training transfers," European Journal of Operational Research, Elsevier, vol. 298(1), pages 337-350.
    8. Luciano Costa & Claudio Contardo & Guy Desaulniers, 2019. "Exact Branch-Price-and-Cut Algorithms for Vehicle Routing," Transportation Science, INFORMS, vol. 53(4), pages 946-985, July.
    9. Guy Desaulniers & Timo Gschwind & Stefan Irnich, 2020. "Variable Fixing for Two-Arc Sequences in Branch-Price-and-Cut Algorithms on Path-Based Models," Transportation Science, INFORMS, vol. 54(5), pages 1526-5447, September.

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