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A Bayesian Analysis of the Style Goods Inventory Problem

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Author Info

  • George R. Murray, Jr.

    (Massachusetts Institute of Technology)

  • Edward A. Silver

    (Arthur D. Little, Inc.)

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    Abstract

    A style goods item has a finite selling period during which the sales rate varies in a seasonal and, to some extent, predictable fashion. There are only a limited number of opportunities to purchase or manufacture the style goods item, and the cost, in general, will depend on the time at which the item is obtained. The unit revenue achieved from sales of the item also varies during the selling season, and, in particular, reaches an appreciably lower terminal salvage value. Previous work on this class of problem has assumed one of the following: (a) There is a known deterministic sales rate during the season. (b) The sales are generated by a stochastic process having exactly known probabilities. Both of these formulations of the problem overlook what we believe to be an essential feature--that initially we have a great uncertainty concerning the sales potential of the item but have an opportunity to develop a better forecast as actual sales become known. The model discussed in this paper treats the sales potential of the item as a subjective random variable whose distribution is changed adaptively (through the use of Bayes' Rule) as the sales history unfolds. We examine several methods for encoding the prior knowledge that lead to a computationally feasible dynamic programming solution to the problem. An interesting feature of this approach is that the dynamic programming state represents both the unsold inventory of the item and the current state of knowledge concerning the sales potential. Numerical examples are discussed, showing the importance of formulating the problem, in a way that includes a state of knowledge that adaptively improves as demand becomes known. Finally, computational shortcuts that make problems of a larger scale computationally feasible are discussed.

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    File URL: http://dx.doi.org/10.1287/mnsc.12.11.785
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 12 (1966)
    Issue (Month): 11 (July)
    Pages: 785-797

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    Handle: RePEc:inm:ormnsc:v:12:y:1966:i:11:p:785-797

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    Cited by:
    1. Mostard, Julien & de Koster, Rene & Teunter, Ruud, 2005. "The distribution-free newsboy problem with resalable returns," International Journal of Production Economics, Elsevier, vol. 97(3), pages 329-342, September.
    2. Vlachos, D. & Dekker, R., 2000. "Return handling options and order quantities for single period products," Econometric Institute Research Papers EI 2000-29/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Mostard, Julien & Teunter, Ruud & de Koster, René, 2011. "Forecasting demand for single-period products: A case study in the apparel industry," European Journal of Operational Research, Elsevier, vol. 211(1), pages 139-147, May.
    4. Agrawal, Narendra & Smith, Stephen A., 2013. "Optimal inventory management for a retail chain with diverse store demands," European Journal of Operational Research, Elsevier, vol. 225(3), pages 393-403.
    5. Wanke, Peter F., 2008. "The uniform distribution as a first practical approach to new product inventory management," International Journal of Production Economics, Elsevier, vol. 114(2), pages 811-819, August.
    6. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
    7. 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.
    8. 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.
    9. Taskin, Selda & Lodree Jr., Emmett J., 2010. "Inventory decisions for emergency supplies based on hurricane count predictions," International Journal of Production Economics, Elsevier, vol. 126(1), pages 66-75, July.
    10. Oberlaender, Michael, 2011. "Dual sourcing of a newsvendor with exponential utility of profit," International Journal of Production Economics, Elsevier, vol. 133(1), pages 370-376, September.
    11. Bitran, Gabriel R. & Wadhwa, Hitendra K. S. (Hitendra Kumar Singh), 1996. "A methodology for demand learning with an application to the optimal pricing of seasonal products," Working papers 3898-96., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    12. Lee, Chih-Ming, 2008. "A Bayesian approach to determine the value of information in the newsboy problem," International Journal of Production Economics, Elsevier, vol. 112(1), pages 391-402, March.
    13. Serel, Doğan A., 2012. "Multi-item quick response system with budget constraint," International Journal of Production Economics, Elsevier, vol. 137(2), pages 235-249.
    14. Hill, Roger M., 1997. "Applying Bayesian methodology with a uniform prior to the single period inventory model," European Journal of Operational Research, Elsevier, vol. 98(3), pages 555-562, May.

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