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Analysis of the Deterministic (s, S) Inventory Problem

Author

Listed:
  • Ananth V. Iyer

    (Graduate School of Business, The University of Chicago, 1101 East 58th Street, Chicago, IL 60637)

  • Linus E. Schrage

    (Graduate School of Business, The University of Chicago, 1101 East 58th Street, Chicago, IL 60637)

Abstract

The traditional or textbook approach for finding an (s, S) inventory policy is to take a demand distribution as given and then find a reorder point s and order up to point S that are optimal for this demand distribution. In reality, the demand distribution may have been obtained by fitting it to some historical demand stream. In contrast, the deterministic (s, S) inventory problem is to directly determine the (s, S) pair that would have been optimal for the original demand stream, bypassing the distribution fitting step. The deterministic (s, S) inventory problem thus chooses parameters s and S which minimize setup, holding and backorder costs when the corresponding (s, S) policy is implemented over n periods with known demands d 1 , d 2 ,..., d n . Our contributions are two: (a) a polynomial time algorithm for finding an optimal (s, S) for the deterministic problem, and (b) an empirical comparison of the two approaches. In (b) we compare the long term average costs of the two approaches as a function of the amount of data available, distributional assumptions, and order lead time.

Suggested Citation

  • Ananth V. Iyer & Linus E. Schrage, 1992. "Analysis of the Deterministic (s, S) Inventory Problem," Management Science, INFORMS, vol. 38(9), pages 1299-1313, September.
    • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:9:p:1299-1313
    DOI: 10.1287/mnsc.38.9.1299
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    Cited by:

    1. Beutel, Anna-Lena & Minner, Stefan, 2012. "Safety stock planning under causal demand forecasting," International Journal of Production Economics, Elsevier, vol. 140(2), pages 637-645.
    2. Ananth. V. Iyer, 2002. "Inventory cost impact of order processing priorities based on demand uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(4), pages 376-390, June.
    3. Özgün Turgut & Florian Taube & Stefan Minner, 2018. "Data-driven retail inventory management with backroom effect," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(4), pages 945-968, October.
    4. Erkip, Nesim Kohen, 2023. "Can accessing much data reshape the theory? Inventory theory under the challenge of data-driven systems," European Journal of Operational Research, Elsevier, vol. 308(3), pages 949-959.
    5. Altay, Nezih & Litteral, Lewis A. & Rudisill, Frank, 2012. "Effects of correlation on intermittent demand forecasting and stock control," International Journal of Production Economics, Elsevier, vol. 135(1), pages 275-283.
    6. Zied Babai, M. & Syntetos, Aris A. & Teunter, Ruud, 2010. "On the empirical performance of (T, s, S) heuristics," European Journal of Operational Research, Elsevier, vol. 202(2), pages 466-472, April.
    7. Brian Downs & Richard Metters & John Semple, 2001. "Managing Inventory with Multiple Products, Lags in Delivery, Resource Constraints, and Lost Sales: A Mathematical Programming Approach," Management Science, INFORMS, vol. 47(3), pages 464-479, March.
    8. Vinayak Deshpande & Ananth V. Iyer & Richard Cho, 2006. "Efficient Supply Chain Management at the U.S. Coast Guard Using Part-Age Dependent Supply Replenishment Policies," Operations Research, INFORMS, vol. 54(6), pages 1028-1040, December.

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