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Heuristic Computation of Periodic-Review Base Stock Inventory Policies

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  • Robin O. Roundy

    (School of Operations Research and Industrial Engineering, Rhodes Hall, Cornell University, Ithaca, New York 14853)

  • John A. Muckstadt

    (School of Operations Research and Industrial Engineering, Rhodes Hall, Cornell University, Ithaca, New York 14853)

Abstract

We study the problem of determining production quantities in each period of an infinite horizon for a single item produced in a capacity-limited facility. The demand for the product is random, and it is independent and identically distributed from period to period. The demand is observed at the beginning of a time period, but it need not be filled until the end of the period. Unfilled demand is backordered. A base stock or order-up-to policy is used. The shortfall is the order-up-to level minus the inventory position. The inventory system is easily understood and managed if we know the distribution of the shortfall. We develop a new approximation for this distribution, and perform extensive computational tests of existing approximations. Our new approximation works extremely well as long as the coefficient of variation of the demand is less than two. For practical applications this is by far the most interesting case. No known approximations work well consistently when the coefficient of variation of the demand is greater than two.

Suggested Citation

  • Robin O. Roundy & John A. Muckstadt, 2000. "Heuristic Computation of Periodic-Review Base Stock Inventory Policies," Management Science, INFORMS, vol. 46(1), pages 104-109, January.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:1:p:104-109
    DOI: 10.1287/mnsc.46.1.104.15129
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    References listed on IDEAS

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    1. Paul Glasserman & Tai-Wen Liu, 1997. "Corrected Diffusion Approximations for a Multistage Production-Inventory System," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 186-201, February.
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    Citations

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    Cited by:

    1. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2016. "Capacitated Multiechelon Inventory Systems: Policies and Bounds," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 570-584, October.
    2. Ganesh Janakiraman & Mahesh Nagarajan & Senthil Veeraraghavan, 2018. "Simple Policies for Managing Flexible Capacity," Manufacturing & Service Operations Management, INFORMS, vol. 20(2), pages 333-346, May.
    3. Hernan Caceres & Dongchen Yu & Alexander Nikolaev, 2018. "Evaluating shortfall distributions in periodic inventory systems with stochastic endogenous demands and lead-times," Annals of Operations Research, Springer, vol. 271(2), pages 405-427, December.
    4. Weidong Chen & Cong Shi & Izak Duenyas, 2020. "Optimal Learning Algorithms for Stochastic Inventory Systems with Random Capacities," Production and Operations Management, Production and Operations Management Society, vol. 29(7), pages 1624-1649, July.
    5. Hossein Abouee-Mehrizi & Opher Baron & Oded Berman, 2014. "Exact Analysis of Capacitated Two-Echelon Inventory Systems with Priorities," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 561-577, October.
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    9. Nir Halman & Diego Klabjan & Mohamed Mostagir & Jim Orlin & David Simchi-Levi, 2009. "A Fully Polynomial-Time Approximation Scheme for Single-Item Stochastic Inventory Control with Discrete Demand," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 674-685, August.
    10. Rodney P. Parker & Roman Kapuscinski, 2004. "Optimal Policies for a Capacitated Two-Echelon Inventory System," Operations Research, INFORMS, vol. 52(5), pages 739-755, October.
    11. 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.
    12. Raa, Birger & Aouam, Tarik, 2023. "A shortfall modelling-based solution approach for stochastic cyclic inventory routing," European Journal of Operational Research, Elsevier, vol. 305(2), pages 674-684.

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