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Multi-item production routing problem with backordering: a MILP approach

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  • Nadjib Brahimi
  • Tarik Aouam

Abstract

The aim of this paper is to present mixed integer linear programming formulations for the production routing problem with backordering (PRP-B) and a new hybrid heuristic to solve the problem. The PRP-B is considered in the context of a supply chain consisting of a production facility with limited production and storage capacities and geographically dispersed points of sale with limited storage capacities. The PRP-B integrates multiple item lot sizing decisions and vehicle routing decisions to the points of sale, where backordering of end customer demands is allowed at a penalty. Two integrated mixed integer programming models are formulated and a solution procedure consisting of a relax-and-fix heuristic combined with a local search algorithm is proposed. The numerical results show that this hybrid heuristic outperforms a state-of-the-art MIP commercial solver, in terms of solution quality and CPU times.

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  • Nadjib Brahimi & Tarik Aouam, 2016. "Multi-item production routing problem with backordering: a MILP approach," International Journal of Production Research, Taylor & Francis Journals, vol. 54(4), pages 1076-1093, February.
    • Handle: RePEc:taf:tprsxx:v:54:y:2016:i:4:p:1076-1093
    DOI: 10.1080/00207543.2015.1047971
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    Cited by:

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    2. Li, Yantong & Chu, Feng & Côté, Jean-François & Coelho, Leandro C. & Chu, Chengbin, 2020. "The multi-plant perishable food production routing with packaging consideration," International Journal of Production Economics, Elsevier, vol. 221(C).
    3. Li, Yantong & Chu, Feng & Chu, Chengbin & Zhu, Zhanguo, 2019. "An efficient three-level heuristic for the large-scaled multi-product production routing problem with outsourcing," European Journal of Operational Research, Elsevier, vol. 272(3), pages 914-927.
    4. 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).
    5. Zakaria Chekoubi & Wajdi Trabelsi & Nathalie Sauer & Ilias Majdouline, 2022. "The Integrated Production-Inventory-Routing Problem with Reverse Logistics and Remanufacturing: A Two-Phase Decomposition Heuristic," Sustainability, MDPI, vol. 14(20), pages 1-30, October.
    6. Alvarez, Aldair & Miranda, Pedro & Rohmer, S.U.K., 2022. "Production routing for perishable products," Omega, Elsevier, vol. 111(C).
    7. Pedro L. Miranda & Reinaldo Morabito & Deisemara Ferreira, 2018. "Optimization model for a production, inventory, distribution and routing problem in small furniture companies," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 30-67, April.
    8. Avci, Mustafa & Yildiz, Seyda Topaloglu, 2019. "A matheuristic solution approach for the production routing problem with visit spacing policy," European Journal of Operational Research, Elsevier, vol. 279(2), pages 572-588.

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