IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v282y2020i3p886-895.html
   My bibliography  Save this article

A branch-and-cut algorithm for the inventory routing problem with pickups and deliveries

Author

Listed:
  • Archetti, Claudia
  • Speranza, M. Grazia
  • Boccia, Maurizio
  • Sforza, Antonio
  • Sterle, Claudio

Abstract

This paper addresses the Inventory Routing Problem with Pickups and Deliveries (IRP-PD). A single commodity has to be picked up from several origins and distributed to several destinations. The commodity is made available at the supplier depot and at the pickup customers, with known amounts in each period of a discretized time horizon. The commodity is consumed by the delivery customers, whose demand, in each period of the time horizon, is known. The vehicles start and end their routes at the supplier depot. The objective is to determine a collection and distribution plan minimizing the sum of routing and inventory costs, satisfying inventory and capacity constraints. A mixed integer linear programming model is presented for the IRP-PD. Valid inequalities are proposed that are adapted from the inventory routing, the vehicle routing and the lot-sizing problems literature. Moreover, a new set of valid inequalities, called interval inequalities, is presented. A branch-and-cut algorithm is designed and tested on a large set of instances. Computational results show that the proposed approach is able to solve to optimality 946 out of 1280 instances. Moreover, the approach outperforms the state-of-the art method for the single vehicle case, increasing the number of instances solved to optimality from 473 to 538 out of 640 instances tested, with 133 new best known solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:282:y:2020:i:3:p:886-895
    DOI: 10.1016/j.ejor.2019.09.056
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719308136
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2019.09.056?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. Lysgaard, Jens, 2006. "Reachability cuts for the vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 175(1), pages 210-223, November.
    2. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Rejoinder on: Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 45-47, July.
    3. Iassinovskaia, Galina & Limbourg, Sabine & Riane, Fouad, 2017. "The inventory-routing problem of returnable transport items with time windows and simultaneous pickup and delivery in closed-loop supply chains," International Journal of Production Economics, Elsevier, vol. 183(PB), pages 570-582.
    4. 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.
    5. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-31, July.
    6. Pasquale Avella & Maurizio Boccia & Laurence A. Wolsey, 2018. "Single-period cutting planes for inventory routing problems," LIDAM Reprints CORE 3009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Agostinho Agra & Marielle Christiansen & Alexandrino Delgado, 2013. "Mixed Integer Formulations for a Short Sea Fuel Oil Distribution Problem," Transportation Science, INFORMS, vol. 47(1), pages 108-124, February.
    8. 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.
    9. Li, Chongshou & Gong, Lijun & Luo, Zhixing & Lim, Andrew, 2019. "A branch-and-price-and-cut algorithm for a pickup and delivery problem in retailing," Omega, Elsevier, vol. 89(C), pages 71-91.
    10. Athanassios Nikolakopoulos & Ioannis Ganas, 2017. "Economic model predictive inventory routing and control," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(3), pages 587-609, September.
    11. Christiansen, Marielle & Fagerholt, Kjetil & Nygreen, Bjørn & Ronen, David, 2013. "Ship routing and scheduling in the new millennium," European Journal of Operational Research, Elsevier, vol. 228(3), pages 467-483.
    12. Roar Grønhaug & Marielle Christiansen & Guy Desaulniers & Jacques Desrosiers, 2010. "A Branch-and-Price Method for a Liquefied Natural Gas Inventory Routing Problem," Transportation Science, INFORMS, vol. 44(3), pages 400-415, August.
    13. Faramroze G. Engineer & Kevin C. Furman & George L. Nemhauser & Martin W. P. Savelsbergh & Jin-Hwa Song, 2012. "A Branch-Price-and-Cut Algorithm for Single-Product Maritime Inventory Routing," Operations Research, INFORMS, vol. 60(1), pages 106-122, February.
    14. 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.
    15. Edirisinghe, N.C.P. & James, R.J.W., 2014. "Fleet routing position-based model for inventory pickup under production shutdown," European Journal of Operational Research, Elsevier, vol. 236(2), pages 736-747.
    16. Jonathan F. Bard & Liu Huang & Patrick Jaillet & Moshe Dror, 1998. "A Decomposition Approach to the Inventory Routing Problem with Satellite Facilities," Transportation Science, INFORMS, vol. 32(2), pages 189-203, May.
    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. 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.
    2. Neves-Moreira, Fábio & Almada-Lobo, Bernardo & Guimarães, Luís & Amorim, Pedro, 2022. "The multi-product inventory-routing problem with pickups and deliveries: Mitigating fluctuating demand via rolling horizon heuristics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
    3. 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.
    4. Mahmutoğulları, Özlem & Yaman, Hande, 2023. "A Branch-and-Cut Algorithm for the Inventory Routing Problem with Product Substitution," Omega, Elsevier, vol. 115(C).
    5. Bertazzi, Luca & Moezi, Sarem Deilami & Maggioni, Francesca, 2021. "The value of integration of full container load, less than container load and air freight shipments in vendor–managed inventory systems," International Journal of Production Economics, Elsevier, vol. 241(C).
    6. Fatima Ezzahra Achamrah & Fouad Riane & Evren Sahin & Sabine Limbourg, 2022. "An Artificial-Immune-System-Based Algorithm Enhanced with Deep Reinforcement Learning for Solving Returnable Transport Item Problems," Sustainability, MDPI, vol. 14(10), pages 1-29, May.

