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Minimizing the logistic ratio in the inventory routing problem

Author

Listed:
  • Claudia Archetti

    (University of Brescia)

  • Guy Desaulniers

    (Ecole Polytechnique de Montréal and GERAD)

  • M. Grazia Speranza

    (University of Brescia)

Abstract

Inventory routing problems (IRPs) aim at minimizing the cost of the total distance traveled over a time horizon discretized in periods, while guaranteeing that the customers do not incur a stock-out event. In an optimal solution of an IRP, the customers in general have no inventory at the end of the horizon. Some inventory may remain only if this does not increase the cost of the distance traveled. To avoid this ending drawback, we consider in this paper as objective function the so-called logistic ratio, which is the ratio of the total routing cost to the total quantity distributed. The logistic ratio gives rise to a new optimization problem whose mathematical programming formulation is non-linear. Using a classical method, we can solve exactly instances with up to 5 vehicles and 15 customers over 3 periods. The solutions are compared with those of a classical IRP, both from the worst-case point of view and computationally. The results show that on average the logistic ratio increases by 20.4 % in the classical IRP on instances with 3 periods and that the percentage decreases when the horizon length increases.

Suggested Citation

  • Claudia Archetti & Guy Desaulniers & M. Grazia Speranza, 2017. "Minimizing the logistic ratio in the inventory routing problem," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 289-306, December.
    • Handle: RePEc:spr:eurjtl:v:6:y:2017:i:4:d:10.1007_s13676-016-0097-9
    DOI: 10.1007/s13676-016-0097-9
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    References listed on IDEAS

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    2. Fokkema, Jan Eise & Land, Martin J. & Coelho, Leandro C. & Wortmann, Hans & Huitema, George B., 2020. "A continuous-time supply-driven inventory-constrained routing problem," Omega, Elsevier, vol. 92(C).
    3. Yun He & Christian Artigues & Cyril Briand & Nicolas Jozefowiez & Sandra Ulrich Ngueveu, 2020. "A Matheuristic with Fixed-Sequence Reoptimization for a Real-Life Inventory Routing Problem," Transportation Science, INFORMS, vol. 54(2), pages 355-374, March.
    4. Alarcon Ortega, Emilio J. & Schilde, Michael & Doerner, Karl F., 2020. "Matheuristic search techniques for the consistent inventory routing problem with time windows and split deliveries," Operations Research Perspectives, Elsevier, vol. 7(C).
    5. Coelho, Leandro Callegari & De Maio, Annarita & Laganà, Demetrio, 2020. "A variable MIP neighborhood descent for the multi-attribute inventory routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 144(C).
    6. Laurent Alfandari & Alborz Hassanzadeh & Ivana Ljubić, 2021. "An Exact Method for Assortment Optimization under the Nested Logit Model," Working Papers hal-02463159, HAL.
    7. Frómeta Moya, Jorge Israel & Pérez Campos, Javier de Jesús, 2021. "Modelo heurístico híbrido para el ruteo vehicular y manejo de inventario en una entidad comercializadora de combustibles. || Hybrid heuristic model for inventory routing management in a fuel comercial," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 31(1), pages 363-383, June.
    8. Ali Pedram & Shahryar Sorooshian & Freselam Mulubrhan & Afshin Abbaspour, 2023. "Incorporating Vehicle-Routing Problems into a Closed-Loop Supply Chain Network Using a Mixed-Integer Linear-Programming Model," Sustainability, MDPI, vol. 15(4), pages 1-24, February.
    9. Alfandari, Laurent & Hassanzadeh, Alborz & Ljubic, Ivana, 2020. "An Exact Method for Assortment Optimization under the Nested Logit Model," ESSEC Working Papers WP2001, ESSEC Research Center, ESSEC Business School, revised 2020.
    10. Archetti, Claudia & Coelho, Leandro C. & Grazia Speranza, M., 2019. "An exact algorithm for the inventory routing problem with logistic ratio," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 96-107.
    11. Nabil Absi & Diego Cattaruzza & Dominique Feillet & Maxime Ogier & Frédéric Semet, 2020. "A Heuristic Branch-Cut-and-Price Algorithm for the ROADEF/EURO Challenge on Inventory Routing," Transportation Science, INFORMS, vol. 54(2), pages 313-329, March.
    12. Chiu, Agustín & Angulo, Gustavo & Larrain, Homero, 2024. "Optimizing the long-term costs of an Inventory Routing Problem using linear relaxation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 183(C).

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