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

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  • 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
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    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.
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    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.

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