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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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    3. Gillen, David & Hasheminia, Hamed, 2013. "Estimating the demand responses for different sizes of air passenger groups," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 24-38.
    4. Fernandes, Rui & Gouveia, Borges & Pinho, Carlos, 2010. "Modeling Overstock," MPRA Paper 25126, University Library of Munich, Germany.
    5. Tyworth, John E., 2018. "A note on lead-time paradoxes and a tale of competing prescriptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 139-150.
    6. 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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    8. Ponte, Borja & Costas, José & Puche, Julio & Pino, Raúl & de la Fuente, David, 2018. "The value of lead time reduction and stabilization: A comparison between traditional and collaborative supply chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 111(C), pages 165-185.
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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).
    11. Nan Yang & Renyu Zhang, 2022. "Comparative Statics Analysis of An Inventory Management Model with Dynamic Pricing, Market Environment Fluctuation, and Delayed Differentiation," Production and Operations Management, Production and Operations Management Society, vol. 31(1), pages 341-357, January.
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    13. 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.
    14. 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.
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