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Continuous Review (s, S) Policies with Lost Sales

Author

Listed:
  • Blyth C. Archibald

    (Dalhousie University)

Abstract

A method is developed to calculate an (s, S) policy that minimizes the average stationary cost in an inventory system with: constant lead time, fixed order cost, linear holding cost per unit time, linear penalty cost per unit short, discrete compound Poisson demand, and lost sales. It is assumed that at most one order is outstanding, or equivalently that S - s > s. The procedure is compared to several easier-to-compute approximate solutions, including one that assumes backordering. Examples are given that reveal that although the backorder solution is different than the lost sales one, the cost penalty of using it in the lost sales situation is small.

Suggested Citation

  • Blyth C. Archibald, 1981. "Continuous Review (s, S) Policies with Lost Sales," Management Science, INFORMS, vol. 27(10), pages 1171-1177, October.
    • Handle: RePEc:inm:ormnsc:v:27:y:1981:i:10:p:1171-1177
    DOI: 10.1287/mnsc.27.10.1171
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    Citations

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    Cited by:

    1. X. Guo & P. Kaminsky & P. Tomecek & M. Yuen, 2011. "Optimal spot market inventory strategies in the presence of cost and price risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(1), pages 109-137, February.
    2. Dominey, M. J. G. & Hill, R. M., 2004. "Performance of approximations for compound Poisson distributed demand in the newsboy problem," International Journal of Production Economics, Elsevier, vol. 92(2), pages 145-155, November.
    3. Hill, Roger M. & Dominey, Matthew J., 2001. "Inventory policies for all-or-nothing demand processes," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 365-371, May.
    4. Anh Ninh, 2021. "Robust newsvendor problems with compound Poisson demands," Annals of Operations Research, Springer, vol. 302(1), pages 327-338, July.
    5. Hill, Roger M. & Johansen, Soren Glud, 2006. "Optimal and near-optimal policies for lost sales inventory models with at most one replenishment order outstanding," European Journal of Operational Research, Elsevier, vol. 169(1), pages 111-132, February.
    6. 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—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.
    7. Li, Jing-An & Wu, Yue & Lai, Kin Keung & Liu, Ke, 2006. "Optimal ordering policy in a distribution system," International Journal of Production Economics, Elsevier, vol. 103(2), pages 527-534, October.
    8. 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.
    9. Marco Bijvank & Woonghee Tim Huh & Ganesh Janakiraman & Wanmo Kang, 2014. "Robustness of Order-Up-to Policies in Lost-Sales Inventory Systems," Operations Research, INFORMS, vol. 62(5), pages 1040-1047, October.
    10. 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.
    11. Kalpakam, S. & Sapna, K. P., 1995. "A two reorder level inventory system with renewal demands," European Journal of Operational Research, Elsevier, vol. 84(2), pages 402-415, July.
    12. Johansen, Soren Glud & Thorstenson, Anders, 1996. "Optimal (r, Q) inventory policies with Poisson demands and lost sales: discounted and undiscounted cases," International Journal of Production Economics, Elsevier, vol. 46(1), pages 359-371, December.
    13. Kim, Eungab & Park, Taeho, 2016. "Admission and inventory control of a single-component make-to-order production system with replenishment setup cost and lead time," European Journal of Operational Research, Elsevier, vol. 255(1), pages 91-102.

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