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On the Optimal Inventory Equation

Author

Listed:
  • R. Bellman

    (The Rand Corporation)

  • I. Glicksberg

    (The Rand Corporation)

  • O. Gross

    (The Rand Corporation)

Abstract

The purpose of this paper is to discuss a number of functional equations which arise in the "optimal inventory" problem. This is a particular case of the general problem of ordering in the face of an uncertain future demand. Actually, an important aspect of the problem is that of determining a suitable criterion of cost, one which is both realistic and analytically malleable.

Suggested Citation

  • R. Bellman & I. Glicksberg & O. Gross, 1955. "On the Optimal Inventory Equation," Management Science, INFORMS, vol. 2(1), pages 83-104, October.
    • Handle: RePEc:inm:ormnsc:v:2:y:1955:i:1:p:83-104
    DOI: 10.1287/mnsc.2.1.83
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    Cited by:

    1. Girlich, Hans-Joachim & Chikan, Attila, 2001. "The origins of dynamic inventory modelling under uncertainty: (the men, their work and connection with the Stanford Studies)," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 351-363, May.
    2. Girardet, Daniel & Spinler, Stefan, 2013. "Surcharge management of kerosene and CO2 costs for airlines under the EU's emission trading," Journal of Air Transport Management, Elsevier, vol. 26(C), pages 25-30.
    3. Powell, Warren B., 2019. "A unified framework for stochastic optimization," European Journal of Operational Research, Elsevier, vol. 275(3), pages 795-821.
    4. Warsing, Donald P. & Wangwatcharakul, Worawut & King, Russell E., 2019. "Computing base-stock levels for a two-stage supply chain with uncertain supply," Omega, Elsevier, vol. 89(C), pages 92-109.
    5. Seifert, Ralf W. & Thonemann, Ulrich W. & Sieke, Marcel A., 2006. "Integrating direct and indirect sales channels under decentralized decision-making," International Journal of Production Economics, Elsevier, vol. 103(1), pages 209-229, September.
    6. Tal Avinadav, 2016. "Stochastic Periodic-Review Models with Duration- and Quantity-Dependent Inventory Costs: Properties and Approximations," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-25, August.
    7. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2011. "Average Cost Single-Stage Inventory Models: An Analysis Using a Vanishing Discount Approach," Operations Research, INFORMS, vol. 59(1), pages 143-155, February.
    8. Nils Rudi & Harry Groenevelt & Taylor R. Randall, 2009. "End-of-Period vs. Continuous Accounting of Inventory-Related Costs," Operations Research, INFORMS, vol. 57(6), pages 1360-1366, December.
    9. Yu, Gang, 1997. "Robust economic order quantity models," European Journal of Operational Research, Elsevier, vol. 100(3), pages 482-493, August.
    10. Girlich, Hans-Joachim, 2003. "Transaction costs in finance and inventory research," International Journal of Production Economics, Elsevier, vol. 81(1), pages 341-350, January.
    11. Harvey M. Wagner, 2002. "And Then There Were None," Operations Research, INFORMS, vol. 50(1), pages 217-226, February.
    12. Martin L. Weitzman, 1971. "Material Balances Under Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 85(2), pages 262-282.
    13. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    14. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
    15. Zeynep Müge Avsar & Melike Baykal‐Gürsoy, 2002. "Inventory control under substitutable demand: A stochastic game application," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(4), pages 359-375, June.
    16. Chris Muris & Horst Raff & Nicolas Schmitt & Frank Stähler, 2023. "Inventory, Sourcing, and the Effects of Trade Costs: Theory and Empirical Evidence," CESifo Working Paper Series 10253, CESifo.
    17. Riezebos, J. & Gaalman, G.J.C., 2009. "A single-item inventory model for expected inventory order crossovers," International Journal of Production Economics, Elsevier, vol. 121(2), pages 601-609, October.
    18. David A. Goldberg & Martin I. Reiman & Qiong Wang, 2021. "A Survey of Recent Progress in the Asymptotic Analysis of Inventory Systems," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1718-1750, June.
    19. Timothy M. Sweda & Irina S. Dolinskaya & Diego Klabjan, 2017. "Optimal Recharging Policies for Electric Vehicles," Transportation Science, INFORMS, vol. 51(2), pages 457-479, May.
    20. Alessandro Arlotto & J. Michael Steele, 2016. "A Central Limit Theorem for Temporally Nonhomogenous Markov Chains with Applications to Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1448-1468, November.
    21. Lu Wang & Vidyadhar Kulkarni & Hanqin Zhang, 2023. "Inventory dispensation and restocking in multiclass inventory systems: A decoupling approach," Production and Operations Management, Production and Operations Management Society, vol. 32(2), pages 469-484, February.
    22. Sreekumar Bhaskaran & Karthik Ramachandran & John Semple, 2010. "A Dynamic Inventory Model with the Right of Refusal," Management Science, INFORMS, vol. 56(12), pages 2265-2281, December.
    23. Cetinkaya, S. & Parlar, M., 1998. "Optimal myopic policy for a stochastic inventory problem with fixed and proportional backorder costs," European Journal of Operational Research, Elsevier, vol. 110(1), pages 20-41, October.
    24. David A. Goldberg & Dmitriy A. Katz-Rogozhnikov & Yingdong Lu & Mayank Sharma & Mark S. Squillante, 2016. "Asymptotic Optimality of Constant-Order Policies for Lost Sales Inventory Models with Large Lead Times," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 898-913, August.

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