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OPTIMAL MARKDOWN PRICING STRATEGY WITH DEMAND LEARNING

Published online by Cambridge University Press:  25 November 2011

H. Dharma Kwon ,
Steven A. Lippman  and
Christopher S. Tang
H. Dharma Kwon
Affiliation:
Department of Business Administration, University of Illinois at Urbana-Champaign, Champaign, IL 61820. E-mail: dhkwon@illinois.edu
Steven A. Lippman
Affiliation:
UCLA Anderson School, UCLA Los Angeles, CA 90095. E-mail: slippman@anderson.ucla.edu; ctang@anderson.ucla.edu
Christopher S. Tang
Affiliation:
UCLA Anderson School, UCLA Los Angeles, CA 90095. E-mail: slippman@anderson.ucla.edu; ctang@anderson.ucla.edu
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Abstract

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When launching a new product, a firm has to set an initial price with incomplete information about demand. However, after observing the demand over a period of time, the firm might decide to mark down the price, especially when the Bayesian updated belief about demand is lower than originally anticipated. We consider the case in which the manufacturer makes three decisions: initial price, when to mark down the price, and the markdown price. Modeling the cumulative demand as a Brownian motion with an unknown drift, we compute the posterior probability distribution of the unknown drift. We then show that it is optimal to mark down the price when the posterior probability is below a computable threshold. This threshold policy enables us to determine the optimal (a) regular price, (b) markdown price, and (c) markdown time. Additionally, we examine the impact of demand volatility and evaluate the value of learning.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 1 , January 2012 , pp. 77 - 104
Copyright
Copyright © Cambridge University Press 2011

References

1.Alvarez, L.H.R. (2003). On the properties of r-excessive mappings for a class of diffusions. Annals of Applied Probability 13: 1517–1533.CrossRefGoogle Scholar
2.Balvers, R.J. & Cosimano, T.F. (1990). Actively learning about demand and the dynamics of price adjustment. The Economic Journal 100: 882–898.Google Scholar
3.Bergemann, D. & Valimaki, J. (2000). Experimentation in markets. Review of Economic Studies 67: 213–234.Google Scholar
4.Bernardo, A.E. & Chowdhry, B. (2002). Resources, real options, and corporate strategy. Journal of Financial Economics 63: 211–234.CrossRefGoogle Scholar
5.Bolton, P. & Harris, C. (1999). Strategic experimentation. Econometrica 67: 349–374.CrossRefGoogle Scholar
6.Borodin, A.N. & Salminen, P. (2002). Handbook of brownian motion: Facts and formulae, 2nd ed.Basel: Birkhauser.Google Scholar
7.Decamps, J.-P., Mariotti, T., & Villeneuve, S. (2005). Investment timing under incomplete information. Mathematics of Operations Research 30: 472–500.Google Scholar
8.Dixit, A. (1992). Investment and hysteresis. The Journal of Economic Perspectives 6: 107–132.CrossRefGoogle Scholar
9.Elmaghraby, W., Lippman, S.A., Tang, C.S., & Yin, R. (2008). Will more purchasing options benefit customers? Production and Operations Management 18: 381–401.CrossRefGoogle Scholar
10.Federgruen, A. & Heching, A. (1999). Combined pricing and inventory control under uncertainty. Operations Research 47: 454–475.Google Scholar
11.Feng, Y. & Gallego, G. (1995). Optimal starting times for end-of-season sales and optimal stopping times for promotional fares. Management Science 41: 1371–1391.CrossRefGoogle Scholar
12.Fisher, M. (2007). Personal communication.Google Scholar
13.Hafner, K. & Stone, B. (2007). iPhone owners crying foul over price cut. New York Times, September 7.Google Scholar
14.Keller, G. & Rady, S. (1999). Optimal experimentation in a changing environment. Review of Economic Studies 66: 475–507.CrossRefGoogle Scholar
15.Lin, K.Y. (2006). Dynamic pricing with real-time demand learning. European Journal of Operational Research 174: 522–538.CrossRefGoogle Scholar
16.Liptser, R.S. & Shiryaev, A.N. (1974). Statistics of random processes I. General theory, 2nd ed.New York: Springer.Google Scholar
17.Markoff, J. (2007). Apple cuts {iPhone} price ahead of holidays. New York Times, September 6.Google Scholar
18.Moscarini, G. & Smith, L. (2001). The optimal level of experimentation. Econometrica 69: 1629–1644.Google Scholar
19.Oksendal, B. (2003). Stochastic differential equations: An introduction with applications, 6th ed.New York: Springer.CrossRefGoogle Scholar
20.Peskir, G. & Shiryaev, A. (2006). Optimal stopping and free-boundary problems. Basel: Birkhauser.Google Scholar
21.Petruzzi, N.C. & Dada, M. (2002). Dynamic pricing and inventory control with learning. Naval Research Logistics 49: 303–325.Google Scholar
22.Ross, S. (1983). Introduction to stochastic dynamic programming. New York: Academic Press.Google Scholar
23.Ryan, R. & Lippman, S.A. (2003). Optimal exit from a project with noisy returns. Probability in the Engineering and Informational Sciences 17: 435–458.CrossRefGoogle Scholar
24.Ryan, R. & Lippman, S.A. (2005). Optimal exit from a deteriorating project with noisy returns. Probability in the Engineering and Informational Sciences 19: 327–343.CrossRefGoogle Scholar
25.Shiryaev, A.N. (1978). Optimal stopping rules. New York: Springer-Verlag.Google Scholar
26.Subrahmanyan, S. & Shoemaker, R. (1996). Developing optimal pricing and inventory policies for retailers who face uncertain demand. Journal of Retailing 72: 7–30.CrossRefGoogle Scholar
27.Talluri, K.T. & van Ryzin, G.J. (2005). The theory and practice of revenue management. New York: Springer.Google Scholar
28.Yin, R. & Rajaram, K. (2007). Joint pricing and inventory control with a Makovian demand model. European Journal of Operational Research 182: 113–126.CrossRefGoogle Scholar