IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v52y2018i3p497-508.html
   My bibliography  Save this article

Single-Period Cutting Planes for Inventory Routing Problems

Author

Listed:
  • Pasquale Avella

    (Dipartimento di Ingegneria, Università del Sannio, 82100 Benevento, Italy)

  • Maurizio Boccia

    (Dipartimento di Ingegneria, Università del Sannio, 82100 Benevento, Italy)

  • Laurence A. Wolsey

    (Center for Operations Research and Econometrics, Université catholique de Louvain, 1348 Louvain-la-Neuve, Belgium)

Abstract

The Inventory Routing Problem (IRP) involves the distribution of one or more products from a supplier to a set of clients over a discrete planning horizon. Each client has a known demand to be met in each period and can only hold a limited amount of stock. The product is shipped through a distribution network by one or more vehicles of limited capacity. The objective is to find replenishment decisions minimizing the sum of the storage and distribution costs. In this paper, we present IRP reformulations under the Maximum Level replenishment policy, derived from a single-period substructure. We define a generic family of valid inequalities, and then introduce two specific subclasses for which the separation problem of generating violated inequalities can be effectively solved. A basic Branch-and-Cut algorithm has been implemented to demonstrate the strength of the single-period reformulations. We present computational results for the benchmark instances with 50 clients and 3 periods and 30 clients and 6 periods.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:52:y:2018:i:3:p:497-508
    DOI: 10.1287/trsc.2016.0729
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/trsc.2016.0729
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.2016.0729?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
    ---><---

    References listed on IDEAS

    as
    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. Jean-Claude Picard & H. Donald Ratliff, 1973. "A Graph-Theoretic Equivalence for Integer Programs," Operations Research, INFORMS, vol. 21(1), pages 261-269, February.
    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. Yossiri Adulyasak & Jean-François Cordeau & Raf Jans, 2014. "Formulations and Branch-and-Cut Algorithms for Multivehicle Production and Inventory Routing Problems," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 103-120, February.
    5. Oğuz Solyalı & Haldun Süral, 2011. "A Branch-and-Cut Algorithm Using a Strong Formulation and an A Priori Tour-Based Heuristic for an Inventory-Routing Problem," Transportation Science, INFORMS, vol. 45(3), pages 335-345, August.
    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. 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.
    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. Skålnes, Jørgen & Ben Ahmed, Mohamed & Hvattum, Lars Magnus & Stålhane, Magnus, 2024. "New benchmark instances for the inventory routing problem," European Journal of Operational Research, Elsevier, vol. 313(3), pages 992-1014.
    2. 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.
    3. 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.
    4. Bertazzi, Luca & Coelho, Leandro C. & De Maio, Annarita & Laganà, Demetrio, 2019. "A matheuristic algorithm for the multi-depot inventory routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 524-544.
    5. Zhouxing Su & Zhipeng Lü & Zhuo Wang & Yanmin Qi & Una Benlic, 2020. "A Matheuristic Algorithm for the Inventory Routing Problem," Transportation Science, INFORMS, vol. 54(2), pages 330-354, March.
    6. Diabat, Ali & Bianchessi, Nicola & Archetti, Claudia, 2024. "On the zero-inventory-ordering policy in the inventory routing problem," European Journal of Operational Research, Elsevier, vol. 312(3), pages 1024-1038.
    7. Ziye Tang & Yang Jiao & R. Ravi, 2022. "Combinatorial Heuristics for Inventory Routing Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 370-384, January.
    8. Bertazzi, Luca & Laganà, Demetrio & Ohlmann, Jeffrey W. & Paradiso, Rosario, 2020. "An exact approach for cyclic inbound inventory routing in a level production system," European Journal of Operational Research, Elsevier, vol. 283(3), pages 915-928.
    9. 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.
    10. Archetti, Claudia & Ljubić, Ivana, 2022. "Comparison of formulations for the Inventory Routing Problem," European Journal of Operational Research, Elsevier, vol. 303(3), pages 997-1008.
    11. 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.
    12. Archetti, Claudia & Speranza, M. Grazia & Boccia, Maurizio & Sforza, Antonio & Sterle, Claudio, 2020. "A branch-and-cut algorithm for the inventory routing problem with pickups and deliveries," European Journal of Operational Research, Elsevier, vol. 282(3), pages 886-895.
    13. Bertazzi, Luca & Chua, Geoffrey A. & Laganà, Demetrio & Paradiso, Rosario, 2022. "Analysis of effective sets of routes for the split-delivery periodic inventory routing problem," European Journal of Operational Research, Elsevier, vol. 298(2), pages 463-477.
    14. 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.
    15. 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).
    16. Masoud Chitsaz & Jean-François Cordeau & Raf Jans, 2019. "A Unified Decomposition Matheuristic for Assembly, Production, and Inventory Routing," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 134-152, February.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. 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.
    9. Skålnes, Jørgen & Ben Ahmed, Mohamed & Hvattum, Lars Magnus & Stålhane, Magnus, 2024. "New benchmark instances for the inventory routing problem," European Journal of Operational Research, Elsevier, vol. 313(3), pages 992-1014.
    10. 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).
    11. Diabat, Ali & Bianchessi, Nicola & Archetti, Claudia, 2024. "On the zero-inventory-ordering policy in the inventory routing problem," European Journal of Operational Research, Elsevier, vol. 312(3), pages 1024-1038.
    12. Yves Crama & Mahmood Rezaei & Martin Savelsbergh & Tom Van Woensel, 2018. "Stochastic Inventory Routing for Perishable Products," Transportation Science, INFORMS, vol. 52(3), pages 526-546, June.
    13. Alvarez, Aldair & Cordeau, Jean-François & Jans, Raf & Munari, Pedro & Morabito, Reinaldo, 2021. "Inventory routing under stochastic supply and demand," Omega, Elsevier, vol. 102(C).
    14. 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.
    15. Çelik, Melih & Archetti, Claudia & Süral, Haldun, 2022. "Inventory routing in a warehouse: The storage replenishment routing problem," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1117-1132.
    16. Qiu, Yuzhuo & Zhou, Dan & Du, Yanan & Liu, Jie & Pardalos, Panos M. & Qiao, Jun, 2021. "The two-echelon production routing problem with cross-docking satellites," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
    17. Bertazzi, Luca & Laganà, Demetrio & Ohlmann, Jeffrey W. & Paradiso, Rosario, 2020. "An exact approach for cyclic inbound inventory routing in a level production system," European Journal of Operational Research, Elsevier, vol. 283(3), pages 915-928.
    18. Archetti, Claudia & Christiansen, Marielle & Grazia Speranza, M., 2018. "Inventory routing with pickups and deliveries," European Journal of Operational Research, Elsevier, vol. 268(1), pages 314-324.
    19. 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.
    20. 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.

    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:inm:ortrsc:v:52:y:2018:i:3:p:497-508. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.