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Delivery Cost Approximations for Inventory Routing Problems in a Rolling Horizon Framework

Author

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  • Patrick Jaillet

    (Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Jonathan F. Bard

    (Graduate Program in Operations Research, Mechanical Engineering Department, The University of Texas at Austin, Austin, Texas 78712)

  • Liu Huang

    (DSC Communications, Austin, Texas 78758-4017)

  • Moshe Dror

    (College of Business and Public Administration, University of Arizona, Tucson, Arizona 85721)

Abstract

The inventory routing problem considered in this paper is concerned with the repeated distribution of a commodity, such as heating oil, over a long period of time to a large number of customers. The problem involves a central depot as well as various satellite facilities which the drivers can visit during their shift to refill their vehicles. The customers maintain a local inventory of the commodity. Their consumption varies daily and cannot be predicted deterministically. In case of a stockout, a direct delivery is made and a penalty cost is incurred. In this paper, we present incremental cost approximations to be used in a rolling horizon framework for the problem of minimizing the total expected annual delivery costs.

Suggested Citation

  • Patrick Jaillet & Jonathan F. Bard & Liu Huang & Moshe Dror, 2002. "Delivery Cost Approximations for Inventory Routing Problems in a Rolling Horizon Framework," Transportation Science, INFORMS, vol. 36(3), pages 292-300, August.
    • Handle: RePEc:inm:ortrsc:v:36:y:2002:i:3:p:292-300
    DOI: 10.1287/trsc.36.3.292.7829
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    References listed on IDEAS

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    Cited by:

    1. Yves Crama & Mahmood Rezaei & Martin Savelsbergh & Tom Van Woensel, 2018. "Stochastic Inventory Routing for Perishable Products," Transportation Science, INFORMS, vol. 52(3), pages 526-546, June.
    2. Ann Melissa Campbell & Martin W. P. Savelsbergh, 2004. "A Decomposition Approach for the Inventory-Routing Problem," Transportation Science, INFORMS, vol. 38(4), pages 488-502, November.
    3. Zhang, Dong & Klabjan, Diego, 2017. "Optimization for gate re-assignment," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 260-284.
    4. Luca Bertazzi & Simona Cherubini, 2013. "An inventory-transportation system with stochastic demand," Computational Management Science, Springer, vol. 10(1), pages 1-20, February.
    5. Zhao, Qiu-Hong & Chen, Shuang & Zang, Cun-Xun, 2008. "Model and algorithm for inventory/routing decision in a three-echelon logistics system," European Journal of Operational Research, Elsevier, vol. 191(3), pages 623-635, December.
    6. Hemmelmayr, Vera & Doerner, Karl F. & Hartl, Richard F. & Savelsbergh, Martin W.P., 2010. "Vendor managed inventory for environments with stochastic product usage," European Journal of Operational Research, Elsevier, vol. 202(3), pages 686-695, May.
    7. Pan, Zhendong & Tang, Jiafu & Fung, Richard Y.K., 2009. "Synchronization of inventory and transportation under flexible vehicle constraint: A heuristics approach using sliding windows and hierarchical tree structure," European Journal of Operational Research, Elsevier, vol. 192(3), pages 824-836, February.
    8. Keskin, Merve & Branke, Juergen & Deineko, Vladimir & Strauss, Arne K., 2023. "Dynamic multi-period vehicle routing with touting," European Journal of Operational Research, Elsevier, vol. 310(1), pages 168-184.
    9. Yossiri Adulyasak & Jean-François Cordeau & Raf Jans, 2015. "Benders Decomposition for Production Routing Under Demand Uncertainty," Operations Research, INFORMS, vol. 63(4), pages 851-867, August.
    10. Ketzenberg, Michael E. & Metters, Richard D., 2020. "Adapting operations to new information technology: A failed “internet of things” application," Omega, Elsevier, vol. 92(C).
    11. E-H Aghezzaf, 2008. "Robust distribution planning for supplier-managed inventory agreements when demand rates and travel times are stationary," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(8), pages 1055-1065, August.
    12. Cárdenas-Barrón, Leopoldo Eduardo & González-Velarde, José Luis & Treviño-Garza, Gerardo & Garza-Nuñez, Dagoberto, 2019. "Heuristic algorithm based on reduce and optimize approach for a selective and periodic inventory routing problem in a waste vegetable oil collection environment," International Journal of Production Economics, Elsevier, vol. 211(C), pages 44-59.
    13. Niakan, Farzad & Rahimi, Mohammad, 2015. "A multi-objective healthcare inventory routing problem; a fuzzy possibilistic approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 80(C), pages 74-94.
    14. Alvarez, Aldair & Cordeau, Jean-François & Jans, Raf & Munari, Pedro & Morabito, Reinaldo, 2021. "Inventory routing under stochastic supply and demand," Omega, Elsevier, vol. 102(C).
    15. Sonntag, Danja R. & Schrotenboer, Albert H. & Kiesmüller, Gudrun P., 2023. "Stochastic inventory routing with time-based shipment consolidation," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1186-1201.
    16. Jeffrey W. Ohlmann & Michael J. Fry & Barrett W. Thomas, 2008. "Route Design for Lean Production Systems," Transportation Science, INFORMS, vol. 42(3), pages 352-370, August.
    17. Yugang Yu & Chengbin Chu & Haoxun Chen & Feng Chu, 2012. "Large scale stochastic inventory routing problems with split delivery and service level constraints," Annals of Operations Research, Springer, vol. 197(1), pages 135-158, August.
    18. Yu, Yugang & Chen, Haoxun & Chu, Feng, 2008. "A new model and hybrid approach for large scale inventory routing problems," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1022-1040, September.
    19. Cordeau, Jean-François & Dell’Amico, Mauro & Falavigna, Simone & Iori, Manuel, 2015. "A rolling horizon algorithm for auto-carrier transportation," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 68-80.
    20. Yu, Y. & Chu, C. & Chen, H.X. & Chu, F., 2010. "Linearization and Decomposition Methods for Large Scale Stochastic Inventory Routing Problem with Service Level Constraints," ERIM Report Series Research in Management ERS-2010-008-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    21. Sayarshad, Hamid R. & Gao, H. Oliver, 2018. "A non-myopic dynamic inventory routing and pricing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 83-98.
    22. Jin-Hwa Song & Martin Savelsbergh, 2007. "Performance Measurement for Inventory Routing," Transportation Science, INFORMS, vol. 41(1), pages 44-54, February.
    23. Ampol Karoonsoontawong & Onwasa Kobkiattawin & Chi Xie, 2019. "Efficient Insertion Heuristic Algorithms for Multi-Trip Inventory Routing Problem with Time Windows, Shift Time Limits and Variable Delivery Time," Networks and Spatial Economics, Springer, vol. 19(2), pages 331-379, June.
    24. Leandro C. Coelho & Jean-François Cordeau & Gilbert Laporte, 2014. "Thirty Years of Inventory Routing," Transportation Science, INFORMS, vol. 48(1), pages 1-19, February.
    25. Huizing, Dylan & Schäfer, Guido & van der Mei, Rob D. & Bhulai, Sandjai, 2020. "The median routing problem for simultaneous planning of emergency response and non-emergency jobs," European Journal of Operational Research, Elsevier, vol. 285(2), pages 712-727.

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