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On Properties of Stochastic Inventory Systems

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  • Yu-Sheng Zheng

    (Decision Sciences Department, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

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    Abstract

    For most order quantity/reorder point inventory systems, the stochastic model, which specifies the demands as stochastic processes, is often more accurate than its deterministic counterpart---the EOQ model. However, the application of the stochastic model has been limited because of the absence of insightful analytical results on the model. This paper analyzes the stochastic order quantity/reorder point model in comparison with a corresponding deterministic EOQ model. Based on simple optimality conditions for the control variables derived in the paper, a sensitivity analysis is carried out, and a number of basic qualitative properties are established for the optimal control parameters. Our main results include the following: (1) in contrast to the deterministic EOQ model, the controllable costs of the stochastic model due to selection of the order quantity (assuming the reorder point is chosen optimally for every order quantity) are actually smaller, while the total costs are clearly larger; the optimal order quantity is larger, but the difference is relatively small when the quantity is large; the cost performance is even less sensitive to choices of the order quantity; (2) the relative increase of the costs incurred by using the quantity determined by the EOQ instead of the optimal from the stochastic model is no more than 1/8, and vanishes when the ordering costs are significant relative to other costs.

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    File URL: http://dx.doi.org/10.1287/mnsc.38.1.87
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 38 (1992)
    Issue (Month): 1 (January)
    Pages: 87-103

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    Handle: RePEc:inm:ormnsc:v:38:y:1992:i:1:p:87-103

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    Related research

    Keywords: inventory/production; sensitivity analysis; stochastic model;

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    Cited by:
    1. Khanra, Avijit & Soman, Chetan A., . "Sensitivity Analysis of the Newsboy Model," IIMA Working Papers WP2013-09-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
    2. Riezebos, Jan, 2006. "Inventory order crossovers," International Journal of Production Economics, Elsevier, vol. 104(2), pages 666-675, December.
    3. Chen, Youhua Frank, 2005. "Fractional programming approach to two stochastic inventory problems," European Journal of Operational Research, Elsevier, vol. 160(1), pages 63-71, January.
    4. Seifert, Daniel & Seifert, Ralf W. & Protopappa-Sieke, Margarita, 2013. "A review of trade credit literature: Opportunities for research in operations," European Journal of Operational Research, Elsevier, vol. 231(2), pages 245-256.
    5. Xu, Kefeng & Evers, Philip T. & Fu, Michael C., 2003. "Estimating customer service in a two-location continuous review inventory model with emergency transshipments," European Journal of Operational Research, Elsevier, vol. 145(3), pages 569-584, March.
    6. Yue, Jinfeng & Wang, Min-Chiang & Chen, Bintong, 2007. "Mean-range based distribution-free procedures to minimize "overage" and "underage" costs," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1103-1116, January.
    7. Andersson, Jonas & Marklund, Johan, 2000. "Decentralized inventory control in a two-level distribution system," European Journal of Operational Research, Elsevier, vol. 127(3), pages 483-506, December.
    8. Langenberg, Kerstin U. & Seifert, Ralf W. & Tancrez, Jean-S├ębastien, 2012. "Aligning supply chain portfolios with product portfolios," International Journal of Production Economics, Elsevier, vol. 135(1), pages 500-513.
    9. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.
    10. Ang, Marcus & Song, Jing-Sheng & Wang, Mingzheng & Zhang, Hanqin, 2013. "On properties of discrete (r, q) and (s, T) inventory systems," European Journal of Operational Research, Elsevier, vol. 229(1), pages 95-105.
    11. Yang, Lei & Yang, Jian & Yu, Gang & Zhang, Hanqin, 2011. "Near-optimal (r,Q) policies for a two-stage serial inventory system with Poisson demand," International Journal of Production Economics, Elsevier, vol. 133(2), pages 728-735, October.
    12. Axsater, Sven, 2001. "Scaling down multi-echelon inventory problems," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 255-261, May.
    13. Fleischmann, Moritz & Kuik, Roelof & Dekker, Rommert, 2002. "Controlling inventories with stochastic item returns: A basic model," European Journal of Operational Research, Elsevier, vol. 138(1), pages 63-75, April.

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