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An exact algorithm for the petrol station replenishment problem

Author

Listed:
  • F Cornillier

    (Université Laval)

  • F F Boctor

    (Université Laval)

  • G Laporte

    (HEC Montréal)

  • J Renaud

    (Université Laval)

Abstract

In the petrol station replenishment problem (PSRP), the aim is to deliver petroleum products to petrol stations by means of an unlimited heterogeneous fleet of compartmented tank trucks. The problem consists of jointly determining quantities to deliver within a given interval, of allocating products to tank truck compartments and of designing delivery routes to stations. This article describes an exact algorithm which decomposes the PSRP into a truck loading problem and a routing problem. An algorithm which makes use of assignment, optimality tests and possibly standard ILP algorithm is proposed to solve the loading problem. The routing problem is handled using two different strategies, based either on a matching approach or on a column generation scheme. This algorithm was extensively tested on randomly generated data and on a real-life case arising in Eastern Quebec.

Suggested Citation

  • F Cornillier & F F Boctor & G Laporte & J Renaud, 2008. "An exact algorithm for the petrol station replenishment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(5), pages 607-615, May.
    • Handle: RePEc:pal:jorsoc:v:59:y:2008:i:5:d:10.1057_palgrave.jors.2602374
    DOI: 10.1057/palgrave.jors.2602374
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Coelho, Leandro C. & Laporte, Gilbert, 2015. "Classification, models and exact algorithms for multi-compartment delivery problems," European Journal of Operational Research, Elsevier, vol. 242(3), pages 854-864.
    2. Sun, Lijun & Zhang, Yuankai & Hu, Xiangpei, 2021. "Economical-traveling-distance-based fleet composition with fuel costs: An application in petrol distribution," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
    3. Ostermeier, Manuel & Henke, Tino & Hübner, Alexander & Wäscher, Gerhard, 2021. "Multi-compartment vehicle routing problems: State-of-the-art, modeling framework and future directions," European Journal of Operational Research, Elsevier, vol. 292(3), pages 799-817.
    4. Cornillier, Fabien & Boctor, Fayez & Renaud, Jacques, 2012. "Heuristics for the multi-depot petrol station replenishment problem with time windows," European Journal of Operational Research, Elsevier, vol. 220(2), pages 361-369.
    5. Bani, Abderrahman & El Hallaoui, Issmail & Corréa, Ayoub Insa & Tahir, Adil, 2023. "Solving a real-world multi-depot multi-period petrol replenishment problem with complex loading constraints," European Journal of Operational Research, Elsevier, vol. 311(1), pages 154-172.
    6. Schmid, Verena & Doerner, Karl F. & Laporte, Gilbert, 2013. "Rich routing problems arising in supply chain management," European Journal of Operational Research, Elsevier, vol. 224(3), pages 435-448.
    7. Manuel Iori & Silvano Martello, 2010. "Routing problems with loading constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 4-27, July.
    8. Furkan Uzar, M. & Çatay, Bülent, 2012. "Distribution planning of bulk lubricants at BP Turkey," Omega, Elsevier, vol. 40(6), pages 870-881.
    9. Carrese, Stefano & Cuneo, Valerio & Nigro, Marialisa & Pizzuti, Raffaele & Ardito, Cosimo Federico & Marseglia, Guido, 2022. "Optimization of downstream fuel logistics based on road infrastructure conditions and exposure to accident events," Transport Policy, Elsevier, vol. 124(C), pages 96-105.
    10. Boctor, Fayez F. & Renaud, Jacques & Cornillier, Fabien, 2011. "Trip packing in petrol stations replenishment," Omega, Elsevier, vol. 39(1), pages 86-98, January.
    11. Pasquale Carotenuto & Stefano Giordani & Alessio Salvatore, 2024. "A Matheuristic Approach for the Multi-Depot Periodic Petrol Station Replenishment Problem," Mathematics, MDPI, vol. 12(3), pages 1-19, January.
    12. Lahyani, Rahma & Coelho, Leandro C. & Khemakhem, Mahdi & Laporte, Gilbert & Semet, Frédéric, 2015. "A multi-compartment vehicle routing problem arising in the collection of olive oil in Tunisia," Omega, Elsevier, vol. 51(C), pages 1-10.
    13. Samira Mirzaei & Sanne Wøhlk, 2019. "A Branch-and-Price algorithm for two multi-compartment vehicle routing problems," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(1), pages 1-33, March.
    14. Katrin Heßler, 2020. "Exact Algorithms for the Multi-Compartment Vehicle Routing Problem with Flexible Compartment Sizes," Working Papers 2007, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    15. Eghbal Akhlaghi, Vahid & Campbell, Ann Melissa & de Matta, Renato E., 2021. "Fuel distribution planning for disasters: Models and case study for Puerto Rico," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    16. Lobo, Benjamin J. & Brown, Donald E. & Gerber, Matthew S. & Grazaitis, Peter J., 2018. "A transient stochastic simulation–optimization model for operational fuel planning in-theater," European Journal of Operational Research, Elsevier, vol. 264(2), pages 637-652.
    17. Samira Mirzaei & Sanne Wøhlk, 2017. "Erratum to: A Branch-and-Price algorithm for two multi-compartment vehicle routing problems," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 6(2), pages 185-218, June.
    18. Heßler, Katrin, 2021. "Exact algorithms for the multi-compartment vehicle routing problem with flexible compartment sizes," European Journal of Operational Research, Elsevier, vol. 294(1), pages 188-205.
    19. Guilherme Baptista & Miguel Vieira & Telmo Pinto, 2024. "An Exact Approach to the Multi-Compartment Vehicle Routing Problem: The Case of a Fuel Distribution Company," Mathematics, MDPI, vol. 12(4), pages 1-14, February.
    20. Vasilii A. Gromov & Konstantin A. Kuznietzov & Timothy Pigden, 2019. "Decision support system for light petroleum products supply chain," Operational Research, Springer, vol. 19(1), pages 219-236, March.
    21. Katrin Heßler & Stefan Irnich, 2023. "Partial Dominance in Branch-Price-and-Cut for the Basic Multicompartment Vehicle-Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 50-65, January.
    22. Katrin Heßler & Stefan Irnich, 2021. "Partial Dominance in Branch-Price-and-Cut for the Basic Multi-Compartment Vehicle-Routing Problem," Working Papers 2115, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    23. Hiba Yahyaoui & Islem Kaabachi & Saoussen Krichen & Abdulkader Dekdouk, 2020. "Two metaheuristic approaches for solving the multi-compartment vehicle routing problem," Operational Research, Springer, vol. 20(4), pages 2085-2108, December.

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