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The Impact of Modeling on Robust Inventory Management Under Demand Uncertainty

Author

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  • Oğuz Solyalı

    (Business Administration Program, Middle East Technical University, Northern Cyprus Campus, Kalkanlı, Mersin 10, Turkey)

  • Jean-François Cordeau

    (Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montreal, Quebec H3C 3J7, Canada; and HEC Montréal, Montréal, Quebec H3T 2A7, Canada)

  • Gilbert Laporte

    (Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montreal, Quebec H3C 3J7, Canada; and HEC Montréal, Montréal, Quebec H3T 2A7, Canada)

Abstract

This study considers a basic inventory management problem with nonzero fixed order costs under interval demand uncertainty. The existing robust formulations obtained by applying well-known robust optimization methodologies become computationally intractable for large problem instances due to the presence of binary variables. This study resolves this intractability issue by proposing a new robust formulation that is shown to be solvable in polynomial time when the initial inventory is zero or negative. Because of the computational efficiency of the new robust formulation, it is implemented on a folding-horizon basis, leading to a new heuristic for the problem. The computational results reveal that the new heuristic is not only superior to the other formulations regarding the computing time needed, but also outperforms the existing robust formulations in terms of the actual cost savings on the larger instances. They also show that the actual cost savings yielded by the new heuristic are close to a lower bound on the optimal expected cost.Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2015.2183 . This paper was accepted by Dimitris Bertsimas, optimization .

Suggested Citation

  • Oğuz Solyalı & Jean-François Cordeau & Gilbert Laporte, 2016. "The Impact of Modeling on Robust Inventory Management Under Demand Uncertainty," Management Science, INFORMS, vol. 62(4), pages 1188-1201, April.
    • Handle: RePEc:inm:ormnsc:v:62:y:2016:i:4:p:1188-1201
    DOI: 10.1287/mnsc.2015.2183
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    References listed on IDEAS

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    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. Aharon Ben-Tal & Boaz Golany & Arkadi Nemirovski & Jean-Philippe Vial, 2005. "Retailer-Supplier Flexible Commitments Contracts: A Robust Optimization Approach," Manufacturing & Service Operations Management, INFORMS, vol. 7(3), pages 248-271, February.
    3. Dimitris Bertsimas & Aurélie Thiele, 2006. "A Robust Optimization Approach to Inventory Theory," Operations Research, INFORMS, vol. 54(1), pages 150-168, February.
    4. Xin Chen & Yuhan Zhang, 2009. "Uncertain Linear Programs: Extended Affinely Adjustable Robust Counterparts," Operations Research, INFORMS, vol. 57(6), pages 1469-1482, December.
    5. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    6. Alper Atamtürk & Muhong Zhang, 2007. "Two-Stage Robust Network Flow and Design Under Demand Uncertainty," Operations Research, INFORMS, vol. 55(4), pages 662-673, August.
    7. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    8. Aharon, Ben-Tal & Boaz, Golany & Shimrit, Shtern, 2009. "Robust multi-echelon multi-period inventory control," European Journal of Operational Research, Elsevier, vol. 199(3), pages 922-935, December.
    9. Chuen-Teck See & Melvyn Sim, 2010. "Robust Approximation to Multiperiod Inventory Management," Operations Research, INFORMS, vol. 58(3), pages 583-594, June.
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    Cited by:

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    3. Thevenin, Simon & Ben-Ammar, Oussama & Brahimi, Nadjib, 2022. "Robust optimization approaches for purchase planning with supplier selection under lead time uncertainty," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1199-1215.
    4. Man Yiu Tsang & Tony Sit & Hoi Ying Wong, 2022. "Adaptive Robust Online Portfolio Selection," Papers 2206.01064, arXiv.org.
    5. Jia, Shuai & Li, Chung-Lun & Meng, Qiang, 2024. "The dry dock scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
    6. Jiankun Sun & Jan A. Van Mieghem, 2019. "Robust Dual Sourcing Inventory Management: Optimality of Capped Dual Index Policies and Smoothing," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 912-931, October.
    7. Li, Shuqin & Jia, Shuai & Tao, Yi & Lin, Xudong, 2024. "Gate appointment design in a container terminal: A robust optimization approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 184(C).
    8. Sun, Yimeng & Qiu, Ruozhen & Sun, Minghe, 2024. "A robust optimization approach for inventory management with limited-time discounts and service-level requirement under demand uncertainty," International Journal of Production Economics, Elsevier, vol. 267(C).
    9. Songtao Zhang & Shuangshuang Li & Siqi Zhang & Min Zhang, 2017. "Decision of Lead-Time Compression and Stable Operation of Supply Chain," Complexity, Hindawi, vol. 2017, pages 1-11, November.
    10. Metzker Soares, Paula & Thevenin, Simon & Adulyasak, Yossiri & Dolgui, Alexandre, 2024. "Adaptive robust optimization for lot-sizing under yield uncertainty," European Journal of Operational Research, Elsevier, vol. 313(2), pages 513-526.

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