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The (s, Q) inventory model with Erlang lead time and deterministic demand

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Listed:
  • Jeon G. Kim
  • Daewon Sun
  • Xin James He
  • Jack C. Hayya

Abstract

We develop a simple, approximately optimal solution to a model with Erlang lead time and deterministic demand. The method is robust to misspecification of the lead time and has good accuracy. We compare our approximate solution to the optimal for the case where we have prior information on the lead‐time distribution, and another where we have no information, except for computer‐generated sample data. It turns out that our solution is as easy as the EOQ's, with an accuracy rate of 99.41% when prior information on the lead‐time distribution is available and 97.54–99.09% when only computer‐generated sample information is available. Apart from supplying the inventory practitioner with an easy heuristic, we gain insights into the efficacy of stochastic lead time models and how these could be used to find the cost and a near‐optimal policy for the general model, where both demand rate and lead time are stochastic. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Suggested Citation

  • Jeon G. Kim & Daewon Sun & Xin James He & Jack C. Hayya, 2004. "The (s, Q) inventory model with Erlang lead time and deterministic demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 906-923, September.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:6:p:906-923
    DOI: 10.1002/nav.20032
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    References listed on IDEAS

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    1. Xin X. He & Susan H. Xu & J. Keith Ord & Jack C. Hayya, 1998. "An Inventory Model with Order Crossover," Operations Research, INFORMS, vol. 46(3-supplem), pages 112-119, June.
    2. Ruud Heuts & Jan de Klein, 1995. "An (s, q) inventory model with stochastic and interrelated lead times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(5), pages 839-859, August.
    3. Ranga V. Ramasesh & J. Keith Ord & Jack C. Hayya & Andrew Pan, 1991. "Sole Versus Dual Sourcing in Stochastic Lead-Time (s, Q) Inventory Models," Management Science, INFORMS, vol. 37(4), pages 428-443, April.
    4. Guillermo Gallego, 1998. "New Bounds and Heuristics for (Q, r) Policies," Management Science, INFORMS, vol. 44(2), pages 219-233, February.
    5. Georghios P. Sphicas & Farrokh Nasri, 1984. "An inventory model with finite‐range stochastic lead times," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(4), pages 609-616, December.
    6. Richard Ehrhardt, 1979. "The Power Approximation for Computing (s, S) Inventory Policies," Management Science, INFORMS, vol. 25(8), pages 777-786, August.
    7. Richard Ehrhardt & Charles Mosier, 1984. "A Revision of the Power Approximation for Computing (s, S) Policies," Management Science, INFORMS, vol. 30(5), pages 618-622, May.
    8. Yu-Sheng Zheng, 1992. "On Properties of Stochastic Inventory Systems," Management Science, INFORMS, vol. 38(1), pages 87-103, January.
    9. Georghios P. Sphicas, 1982. "Technical Note—On the Solution of an Inventory Model with Variable Lead Times," Operations Research, INFORMS, vol. 30(2), pages 404-410, April.
    10. Paknejad, M. Javad & Nasri, Farrokh & Affisco, John F., 1992. "Lead-time variability reduction in stochastic inventory models," European Journal of Operational Research, Elsevier, vol. 62(3), pages 311-322, November.
    11. Matthew J. Liberatore, 1979. "Technical Note—The EOQ Model under Stochastic Lead Time," Operations Research, INFORMS, vol. 27(2), pages 391-396, April.
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    Cited by:

    1. Babai, M. Zied & Dai, Yong & Li, Qinyun & Syntetos, Aris & Wang, Xun, 2022. "Forecasting of lead-time demand variance: Implications for safety stock calculations," European Journal of Operational Research, Elsevier, vol. 296(3), pages 846-861.
    2. John P. Saldanha & Bradley S. Price & Douglas J. Thomas, 2023. "A nonparametric approach for setting safety stock levels," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1150-1168, April.

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