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Alternative formulations and improved bounds for the multi-depot fleet size and mix vehicle routing problem

Author

Listed:
  • Rahma Lahyani

    (Alfaisal University, College of Business
    Institut Supérieur de Gestion Industrielle)

  • Leandro C. Coelho

    (Interuniversity Research Center on Enterprise Network, Logistics and Transportation
    Université Laval
    Canada Research Chair in Integrated Logistics
    Groningen University)

  • Jacques Renaud

    (Interuniversity Research Center on Enterprise Network, Logistics and Transportation
    Université Laval)

Abstract

In this paper, we compare different formulations of the multi-depot fleet size and mix vehicle routing problem (MDFSMVRP). This problem extends the multi-depot vehicle routing problem and the fleet size and mix vehicle routing problem, two logistics problems that have been extensively studied for many decades. This difficult vehicle routing problem combines complex assignment and routing decisions under the objective of minimizing fixed vehicle costs and variable routing costs. We first propose five distinct formulations to model the MDFSMVRP. We introduce a three-index formulation with an explicit vehicle index and a two-index formulation in which only vehicle types are identified. Other formulations are obtained by defining aggregated and disaggregated loading variables. The last formulation makes use of capacity-indexed variables. For each formulation, we summarize known and propose new valid inequalities, including symmetry breaking, lexicographic ordering, routing, and rounded capacity cuts. We then implement branch-and-cut and branch-and-bound algorithms for these formulations, and we fed them into a general purpose solver. We compare the bounds provided by the formulations on a commonly used set of instances in the MDFSMVRP literature, containing up to nine depots and 360 customers, and on newly generated instances. Our in-depth analysis of the five formulations shows which formulations tend to perform better on each type of instance. Moreover, our results have considerably improved available lower bounds on all instances and significantly improved quality of upper bounds that can be obtained by means of currently available methods.

Suggested Citation

  • Rahma Lahyani & Leandro C. Coelho & Jacques Renaud, 2018. "Alternative formulations and improved bounds for the multi-depot fleet size and mix vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 125-157, January.
    • Handle: RePEc:spr:orspec:v:40:y:2018:i:1:d:10.1007_s00291-017-0494-y
    DOI: 10.1007/s00291-017-0494-y
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    References listed on IDEAS

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    1. Gouveia, Luis, 1995. "A result on projection for the vehicle routing ptoblem," European Journal of Operational Research, Elsevier, vol. 85(3), pages 610-624, September.
    2. Perl, Jossef & Daskin, Mark S., 1985. "A warehouse location-routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 19(5), pages 381-396, October.
    3. Karaoglan, Ismail & Altiparmak, Fulya & Kara, Imdat & Dengiz, Berna, 2012. "The location-routing problem with simultaneous pickup and delivery: Formulations and a heuristic approach," Omega, Elsevier, vol. 40(4), pages 465-477.
    4. Kulkarni, R. V. & Bhave, P. R., 1985. "Integer programming formulations of vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 20(1), pages 58-67, April.
    5. Thibaut Vidal & Teodor Gabriel Crainic & Michel Gendreau & Nadia Lahrichi & Walter Rei, 2012. "A Hybrid Genetic Algorithm for Multidepot and Periodic Vehicle Routing Problems," Operations Research, INFORMS, vol. 60(3), pages 611-624, June.
    6. Campos, V. & Corberan, A. & Mota, E., 1991. "Polyhedral results for a vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 52(1), pages 75-85, May.
    7. Araque, J. & Hall, L. & Magnanti, T., 1990. "Capacitated trees, capacitated routing, and associated polyhedra," LIDAM Discussion Papers CORE 1990061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Vidal, Thibaut & Crainic, Teodor Gabriel & Gendreau, Michel & Prins, Christian, 2014. "Implicit depot assignments and rotations in vehicle routing heuristics," European Journal of Operational Research, Elsevier, vol. 237(1), pages 15-28.
    9. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    10. W. W. Garvin & H. W. Crandall & J. B. John & R. A. Spellman, 1957. "Applications of Linear Programming in the Oil Industry," Management Science, INFORMS, vol. 3(4), pages 407-430, July.
    11. Michel Gendreau & Gilbert Laporte & Frédéric Semet, 1997. "The Covering Tour Problem," Operations Research, INFORMS, vol. 45(4), pages 568-576, August.
    12. Prodhon, Caroline & Prins, Christian, 2014. "A survey of recent research on location-routing problems," European Journal of Operational Research, Elsevier, vol. 238(1), pages 1-17.
    13. Gillett, Billy E & Johnson, Jerry G, 1976. "Multi-terminal vehicle-dispatch algorithm," Omega, Elsevier, vol. 4(6), pages 711-718.
    14. Bektaş, Tolga & Gouveia, Luis, 2014. "Requiem for the Miller–Tucker–Zemlin subtour elimination constraints?," European Journal of Operational Research, Elsevier, vol. 236(3), pages 820-832.
    15. Liu, Shuguang, 2013. "A hybrid population heuristic for the heterogeneous vehicle routing problems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 54(C), pages 67-78.
    16. Hanif D. Sherali & J. Cole Smith, 2001. "Improving Discrete Model Representations via Symmetry Considerations," Management Science, INFORMS, vol. 47(10), pages 1396-1407, October.
    17. Gilbert Laporte, 2009. "Fifty Years of Vehicle Routing," Transportation Science, INFORMS, vol. 43(4), pages 408-416, November.
    18. Salhi, Said & Rand, Graham K., 1993. "Incorporating vehicle routing into the vehicle fleet composition problem," European Journal of Operational Research, Elsevier, vol. 66(3), pages 313-330, May.
    19. Onur Can Saka & Sinan Gürel & Tom Van Woensel, 2017. "Using cost change estimates in a local search heuristic for the pollution routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 557-587, March.
    20. Coelho, Leandro C. & Laporte, Gilbert, 2014. "Improved solutions for inventory-routing problems through valid inequalities and input ordering," International Journal of Production Economics, Elsevier, vol. 155(C), pages 391-397.
    21. Jean-Claude Picard & Maurice Queyranne, 1978. "The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling," Operations Research, INFORMS, vol. 26(1), pages 86-110, February.
    22. Salhi, S. & Sari, M., 1997. "A multi-level composite heuristic for the multi-depot vehicle fleet mix problem," European Journal of Operational Research, Elsevier, vol. 103(1), pages 95-112, November.
    23. Luis Gouveia, 1995. "A 2n Constraint Formulation for the Capacitated Minimal Spanning Tree Problem," Operations Research, INFORMS, vol. 43(1), pages 130-141, February.
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