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Branch-and-Price-and-Cut for the Periodic Vehicle Routing Problem with Flexible Schedule Structures

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  • Ann-Kathrin Rothenbächer

    (Gutenberg School of Management and Economics, Johannes Gutenberg University, Mainz D-55099, Germany)

Abstract

This paper addresses the periodic vehicle routing problem with time windows (PVRPTW). Therein, customers require one or several visits during a planning horizon of several periods. The possible visiting patterns (schedules) per customer are limited. In the classical PVRPTW, it is common to assume that each customer requires a specific visit frequency and offers all corresponding schedules with regular intervals between the visits. In this paper, we permit all kinds of schedule structures and the choice of the service frequency. We present an exact branch-and-price-and-cut algorithm for the classical PVRPTW and its variant with flexible schedules. The pricing problems are elementary shortest-path problems with resource constraints. They can be based on one of two new types of networks and solved with a labeling algorithm, which uses several known acceleration techniques, such as the n g -path relaxation and dynamic halfway points within bidirectional labeling. For instances in which schedule sets fulfill a certain symmetry condition, we present specialized improvements of the algorithm, such as constraint aggregation and symmetry breaking. Computational tests on benchmark instances for the PVRPTW show the effectiveness of our algorithm. Furthermore, we analyze the impact of different schedule structures on run times and objective function values. The online appendix is available at https://doi.org/10.1287/trsc.2018.0855 .

Suggested Citation

  • Ann-Kathrin Rothenbächer, 2019. "Branch-and-Price-and-Cut for the Periodic Vehicle Routing Problem with Flexible Schedule Structures," Transportation Science, INFORMS, vol. 53(3), pages 850-866, May.
    • Handle: RePEc:inm:ortrsc:v:53:y:2019:i:3:p:850-866
    DOI: 10.1287/trsc.2018.0855
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    References listed on IDEAS

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    1. Peter Francis & Karen Smilowitz & Michal Tzur, 2006. "The Period Vehicle Routing Problem with Service Choice," Transportation Science, INFORMS, vol. 40(4), pages 439-454, November.
    2. Hemmelmayr, Vera C. & Doerner, Karl F. & Hartl, Richard F., 2009. "A variable neighborhood search heuristic for periodic routing problems," European Journal of Operational Research, Elsevier, vol. 195(3), pages 791-802, June.
    3. Peter Francis & Karen Smilowitz & Michal Tzur, 2007. "Flexibility and complexity in periodic distribution problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(2), pages 136-150, March.
    4. Claudia Bode & Stefan Irnich, 2015. "In-Depth Analysis of Pricing Problem Relaxations for the Capacitated Arc-Routing Problem," Transportation Science, INFORMS, vol. 49(2), pages 369-383, May.
    5. J-F Cordeau & G Laporte & A Mercier, 2004. "Improved tabu search algorithm for the handling of route duration constraints in vehicle routing problems with time windows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(5), pages 542-546, May.
    6. Michel Gamache & François Soumis & Gérald Marquis & Jacques Desrosiers, 1999. "A Column Generation Approach for Large-Scale Aircrew Rostering Problems," Operations Research, INFORMS, vol. 47(2), pages 247-263, April.
    7. M. Gaudioso & G. Paletta, 1992. "A Heuristic for the Periodic Vehicle Routing Problem," Transportation Science, INFORMS, vol. 26(2), pages 86-92, May.
    8. Rasmussen, Matias Sevel & Justesen, Tor & Dohn, Anders & Larsen, Jesper, 2012. "The Home Care Crew Scheduling Problem: Preference-based visit clustering and temporal dependencies," European Journal of Operational Research, Elsevier, vol. 219(3), pages 598-610.
    9. Ann-Kathrin Rothenbächer & Michael Drexl & Stefan Irnich, 2018. "Branch-and-Price-and-Cut for the Truck-and-Trailer Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 52(5), pages 1174-1190, October.
    10. 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).
    11. Christian Tilk & Stefan Irnich, 2017. "Dynamic Programming for the Minimum Tour Duration Problem," Transportation Science, INFORMS, vol. 51(2), pages 549-565, May.
    12. Stefan Irnich & Guy Desaulniers, 2005. "Shortest Path Problems with Resource Constraints," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 33-65, Springer.
    13. Eveborn, Patrik & Flisberg, Patrik & Ronnqvist, Mikael, 2006. "Laps Care--an operational system for staff planning of home care," European Journal of Operational Research, Elsevier, vol. 171(3), pages 962-976, June.
    14. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    15. Tan, C.C.R. & Beasley, J.E., 1984. "A heuristic algorithm for the period vehicle routing problem," Omega, Elsevier, vol. 12(5), pages 497-504.
    16. Villeneuve, Daniel & Desaulniers, Guy, 2005. "The shortest path problem with forbidden paths," European Journal of Operational Research, Elsevier, vol. 165(1), pages 97-107, August.
    17. Roberto Roberti & Aristide Mingozzi, 2014. "Dynamic ng-Path Relaxation for the Delivery Man Problem," Transportation Science, INFORMS, vol. 48(3), pages 413-424, August.
    18. Theodore Athanasopoulos & Ioannis Minis, 2013. "Efficient techniques for the multi-period vehicle routing problem with time windows within a branch and price framework," Annals of Operations Research, Springer, vol. 206(1), pages 1-22, July.
    19. Tilk, Christian & Rothenbächer, Ann-Kathrin & Gschwind, Timo & Irnich, Stefan, 2017. "Asymmetry matters: Dynamic half-way points in bidirectional labeling for solving shortest path problems with resource constraints faster," European Journal of Operational Research, Elsevier, vol. 261(2), pages 530-539.
    20. 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.
    21. J-F Cordeau & G Laporte & A Mercier, 2001. "A unified tabu search heuristic for vehicle routing problems with time windows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(8), pages 928-936, August.
    22. 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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