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Mixed integer and heuristics model for the inventory routing problem in fuel delivery

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  • Vidović, Milorad
  • Popović, Dražen
  • Ratković, Branislava

Abstract

This paper presents solution approaches for the multi-product multi-period Inventory Routing Problem (IRP) in fuel delivery. A homogeneous fleet of vehicles with compartments is used for fuel distribution from one depot to a set of petrol stations that have deterministic fuel consumption. The IRP consists of two mutually dependent sub-problems, those of inventory and routing, in a Vendor Management Inventory (VMI) environment in which suppliers determine the quantities and time periods of the deliveries. For solving the IRP, we propose a Mixed Integer Programming (MIP) model and a heuristic approach with and without fleet size costs, to observe the impact of these costs on the solutions that are obtained. The heuristics model is based on constructive heuristics with two Variable Neighborhood Descent (VND) search types: a local intra-period search and a large inter-period neighborhood search. Both of these approaches were tested on numerical examples for which the results, together with the performances of the proposed models, are presented. A combination of good computational time and good quality solutions suggests the use of the proposed heuristics on problems with realistic dimensions where the MIP model cannot find an optimal solution in a reasonable amount of time.

Suggested Citation

  • Vidović, Milorad & Popović, Dražen & Ratković, Branislava, 2014. "Mixed integer and heuristics model for the inventory routing problem in fuel delivery," International Journal of Production Economics, Elsevier, vol. 147(PC), pages 593-604.
    • Handle: RePEc:eee:proeco:v:147:y:2014:i:pc:p:593-604
    DOI: 10.1016/j.ijpe.2013.04.034
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    3. Hadi Jahangir & Mohammad Mohammadi & Seyed Hamid Reza Pasandideh & Neda Zendehdel Nobari, 2019. "Comparing performance of genetic and discrete invasive weed optimization algorithms for solving the inventory routing problem with an incremental delivery," Journal of Intelligent Manufacturing, Springer, vol. 30(6), pages 2327-2353, August.
    4. Ostermeier, Manuel & Henke, Tino & Hübner, Alexander & Wäscher, Gerhard, 2021. "Multi-compartment vehicle routing problems: State-of-the-art, modeling framework and future directions," European Journal of Operational Research, Elsevier, vol. 292(3), pages 799-817.
    5. Alaei, Saeed & Setak, Mostafa, 2015. "Multi objective coordination of a supply chain with routing and service level consideration," International Journal of Production Economics, Elsevier, vol. 167(C), pages 271-281.
    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. Lobo, Benjamin J. & Brown, Donald E. & Gerber, Matthew S. & Grazaitis, Peter J., 2018. "A transient stochastic simulation–optimization model for operational fuel planning in-theater," European Journal of Operational Research, Elsevier, vol. 264(2), pages 637-652.
    8. Fokkema, Jan Eise & Land, Martin J. & Coelho, Leandro C. & Wortmann, Hans & Huitema, George B., 2020. "A continuous-time supply-driven inventory-constrained routing problem," Omega, Elsevier, vol. 92(C).
    9. Bani, Abderrahman & El Hallaoui, Issmail & Corréa, Ayoub Insa & Tahir, Adil, 2023. "Solving a real-world multi-depot multi-period petrol replenishment problem with complex loading constraints," European Journal of Operational Research, Elsevier, vol. 311(1), pages 154-172.
    10. Soysal, Mehmet & Bloemhof-Ruwaard, Jacqueline M. & Haijema, Rene & van der Vorst, Jack G.A.J., 2015. "Modeling an Inventory Routing Problem for perishable products with environmental considerations and demand uncertainty," International Journal of Production Economics, Elsevier, vol. 164(C), pages 118-133.
    11. Gu, Wenjuan & Archetti, Claudia & Cattaruzza, Diego & Ogier, Maxime & Semet, Frédéric & Speranza, M. Grazia, 2024. "Vehicle routing problems with multiple commodities: A survey," European Journal of Operational Research, Elsevier, vol. 317(1), pages 1-15.
    12. Cheng, Chun & Qi, Mingyao & Wang, Xingyi & Zhang, Ying, 2016. "Multi-period inventory routing problem under carbon emission regulations," International Journal of Production Economics, Elsevier, vol. 182(C), pages 263-275.
    13. Alinaghian, Mahdi & Shokouhi, Nadia, 2018. "Multi-depot multi-compartment vehicle routing problem, solved by a hybrid adaptive large neighborhood search," Omega, Elsevier, vol. 76(C), pages 85-99.
    14. Cho, Jaeyoung & Lim, Gino J. & Kim, Seon Jin & Biobaku, Taofeek, 2018. "Liquefied natural gas inventory routing problem under uncertain weather conditions," International Journal of Production Economics, Elsevier, vol. 204(C), pages 18-29.
    15. Lahyani, Rahma & Coelho, Leandro C. & Khemakhem, Mahdi & Laporte, Gilbert & Semet, Frédéric, 2015. "A multi-compartment vehicle routing problem arising in the collection of olive oil in Tunisia," Omega, Elsevier, vol. 51(C), pages 1-10.

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