    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. 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.
    2. 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.
    3. Leandro C. Coelho & Jean-François Cordeau & Gilbert Laporte, 2014. "Thirty Years of Inventory Routing," Transportation Science, INFORMS, vol. 48(1), pages 1-19, February.
    4. 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.
    5. Fatima Ezzahra Achamrah & Fouad Riane & Evren Sahin & Sabine Limbourg, 2022. "An Artificial-Immune-System-Based Algorithm Enhanced with Deep Reinforcement Learning for Solving Returnable Transport Item Problems," Sustainability, MDPI, vol. 14(10), pages 1-29, May.
    6. Asghari, Mohammad & Mirzapour Al-e-hashem, S. Mohammad J., 2020. "A green delivery-pickup problem for home hemodialysis machines; sharing economy in distributing scarce resources," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 134(C).
    7. Mutlu, Fatih & Msakni, Mohamed K. & Yildiz, Hakan & Sönmez, Erkut & Pokharel, Shaligram, 2016. "A comprehensive annual delivery program for upstream liquefied natural gas supply chain," European Journal of Operational Research, Elsevier, vol. 250(1), pages 120-130.
    8. Agra, Agostinho & Christiansen, Marielle & Delgado, Alexandrino & Simonetti, Luidi, 2014. "Hybrid heuristics for a short sea inventory routing problem," European Journal of Operational Research, Elsevier, vol. 236(3), pages 924-935.
    9. Neves-Moreira, Fábio & Almada-Lobo, Bernardo & Guimarães, Luís & Amorim, Pedro, 2022. "The multi-product inventory-routing problem with pickups and deliveries: Mitigating fluctuating demand via rolling horizon heuristics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
    10. Dimitri J. Papageorgiou & Myun-Seok Cheon & George Nemhauser & Joel Sokol, 2015. "Approximate Dynamic Programming for a Class of Long-Horizon Maritime Inventory Routing Problems," Transportation Science, INFORMS, vol. 49(4), pages 870-885, November.
    11. Hemmati, Ahmad & Hvattum, Lars Magnus & Christiansen, Marielle & Laporte, Gilbert, 2016. "An iterative two-phase hybrid matheuristic for a multi-product short sea inventory-routing problem," European Journal of Operational Research, Elsevier, vol. 252(3), pages 775-788.
    12. Wang, Zheng, 2018. "Delivering meals for multiple suppliers: Exclusive or sharing logistics service," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 496-512.
    13. 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.
    14. A. Mor & M. G. Speranza, 2022. "Vehicle routing problems over time: a survey," Annals of Operations Research, Springer, vol. 314(1), pages 255-275, July.
    15. 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.
    16. Papageorgiou, Dimitri J. & Nemhauser, George L. & Sokol, Joel & Cheon, Myun-Seok & Keha, Ahmet B., 2014. "MIRPLib – A library of maritime inventory routing problem instances: Survey, core model, and benchmark results," European Journal of Operational Research, Elsevier, vol. 235(2), pages 350-366.
    17. 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.
    18. 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.
    19. 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.
    20. Zhou, Jian & Li, Hui & Gu, Yujie & Zhao, Mingxuan & Xie, Xuehui & Zheng, Haoran & Fang, Xinghua, 2021. "A novel two-phase approach for the bi-objective simultaneous delivery and pickup problem with fuzzy pickup demands," International Journal of Production Economics, Elsevier, vol. 234(C).

    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:eee:ejores:v:282:y:2020:i:3:p:886-895. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.