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Myopic Policies for Some Inventory Models with Uncertain Demand Distributions

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  • William S. Lovejoy

    (Graduate School of Business, Stanford University, Stanford, California 94305-5015)

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    Abstract

    The majority of papers on stochastic inventory theory make the assumption that the distribution of consumer demand in each time period is known with certainty. While this assumption is unsupported in many applied contexts, it is conventionally held that more realistic models are more difficult to solve and will not yield simple operational policies. This paper shows that a simple inventory policy based upon a critical fractile can be optimal or near-optimal in some inventory models with parameter adaptive demand processes. In these, some parameter of the demand distribution is not known with certainty, and estimates of the parameter are updated in a statistical fashion as demand is observed through time. Examples include exponentially smoothed forecasts and Bayesian updating of parameter estimates. Bounds on the value loss relative to optimal cost, when using the critical fractile policy, can be calculated directly from the problem data. Some numerical examples illustrate the technique.

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    File URL: http://dx.doi.org/10.1287/mnsc.36.6.724
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 36 (1990)
    Issue (Month): 6 (June)
    Pages: 724-738

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    Handle: RePEc:inm:ormnsc:v:36:y:1990:i:6:p:724-738

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    Related research

    Keywords: inventory models; myopic solutions; dependent demand; Bayesian analysis;

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    Cited by:
    1. Larson, C. Erik & Olson, Lars J. & Sharma, Sunil, 2001. "Optimal Inventory Policies when the Demand Distribution Is Not Known," Journal of Economic Theory, Elsevier, vol. 101(1), pages 281-300, November.
    2. Choi, Tsan-Ming, 2007. "Pre-season stocking and pricing decisions for fashion retailers with multiple information updating," International Journal of Production Economics, Elsevier, vol. 106(1), pages 146-170, March.
    3. Snyder, Ralph D. & Koehler, Anne B. & Ord, J. Keith, 2002. "Forecasting for inventory control with exponential smoothing," International Journal of Forecasting, Elsevier, vol. 18(1), pages 5-18.
    4. Tan, Tarkan & Gullu, Refik & Erkip, Nesim, 2007. "Modelling imperfect advance demand information and analysis of optimal inventory policies," European Journal of Operational Research, Elsevier, vol. 177(2), pages 897-923, March.
    5. Petruzzi, Nicholas & Monahan, George E., 2002. "Managing Fashion Goods Inventories:," Working Papers 02-0117, University of Illinois at Urbana-Champaign, College of Business.
    6. Xu, Ningxiong, 2008. "Myopic policy for a two-product and multi-period supply contract with different delivery lead times and storage limitation," International Journal of Production Economics, Elsevier, vol. 115(1), pages 179-188, September.
    7. Erhan Bayraktar & Mike Ludkovski, 2012. "Inventory Management with Partially Observed Nonstationary Demand," Papers 1206.6283, arXiv.org.
    8. Iida, Tetsuo, 2002. "A non-stationary periodic review production-inventory model with uncertain production capacity and uncertain demand," European Journal of Operational Research, Elsevier, vol. 140(3), pages 670-683, August.
    9. Snyder, Ralph D. & Koehler, Anne B. & Hyndman, Rob J. & Ord, J. Keith, 2004. "Exponential smoothing models: Means and variances for lead-time demand," European Journal of Operational Research, Elsevier, vol. 158(2), pages 444-455, October.
    10. Iida, Tetsuo, 1999. "The infinite horizon non-stationary stochastic inventory problem: Near myopic policies and weak ergodicity," European Journal of Operational Research, Elsevier, vol. 116(2), pages 405-422, July.
    11. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.
    12. Graves, Stephen C., 1997. "A single-item inventory model for a non-stationary demand process," Working papers WP 3944-97., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    13. Zotteri, Giulio & Verganti, Roberto, 2001. "Multi-level approaches to demand management in complex environments: an analytical model," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 221-233, May.
    14. Choi, Tsan-Ming & Chow, Pui-Sze, 2008. "Mean-variance analysis of Quick Response Program," International Journal of Production Economics, Elsevier, vol. 114(2), pages 456-475, August.

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