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Critical Number Policies for Inventory Models with Periodic Data

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  • Paul Zipkin

    (Columbia University, Graduate School of Business, New York, New York 10027)

Abstract

We consider an infinite-horizon in problem with stochastic demands where the data vary periodically. Karlin (Karlin, S. 1960a. Dynamic inventory policy with varying stochastic demands. Management Sci. 6 231--258; Karlin, S. 1960b. Optimal policy for dynamic inventory process with stochastic demands subject to seasonal variations. J. SIAM 8 611--629.) shows that a periodic critical-number policy is optimal and presents an algorithm for computing the critical numbers, assuming discounted costs. Here we develop an alternative, conceptually simpler approach to these problems. The results include a proof of the optimality of such policies for the average-cost case, and a qualitative description of the behavior of the optimal policy as "smoothing" fluctuations in the data.

Suggested Citation

  • Paul Zipkin, 1989. "Critical Number Policies for Inventory Models with Periodic Data," Management Science, INFORMS, vol. 35(1), pages 71-80, January.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:1:p:71-80
    DOI: 10.1287/mnsc.35.1.71
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    Cited by:

    1. Özen, Ulaş & Doğru, Mustafa K. & Armagan Tarim, S., 2012. "Static-dynamic uncertainty strategy for a single-item stochastic inventory control problem," Omega, Elsevier, vol. 40(3), pages 348-357.
    2. Owen Q. Wu & Hong Chen, 2010. "Optimal Control and Equilibrium Behavior of Production-Inventory Systems," Management Science, INFORMS, vol. 56(8), pages 1362-1379, August.
    3. Ehrenthal, J.C.F. & Honhon, D. & Van Woensel, T., 2014. "Demand seasonality in retail inventory management," European Journal of Operational Research, Elsevier, vol. 238(2), pages 527-539.
    4. Iida, Tetsuo, 2002. "A non-stationary periodic review production-inventory model with uncertain production capacity and uncertain demand," European Journal of Operational Research, Elsevier, vol. 140(3), pages 670-683, August.
    5. Iida, Tetsuo, 1999. "The infinite horizon non-stationary stochastic inventory problem: Near myopic policies and weak ergodicity," European Journal of Operational Research, Elsevier, vol. 116(2), pages 405-422, July.
    6. Özalp Özer & Wei Wei, 2004. "Inventory Control with Limited Capacity and Advance Demand Information," Operations Research, INFORMS, vol. 52(6), pages 988-1000, December.
    7. Noah Gans & Yong-Pin Zhou, 2002. "Managing Learning and Turnover in Employee Staffing," Operations Research, INFORMS, vol. 50(6), pages 991-1006, December.
    8. Gavirneni, Srinagesh & Morton, Thomas E., 1999. "Inventory control under speculation: Myopic heuristics and exact procedures," European Journal of Operational Research, Elsevier, vol. 117(2), pages 211-221, September.
    9. Gokhan Metan & Aurélie Thiele, 2016. "Protecting the data-driven newsvendor against rare events: a correction-term approach," Computational Management Science, Springer, vol. 13(3), pages 459-482, July.
    10. Fangruo Chen, 2000. "Sales-Force Incentives and Inventory Management," Manufacturing & Service Operations Management, INFORMS, vol. 2(2), pages 186-202, February.
    11. Gavirneni, Srinagesh, 2006. "Price fluctuations, information sharing, and supply chain performance," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1651-1663, November.
    12. Satya S. Malladi & Alan L. Erera & Chelsea C. White, 2023. "Inventory control with modulated demand and a partially observed modulation process," Annals of Operations Research, Springer, vol. 321(1), pages 343-369, February.
    13. Avi Herbon & Konstantin Kogan, 2014. "Time-dependent and independent control rules for coordinated production and pricing under demand uncertainty and finite planning horizons," Annals of Operations Research, Springer, vol. 223(1), pages 195-216, December.
    14. Iida, Tetsuo, 2001. "The infinite horizon non-stationary stochastic multi-echelon inventory problem and near-myopic policies," European Journal of Operational Research, Elsevier, vol. 134(3), pages 525-539, November.
    15. 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.
    16. Fangruo Chen & Jing-Sheng Song, 2001. "Optimal Policies for Multiechelon Inventory Problems with Markov-Modulated Demand," Operations Research, INFORMS, vol. 49(2), pages 226-234, April.
    17. Li Chen & Jing-Sheng Song & Yue Zhang, 2017. "Serial Inventory Systems with Markov-Modulated Demand: Derivative Bounds, Asymptotic Analysis, and Insights," Operations Research, INFORMS, vol. 65(5), pages 1231-1249, October.
    18. Argon, Nilay Tanik & Gullu, Refik & Erkip, Nesim, 2001. "Analysis of an inventory system under backorder correlated deterministic demand and geometric supply process," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 247-254, May.
    19. Chen, Frank Y. & Krass, Dmitry, 2001. "Inventory models with minimal service level constraints," European Journal of Operational Research, Elsevier, vol. 134(1), pages 120-140, October.
    20. Srinagesh Gavirneni & Sridhar Tayur, 1999. "Managing a Customer Following a Target Reverting Policy," Manufacturing & Service Operations Management, INFORMS, vol. 1(2), pages 157-173.
    21. 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.
    22. Boxiao Chen, 2021. "Data‐Driven Inventory Control with Shifting Demand," Production and Operations Management, Production and Operations Management Society, vol. 30(5), pages 1365-1385, May.
    23. Tetsuo Iida & Paul H. Zipkin, 2006. "Approximate Solutions of a Dynamic Forecast-Inventory Model," Manufacturing & Service Operations Management, INFORMS, vol. 8(4), pages 407-425, October.

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