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Planning Horizons for a Stochastic Lead-Time Inventory Model

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  • Matthew J. Liberatore

    (FMC Corporation, Philadelphia, Pennsylvania)

Abstract

The planning-horizon literature has thus far focused on the analysis of deterministic lead-time inventory systems. We show that under certain conditions several planning-horizon theorems hold in the stochastic lead-time case as well. Specifically, demands are assumed non-interchangeable and deterministic; thus production runs are assigned to sets of specific demands and can only be used in the satisfaction of those demands. When holding, backlogging, setup (ordering), and variable production costs are stationary over time, and when the lead-time distribution is invariant over time, it is always optimal to produce for sets of consecutive integral demands. Production dates for specific shipments follow from convexity properties. Building upon these results, we prove several planning-horizon theorems (of the Wagner-Whitin and Zabel varieties). A forward dynamic programming recursion is given. These results are shown to generalize those of the basic dynamic lot-size model. We present a numerical example that illustrates the sensitivity of the optimal policy to changes in lead-time variance.

Suggested Citation

  • Matthew J. Liberatore, 1977. "Planning Horizons for a Stochastic Lead-Time Inventory Model," Operations Research, INFORMS, vol. 25(6), pages 977-988, December.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:6:p:977-988
    DOI: 10.1287/opre.25.6.977
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    Cited by:

    1. Osman Alp & Nesim K. Erkip & Refik Güllü, 2003. "Optimal Lot-Sizing/Vehicle-Dispatching Policies Under Stochastic Lead Times and Stepwise Fixed Costs," Operations Research, INFORMS, vol. 51(1), pages 160-166, February.
    2. Thevenin, Simon & Ben-Ammar, Oussama & Brahimi, Nadjib, 2022. "Robust optimization approaches for purchase planning with supplier selection under lead time uncertainty," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1199-1215.
    3. M. Ganesh Kumar & R. Uthayakumar, 2019. "A two-echelon integrated inventory model under generalized lead time distribution with variable backordering rate," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(4), pages 552-562, August.
    4. Jing-Sheng Song & Candace A. Yano & Panupol Lerssrisuriya, 2000. "Contract Assembly: Dealing with Combined Supply Lead Time and Demand Quantity Uncertainty," Manufacturing & Service Operations Management, INFORMS, vol. 2(3), pages 287-296, July.
    5. Rabin Kumar Mallick & Kartik Patra & Shyamal Kumar Mondal, 2020. "Mixture inventory model of lost sale and back-order with stochastic lead time demand on permissible delay in payments," Annals of Operations Research, Springer, vol. 292(1), pages 341-369, September.
    6. Jong-Wuu Wu & Wen-Chuan Lee & Hui-Yin Tsai, 2002. "A Note on Minimax Mixture of Distributions Free Procedure for Inventory Model with Variable Lead Time," Quality & Quantity: International Journal of Methodology, Springer, vol. 36(3), pages 311-323, August.

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