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The Effect of Lead Time and Demand Uncertainties in ( r, q ) Inventory Systems

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  • Jing-Sheng Song

    (The Fuqua School of Business, Duke University, Durham, North Carolina 27708, and Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200052, China)

  • Hanqin Zhang

    (Institute of Applied Mathematics, Academia Sinica, Beijing 100080, China, and Business School, National University of Singapore, Singapore)

  • Yumei Hou

    (Yanshan University, Qinhuangdao 066004, Hebei Province, China)

  • Mingzheng Wang

    (Dalian University of Technology, Dalian 116024, China)

Abstract

We study a single-item (r, q) inventory system, where r is the reorder point and q is the order quantity. The demand is a compound-Poisson process. We investigate the behavior of the optimal policy parameters and the long-run average cost of the system in response to stochastically shorter or less-variable lead times. We show that although some of the properties of the base-stock system can be extended to this more general model, some cannot. The same findings also apply when the comparison is conducted on the lead-time demand distributions.

Suggested Citation

  • Jing-Sheng Song & Hanqin Zhang & Yumei Hou & Mingzheng Wang, 2010. "The Effect of Lead Time and Demand Uncertainties in ( r, q ) Inventory Systems," Operations Research, INFORMS, vol. 58(1), pages 68-80, February.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:1:p:68-80
    DOI: 10.1287/opre.1090.0711
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    References listed on IDEAS

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    4. Cobb, Barry R. & Johnson, Alan W. & Rumí, Rafael & Salmerón, Antonio, 2015. "Accurate lead time demand modeling and optimal inventory policies in continuous review systems," International Journal of Production Economics, Elsevier, vol. 163(C), pages 124-136.
    5. Tyworth, John E. & Saldanha, John, 2014. "The lead-time reliability paradox and inconsistent value-of-reliability estimates," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 70(C), pages 76-85.
    6. Kumar Muthuraman & Sridhar Seshadri & Qi Wu, 2015. "Inventory Management with Stochastic Lead Times," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 302-327, February.
    7. Fernandes, Rui & Gouveia, Borges & Pinho, Carlos, 2010. "Modeling Overstock," MPRA Paper 25126, University Library of Munich, Germany.
    8. Fleischhacker, Adam J. & Fok, Pak-Wing, 2015. "On the relationship between entropy, demand uncertainty, and expected loss," European Journal of Operational Research, Elsevier, vol. 245(2), pages 623-628.
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    10. Saldanha, John P., 2022. "Estimating the reorder point for a fill-rate target under a continuous review policy in the presence of non-standard lead-time demand distributions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
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