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An (s, q) inventory model with stochastic and interrelated lead times

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  • Ruud Heuts
  • Jan de Klein

Abstract

In this article we introduce a lead time mechanism that allows simultaneous order arrivals. This mechanism ensures that orders never cross each other. For the continuous review (s, q) inventory system with constant demand, we show that the allowance of batch arrivals gives rise to a discontinuous cost function. By exploiting the special structure of this cost function, a search algorithm is derived that yields the optimal order strategy in a reasonable amount of time. The search is restricted to integer order strategies only. We also consider an approximate method of solution that is based on a related model with a continuous cost function. The results obtained by this approximation are, in general, very satisfactory. © 1995 John Wiley & Sons, Inc.

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  • 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.
    • Handle: RePEc:wly:navres:v:42:y:1995:i:5:p:839-859
    DOI: 10.1002/1520-6750(199508)42:53.0.CO;2-8
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    References listed on IDEAS

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    1. Awi Federgruen & Yu-Sheng Zheng, 1992. "An Efficient Algorithm for Computing an Optimal (r, Q) Policy in Continuous Review Stochastic Inventory Systems," Operations Research, INFORMS, vol. 40(4), pages 808-813, August.
    2. Donald Gross & A. Soriano, 1969. "The Effect of Reducing Leadtime on Inventory Levels-Simulation Analysis," Management Science, INFORMS, vol. 16(2), pages 61-76, October.
    3. Yu‐Sheng Zheng & Fangruo Chen, 1992. "Inventory policies with quantized ordering," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 285-305, April.
    4. 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.
    5. Paul Zipkin, 1986. "Stochastic leadtimes in continuous‐time inventory models," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(4), pages 763-774, November.
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    Cited by:

    1. Janssen, F.B.S.L.P. & Heuts, R.M.J. & de Kok, T., 1996. "On the (R,s,Q) Inventory Model when Demand is Modelled as a Compound Process," Other publications TiSEM 95c56aed-8108-4122-a689-5, Tilburg University, School of Economics and Management.
    2. 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.
    3. Janssen, F.B.S.L.P. & Heuts, R.M.J. & de Kok, T., 1996. "On the (R,s,Q) Inventory Model when Demand is Modelled as a Compound Process," Discussion Paper 1996-11, Tilburg University, Center for Economic Research.
    4. Ya Ping Fang & Kaiwen Meng & Xiao Qi Yang, 2012. "Piecewise Linear Multicriteria Programs: The Continuous Case and Its Discontinuous Generalization," Operations Research, INFORMS, vol. 60(2), pages 398-409, April.

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