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Inventory Planning with Forecast Updates: Approximate Solutions and Cost Error Bounds

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  • Xiangwen Lu

    (Cisco Systems, 210 West Tasman Drive, San Jose, California 95134)

  • Jing-Sheng Song

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Amelia Regan

    (Computer Science-Systems, School of Information and Computer Science, University of California, Irvine, California 92697)

Abstract

We consider a finite-horizon, periodic-review inventory model with demand forecasting updates following the martingale model of forecast evolution (MMFE). The optimal policy is a state-dependent base-stock policy, which, however, is computationally intractable to obtain. We develop tractable bounds on the optimal base-stock levels and use them to devise a general class of heuristic solutions. Through this analysis, we identify a necessary and sufficient condition for the myopic policy to be optimal. Finally, to assess the effectiveness of the heuristic policies, we develop upper bounds on their value loss relative to optimal cost. These solution bounds and cost error bounds also work for general dynamic inventory models with nonstationary and autocorrelated demands. Numerical results are presented to illustrate the results.

Suggested Citation

  • Xiangwen Lu & Jing-Sheng Song & Amelia Regan, 2006. "Inventory Planning with Forecast Updates: Approximate Solutions and Cost Error Bounds," Operations Research, INFORMS, vol. 54(6), pages 1079-1097, December.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:6:p:1079-1097
    DOI: 10.1287/opre.1060.0338
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    References listed on IDEAS

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    9. Feng Cheng* & Markus Ettl & Yingdong Lu & David D. Yao, 2012. "A Production–Inventory Model for a Push–Pull Manufacturing System with Capacity and Service Level Constraints," Production and Operations Management, Production and Operations Management Society, vol. 21(4), pages 668-681, July.
    10. Amar Sapra & Van-Anh Truong & Rachel Q. Zhang, 2010. "How Much Demand Should Be Fulfilled?," Operations Research, INFORMS, vol. 58(3), pages 719-733, June.
    11. Zhu, Stuart X., 2017. "Approximate solutions and cost error bounds for quantity flexibility replenishment," International Journal of Production Economics, Elsevier, vol. 193(C), pages 306-315.
    12. Katy S. Azoury & Julia Miyaoka, 2009. "Optimal Policies and Approximations for a Bayesian Linear Regression Inventory Model," Management Science, INFORMS, vol. 55(5), pages 813-826, May.
    13. Xiang, Mengyuan & Rossi, Roberto & Martin-Barragan, Belen & Tarim, S. Armagan, 2023. "A mathematical programming-based solution method for the nonstationary inventory problem under correlated demand," European Journal of Operational Research, Elsevier, vol. 304(2), pages 515-524.
    14. 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.
    15. 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.
    16. 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.
    17. Felix Papier, 2016. "Supply Allocation Under Sequential Advance Demand Information," Operations Research, INFORMS, vol. 64(2), pages 341-361, April.
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    20. Inna Babenko Viktorovna & Pavel Pochechun Ivanovich, 2016. "Issues of Forming Inventory Management System in Small Businesses," International Review of Management and Marketing, Econjournals, vol. 6(3), pages 522-527.
    21. Tong Wang & Atalay Atasu & Mümin Kurtuluş, 2012. "A Multiordering Newsvendor Model with Dynamic Forecast Evolution," Manufacturing & Service Operations Management, INFORMS, vol. 14(3), pages 472-484, July.
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    23. Retsef Levi & Robin O. Roundy & David B. Shmoys & Van Anh Truong, 2008. "Approximation Algorithms for Capacitated Stochastic Inventory Control Models," Operations Research, INFORMS, vol. 56(5), pages 1184-1199, October.

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