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Production Smoothing with Stochastic Demand I: Finite Horizon Case

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  • Matthew J. Sobel

    (Yale University)

Abstract

Beckmann [1] and Mills [7] consider production smoothing problems in which demands are random variables. This paper generalizes and extends Beckmann's results which predicate backlogging of excess demand. Convex expected holding and penalty cost functions pertain to inventory and the cost of changing the production rate is proportional to the change. The model has a finite horizon and permits nonstationary costs and demand distributions. Beckmann shows that two curves in the plane determine an optimal policy (minimum expected discounted cost) each period. It is shown here that the curves have slopes between minus one and zero, are differentiable, and are bounded by two straight lines with a slope of minus one. The results are not changed by an upper bound on the quantity produced or by a lag between the time a product is manufactured and the time it is available to satisfy demand.

Suggested Citation

  • Matthew J. Sobel, 1969. "Production Smoothing with Stochastic Demand I: Finite Horizon Case," Management Science, INFORMS, vol. 16(3), pages 195-207, November.
    • Handle: RePEc:inm:ormnsc:v:16:y:1969:i:3:p:195-207
    DOI: 10.1287/mnsc.16.3.195
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    Cited by:

    1. Gérard P. Cachon & Taylor Randall & Glen M. Schmidt, 2007. "In Search of the Bullwhip Effect," Manufacturing & Service Operations Management, INFORMS, vol. 9(4), pages 457-479, April.
    2. Li Chen & Hau L. Lee, 2012. "Bullwhip Effect Measurement and Its Implications," Operations Research, INFORMS, vol. 60(4), pages 771-784, August.
    3. Robert N. Boute & Jan A. Van Mieghem, 2015. "Global Dual Sourcing and Order Smoothing: The Impact of Capacity and Lead Times," Management Science, INFORMS, vol. 61(9), pages 2080-2099, September.
    4. Xiuli Chao & Sridhar Seshadri & Michael Pinedo, 2008. "Optimal capacity in a coordinated supply chain," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(2), pages 130-141, March.
    5. Cantor, David E. & Katok, Elena, 2012. "Production smoothing in a serial supply chain: A laboratory investigation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(4), pages 781-794.
    6. Matthew J. Sobel & Rachel Q. Zhang, 2001. "Inventory Policies for Systems with Stochastic and Deterministic Demand," Operations Research, INFORMS, vol. 49(1), pages 157-162, February.

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