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A Fractiles Perspective to the Joint Price/Quantity Newsvendor Model

Author

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  • Gal Raz

    (Australian Graduate School of Management, University of New South Wales, Sydney, New South Wales 2052, Australia)

  • Evan L. Porteus

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

Abstract

Pricing and quantity decisions are critical to many firms across different industries. We study the joint price/quantity newsvendor model where only a single quantity and price decision is made, such as a fashion or holiday product that cannot be replenished and where the price is advertised nationally and cannot be changed. Demand is uncertain and sensitive to price. We develop a method for easily finding the optimal price and quantity that applies to more general cases than the usual one in which uncertainty is either additive, multiplicative, or a combination of the two. We represent a quantity by its fractile of the probability distribution of demand for a given price. We use a standard approach to approximating a given distribution with a finite number of representative fractiles and assume that these fractile functions are piecewise linear functions of the price. We identify effects that are not usually seen in a joint price/quantity newsvendor model. For example, although the optimal quantity is a decreasing function of the unit cost, the optimal price can be nonmonotone in the unit cost and we shed insight into why. We illustrate that using a simplified structure of demand uncertainty can result in substantially lower profits.

Suggested Citation

  • Gal Raz & Evan L. Porteus, 2006. "A Fractiles Perspective to the Joint Price/Quantity Newsvendor Model," Management Science, INFORMS, vol. 52(11), pages 1764-1777, November.
    • Handle: RePEc:inm:ormnsc:v:52:y:2006:i:11:p:1764-1777
    DOI: 10.1287/mnsc.1060.0584
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    References listed on IDEAS

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    1. Lode Li, 1988. "A Stochastic Theory of the Firm," Mathematics of Operations Research, INFORMS, vol. 13(3), pages 447-466, August.
    2. Yakov Amihud & Haim Mendelson, 1983. "Price Smoothing and Inventory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 87-98.
    3. Nicholas C. Petruzzi & Maqbool Dada, 1999. "Pricing and the Newsvendor Problem: A Review with Extensions," Operations Research, INFORMS, vol. 47(2), pages 183-194, April.
    4. Zabel, Edward, 1972. "Multiperiod monopoly under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(3), pages 524-536, December.
    5. Awi Federgruen & Aliza Heching, 1999. "Combined Pricing and Inventory Control Under Uncertainty," Operations Research, INFORMS, vol. 47(3), pages 454-475, June.
    6. E. Zabel, 1970. "Monopoly and Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(2), pages 205-219.
    7. T. M. Whitin, 1955. "Inventory Control and Price Theory," Management Science, INFORMS, vol. 2(1), pages 61-68, October.
    8. Netessine, Serguei, 2006. "Dynamic pricing of inventory/capacity with infrequent price changes," European Journal of Operational Research, Elsevier, vol. 174(1), pages 553-580, October.
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    Citations

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    Cited by:

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    3. Yang, Yang & Liu, Jie, 2023. "Price timing and financing strategies for a capital-constrained supply chain with price-dependent stochastic demand," International Journal of Production Economics, Elsevier, vol. 261(C).
    4. Michael Salinger & Miguel Ampudia, 2011. "Simple Economics of the Price-Setting Newsvendor Problem," Management Science, INFORMS, vol. 57(11), pages 1996-1998, November.
    5. Ayşe Kocabıyıkoğlu & Ioana Popescu, 2011. "An Elasticity Approach to the Newsvendor with Price-Sensitive Demand," Operations Research, INFORMS, vol. 59(2), pages 301-312, April.
    6. Xiong‐zhi Wang & Guo‐qing Wang, 2019. "Integrating dynamic pricing and inventory control for fresh‐agri product under consumer choice," Australian Economic Papers, Wiley Blackwell, vol. 58(1), pages 96-111, March.
    7. He, Yuanjie, 2013. "Sequential price and quantity decisions under supply and demand risks," International Journal of Production Economics, Elsevier, vol. 141(2), pages 541-551.
    8. Guo, Peijun & Tanaka, Hideo, 2010. "Decision making with interval probabilities," European Journal of Operational Research, Elsevier, vol. 203(2), pages 444-454, June.
    9. Jochen Schlapp & Moritz Fleischmann & Danja Sonntag, 2022. "Inventory timing: How to serve a stochastic season," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 2891-2906, July.
    10. van der Laan, Niels & Teunter, Ruud H. & Romeijnders, Ward & Kilic, Onur A., 2022. "The data-driven newsvendor problem: Achieving on-target service-levels using distributionally robust chance-constrained optimization," International Journal of Production Economics, Elsevier, vol. 249(C).
    11. Boutselis, Petros & McNaught, Ken, 2014. "Finite-Time Horizon Logistics Decision Making Problems: Consideration of a Wider Set of Factors," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Blecker, Thorsten & Kersten, Wolfgang & Ringle, Christian M. (ed.), Innovative Methods in Logistics and Supply Chain Management: Current Issues and Emerging Practices. Proceedings of the Hamburg International Conferenc, volume 19, pages 249-274, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.
    12. Zhao, Xuan & Atkins, Derek & Hu, Ming & Zhang, Wensi, 2017. "Revenue management under joint pricing and capacity allocation competition," European Journal of Operational Research, Elsevier, vol. 257(3), pages 957-970.
    13. Xiuyan Ma, 2019. "Pricing to the Scenario: Price-Setting Newsvendor Models for Innovative Products," Mathematics, MDPI, vol. 7(9), pages 1-15, September.

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