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Comparison of formulations for the Inventory Routing Problem

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  • Archetti, Claudia
  • Ljubić, Ivana

Abstract

In this paper we propose an analysis and comparison of the strength of the lower bound, measured as the value of the linear programming relaxation, of different formulations for the Inventory Routing Problem (IRP). In particular, we first focus on aggregated formulations, i.e., formulations where variables have no index associated with vehicles, and we analyse the link between compact formulations and their counterparts involving exponentially many constraints. We show that they are equivalent in terms of value of the linear relaxation. In addition, we study the link between aggregated and disaggregated formulations, i.e., formulations where variables have an index related to vehicles. Also in this case, we show that aggregated and disaggregated formulations are equivalent in terms of the value of the corresponding linear relaxation. To the best of our knowledge, this analysis has never been done for the IRP, which instead is gaining a lot of popularity in the literature. Finally, we propose different exact solution approaches based on the aggregated formulations and we compare them with state-of-the-art exact methods for the IRP. Results show that the approaches based on aggregated formulations are competitive in terms of quality of both upper and lower bounds.

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  • 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.
    • Handle: RePEc:eee:ejores:v:303:y:2022:i:3:p:997-1008
    DOI: 10.1016/j.ejor.2021.12.051
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    6. 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.
    7. Gouveia, Luis, 1995. "A result on projection for the vehicle routing ptoblem," European Journal of Operational Research, Elsevier, vol. 85(3), pages 610-624, September.
    8. Letchford, Adam N. & Salazar-González, Juan-José, 2015. "Stronger multi-commodity flow formulations of the Capacitated Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 244(3), pages 730-738.
    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. 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.
    11. Claudia Archetti & Luca Bertazzi & Alain Hertz & M. Grazia Speranza, 2012. "A Hybrid Heuristic for an Inventory Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 101-116, February.
    12. 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.
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