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Approximation Algorithms for the Stochastic Lot-Sizing Problem with Order Lead Times

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  • Retsef Levi

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Cong Shi

    (Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109)

Abstract

We develop new algorithmic approaches to compute provably near-optimal policies for multiperiod stochastic lot-sizing inventory models with positive lead times, general demand distributions, and dynamic forecast updates. The policies that are developed have worst-case performance guarantees of 3 and typically perform very close to optimal in extensive computational experiments. The newly proposed algorithms employ a novel randomized decision rule. We believe that these new algorithmic and performance analysis techniques could be used in designing provably near-optimal randomized algorithms for other stochastic inventory control models and more generally in other multistage stochastic control problems.

Suggested Citation

  • Retsef Levi & Cong Shi, 2013. "Approximation Algorithms for the Stochastic Lot-Sizing Problem with Order Lead Times," Operations Research, INFORMS, vol. 61(3), pages 593-602, June.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:3:p:593-602
    DOI: 10.1287/opre.2013.1162
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    References listed on IDEAS

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    10. Yossi Aviv & Awi Federgruen, 2001. "Capacitated Multi-Item Inventory Systems with Random and Seasonally Fluctuating Demands: Implications for Postponement Strategies," Management Science, INFORMS, vol. 47(4), pages 512-531, April.
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    Citations

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    Cited by:

    1. Tian, Xuecheng & Wang, Shuaian & Laporte, Gilbert & Yang, Ying, 2024. "Determinism versus uncertainty: Examining the worst-case expected performance of data-driven policies," European Journal of Operational Research, Elsevier, vol. 318(1), pages 242-252.
    2. Huanan Zhang & Cong Shi & Xiuli Chao, 2016. "Technical Note—Approximation Algorithms for Perishable Inventory Systems with Setup Costs," Operations Research, INFORMS, vol. 64(2), pages 432-440, April.
    3. Gah-Yi Ban, 2020. "Confidence Intervals for Data-Driven Inventory Policies with Demand Censoring," Operations Research, INFORMS, vol. 68(2), pages 309-326, March.
    4. Hao Yuan & Qi Luo & Cong Shi, 2021. "Marrying Stochastic Gradient Descent with Bandits: Learning Algorithms for Inventory Systems with Fixed Costs," Management Science, INFORMS, vol. 67(10), pages 6089-6115, October.
    5. Retsef Levi & Robin Roundy & Van Anh Truong & Xinshang Wang, 2017. "Provably Near-Optimal Balancing Policies for Multi-Echelon Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 256-276, January.
    6. Akartunalı, Kerem & Dauzère-Pérès, Stéphane, 2022. "Dynamic lot sizing with stochastic demand timing," European Journal of Operational Research, Elsevier, vol. 302(1), pages 221-229.
    7. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    8. Andrew F. Siegel & Michael R. Wagner, 2021. "Profit Estimation Error in the Newsvendor Model Under a Parametric Demand Distribution," Management Science, INFORMS, vol. 67(8), pages 4863-4879, August.
    9. Xiuli Chao & Xiting Gong & Cong Shi & Huanan Zhang, 2015. "Approximation Algorithms for Perishable Inventory Systems," Operations Research, INFORMS, vol. 63(3), pages 585-601, June.
    10. Van-Anh Truong, 2014. "Approximation Algorithm for the Stochastic Multiperiod Inventory Problem via a Look-Ahead Optimization Approach," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1039-1056, November.
    11. Huanan Zhang & Cong Shi & Chao Qin & Cheng Hua, 2016. "Stochastic regret minimization for revenue management problems with nonstationary demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(6), pages 433-448, September.
    12. Darina Graczová & Peter Jacko, 2014. "Generalized Restless Bandits and the Knapsack Problem for Perishable Inventories," Operations Research, INFORMS, vol. 62(3), pages 696-711, June.
    13. Cong Shi & Huanan Zhang & Xiuli Chao & Retsef Levi, 2014. "Approximation algorithms for capacitated stochastic inventory systems with setup costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(4), pages 304-319, June.
    14. Hossein Jahandideh & Kumar Rajaram & Kevin McCardle, 2020. "Production Campaign Planning Under Learning and Decay," Manufacturing & Service Operations Management, INFORMS, vol. 22(3), pages 615-632, May.
    15. Awi Federgruen & Zhe Liu & Lijian Lu, 2022. "Dual sourcing: Creating and utilizing flexible capacities with a second supply source," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 2789-2805, July.
    16. Xiuli Chao & Xiting Gong & Cong Shi & Chaolin Yang & Huanan Zhang & Sean X. Zhou, 2018. "Approximation Algorithms for Capacitated Perishable Inventory Systems with Positive Lead Times," Management Science, INFORMS, vol. 64(11), pages 5038-5061, November.
    17. Alexandar Angelus & Özalp Özer, 2016. "Knowledge You Can Act on: Optimal Policies for Assembly Systems with Expediting and Advance Demand Information," Operations Research, INFORMS, vol. 64(6), pages 1338-1371, December.

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