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Sustainable Inventory with Robust Periodic-Affine Policies and Application to Medical Supply Chains

Author

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  • Chaithanya Bandi

    (Kellogg School of Management, Northwestern University, Evanston, Illinois 60208)

  • Eojin Han

    (Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

  • Omid Nohadani

    (Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

Abstract

We introduce a new class of adaptive policies called periodic-affine policies , which allows a decision maker to optimally manage and control large-scale newsvendor networks in the presence of uncertain demand without distributional assumptions. These policies are data-driven and model many features of the demand such as correlation and remain robust to parameter misspecification. We present a model that can be generalized to multiproduct settings and extended to multiperiod problems. This is accomplished by modeling the uncertain demand via sets. In this way, it offers a natural framework to study competing policies such as base-stock, affine, and approximative approaches with respect to their profit, sensitivity to parameters and assumptions, and computational scalability. We show that the periodic-affine policies are sustainable—that is, time consistent—because they warrant optimality both within subperiods and over the entire planning horizon. This approach is tractable and free of distributional assumptions, and, hence, suited for real-world applications. We provide efficient algorithms to obtain the optimal periodic-affine policies and demonstrate their advantages on the sales data from one of India’s largest pharmacy retailers.

Suggested Citation

  • Chaithanya Bandi & Eojin Han & Omid Nohadani, 2019. "Sustainable Inventory with Robust Periodic-Affine Policies and Application to Medical Supply Chains," Management Science, INFORMS, vol. 65(10), pages 4636-4655, October.
  • Handle: RePEc:inm:ormnsc:v:65:y:2019:i:10:p:4636-4655
    DOI: 10.1287/mnsc.2018.3152
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    References listed on IDEAS

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    1. Samuel Karlin, 1960. "Dynamic Inventory Policy with Varying Stochastic Demands," Management Science, INFORMS, vol. 6(3), pages 231-258, April.
    2. Stephen C. Graves & Sean P. Willems, 2000. "Optimizing Strategic Safety Stock Placement in Supply Chains," Manufacturing & Service Operations Management, INFORMS, vol. 2(1), pages 68-83, June.
    3. Gregory S. Crawford & Matthew Shum, 2005. "Uncertainty and Learning in Pharmaceutical Demand," Econometrica, Econometric Society, vol. 73(4), pages 1137-1173, July.
    4. 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.
    5. A. Federgruen & P. Zipkin, 1986. "An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 208-215, May.
    6. Alp Muharremoglu & John N. Tsitsiklis, 2008. "A Single-Unit Decomposition Approach to Multiechelon Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1089-1103, October.
    7. Michael C. Fu, 1994. "Sample Path Derivatives for (s, S) Inventory Systems," Operations Research, INFORMS, vol. 42(2), pages 351-364, April.
    8. Jan A. Van Mieghem & Nils Rudi, 2002. "Newsvendor Networks: Inventory Management and Capacity Investment with Discretionary Activities," Manufacturing & Service Operations Management, INFORMS, vol. 4(4), pages 313-335, August.
    9. Suresh P. Sethi & Feng Cheng, 1997. "Optimality of ( s , S ) Policies in Inventory Models with Markovian Demand," Operations Research, INFORMS, vol. 45(6), pages 931-939, December.
    10. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    11. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    12. Guerrero, W.J. & Yeung, T.G. & Guéret, C., 2013. "Joint-optimization of inventory policies on a multi-product multi-echelon pharmaceutical system with batching and ordering constraints," European Journal of Operational Research, Elsevier, vol. 231(1), pages 98-108.
    13. Paul Glasserman & Sridhar Tayur, 1995. "Sensitivity Analysis for Base-Stock Levels in Multiechelon Production-Inventory Systems," Management Science, INFORMS, vol. 41(2), pages 263-281, February.
    14. Kaj Rosling, 1989. "Optimal Inventory Policies for Assembly Systems Under Random Demands," Operations Research, INFORMS, vol. 37(4), pages 565-579, August.
    15. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
    16. Thomas E. Morton, 1978. "The Nonstationary Infinite Horizon Inventory Problem," Management Science, INFORMS, vol. 24(14), pages 1474-1482, October.
    17. Dimitris Bertsimas & Dan A. Iancu & Pablo A. Parrilo, 2010. "Optimality of Affine Policies in Multistage Robust Optimization," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 363-394, May.
    18. A. Federgruen & P. Zipkin, 1986. "An Inventory Model with Limited Production Capacity and Uncertain Demands I. The Average-Cost Criterion," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 193-207, May.
    19. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
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