IDEAS home Printed from https://ideas.repec.org/a/spr/eurjtl/v6y2017i4d10.1007_s13676-016-0097-9.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13676-016-0097-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13676-016-0097-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Guy Desaulniers, 2010. "Branch-and-Price-and-Cut for the Split-Delivery Vehicle Routing Problem with Time Windows," Operations Research, INFORMS, vol. 58(1), pages 179-192, February.
    2. 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).
    3. 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.
    4. Claudia Archetti & Luca Bertazzi & Gilbert Laporte & Maria Grazia Speranza, 2007. "A Branch-and-Cut Algorithm for a Vendor-Managed Inventory-Routing Problem," Transportation Science, INFORMS, vol. 41(3), pages 382-391, August.
    5. Maria Battarra & Güneş Erdoğan & Daniele Vigo, 2014. "Exact Algorithms for the Clustered Vehicle Routing Problem," Operations Research, INFORMS, vol. 62(1), pages 58-71, February.
    6. Leandro C. Coelho & Jean-François Cordeau & Gilbert Laporte, 2014. "Thirty Years of Inventory Routing," Transportation Science, INFORMS, vol. 48(1), pages 1-19, February.
    7. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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. 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.
    4. 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).
    5. 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.
    6. 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.
    7. 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).
    8. 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).
    9. 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.
    10. Laurent Alfandari & Alborz Hassanzadeh & Ivana Ljubić, 2021. "An Exact Method for Assortment Optimization under the Nested Logit Model," Working Papers hal-02463159, HAL.
    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guy Desaulniers & Jørgen G. Rakke & Leandro C. Coelho, 2016. "A Branch-Price-and-Cut Algorithm for the Inventory-Routing Problem," Transportation Science, INFORMS, vol. 50(3), pages 1060-1076, August.
    2. 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.
    3. Annelieke C. Baller & Said Dabia & Guy Desaulniers & Wout E. H. Dullaert, 2021. "The Inventory Routing Problem with Demand Moves," SN Operations Research Forum, Springer, vol. 2(1), pages 1-61, March.
    4. 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).
    5. Zhenzhen Zhang & Zhixing Luo & Roberto Baldacci & Andrew Lim, 2021. "A Benders Decomposition Approach for the Multivehicle Production Routing Problem with Order-up-to-Level Policy," Transportation Science, INFORMS, vol. 55(1), pages 160-178, 1-2.
    6. Cárdenas-Barrón, Leopoldo Eduardo & González-Velarde, José Luis & Treviño-Garza, Gerardo & Garza-Nuñez, Dagoberto, 2019. "Heuristic algorithm based on reduce and optimize approach for a selective and periodic inventory routing problem in a waste vegetable oil collection environment," International Journal of Production Economics, Elsevier, vol. 211(C), pages 44-59.
    7. Claudia Archetti & Natashia Boland & Grazia Speranza, 2017. "A Matheuristic for the Multivehicle Inventory Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 377-387, August.
    8. Hu, Weihong & Toriello, Alejandro & Dessouky, Maged, 2018. "Integrated inventory routing and freight consolidation for perishable goods," European Journal of Operational Research, Elsevier, vol. 271(2), pages 548-560.
    9. Manousakis, Eleftherios & Repoussis, Panagiotis & Zachariadis, Emmanouil & Tarantilis, Christos, 2021. "Improved branch-and-cut for the Inventory Routing Problem based on a two-commodity flow formulation," European Journal of Operational Research, Elsevier, vol. 290(3), pages 870-885.
    10. Agra, Agostinho & Christiansen, Marielle & Wolsey, Laurence, 2022. "Improved models for a single vehicle continuous-time inventory routing problem with pickups and deliveries," European Journal of Operational Research, Elsevier, vol. 297(1), pages 164-179.
    11. Jia, Menglei & Chen, Feng, 2023. "Upward scalable vehicle routing problem of automobile inbound logistics with pickup flexibility," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    12. Roel G. van Anholt & Leandro C. Coelho & Gilbert Laporte & Iris F. A. Vis, 2016. "An Inventory-Routing Problem with Pickups and Deliveries Arising in the Replenishment of Automated Teller Machines," Transportation Science, INFORMS, vol. 50(3), pages 1077-1091, August.
    13. Skålnes, Jørgen & Andersson, Henrik & Desaulniers, Guy & Stålhane, Magnus, 2022. "An improved formulation for the inventory routing problem with time-varying demands," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1189-1201.
    14. Felipe Lagos & Natashia Boland & Martin Savelsbergh, 2020. "The Continuous-Time Inventory-Routing Problem," Transportation Science, INFORMS, vol. 54(2), pages 375-399, March.
    15. 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.
    16. Pasquale Avella & Maurizio Boccia & Laurence A. Wolsey, 2018. "Single-Period Cutting Planes for Inventory Routing Problems," Transportation Science, INFORMS, vol. 52(3), pages 497-508, June.
    17. AVELLA, Pasquale & BOCCIA, Maurizio & WOLSEY, Laurence A., 2014. "Single-period cutting planes for inventory routing problems," LIDAM Discussion Papers CORE 2014055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Touzout, Faycal A. & Ladier, Anne-Laure & Hadj-Hamou, Khaled, 2022. "An assign-and-route matheuristic for the time-dependent inventory routing problem," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1081-1097.
    19. Schenekemberg, Cleder M. & Scarpin, Cassius T. & Pécora, José E. & Guimarães, Thiago A. & Coelho, Leandro C., 2021. "The two-echelon production-routing problem," European Journal of Operational Research, Elsevier, vol. 288(2), pages 436-449.
    20. 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).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:eurjtl:v:6:y:2017:i:4:d:10.1007_s13676-016-0097-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.