Department Civil Engineering, Technical University of Madrid, Madrid, Spain. Conento S.L.U., Madrid, Spain. Solute Ingenieros, San Sebastián de los Reyes, Madrid, Spain.
In this paper, we address the problem of dynamic pricing to optimize the revenue coming from the sales of a limited inventory in a finite time-horizon. A priori, the demand is assumed to be unknown. The seller must learn on the fly. We first deal with the simplest case, involving only one class of product for sale. Furthermore the general situation is considered with a finite number of product classes for sale. In particular, a case in point is the sale of tickets for events related to culture and leisure; in this case, typically the tickets are sold months before the event, thus, uncertainty over actual demand levels is a very a common occurrence. We propose a heuristic strategy of adaptive dynamic pricing, based on experience gained from the past, taking into account, for each time period, the available inventory, the time remaining to reach the horizon, and the profit made in previous periods. In the computational simulations performed, the demand is updated dynamically based on the prices being offered, as well as on the remaining time and inventory. The simulations show a significant profit over the fixed-price strategy, confirming the practical usefulness of the proposed strategy. We develop a tool allowing us to test different dynamic pricing strategies designed to fit market conditions and seller's objectives, which will facilitate data analysis and decision-making in the face of the problem of dynamic pricing.
Vázquez-Gallo, M. , Estévez, M. and Egido, S. (2014) Active Learning and Dynamic Pricing Policies. American Journal of Operations Research, 4, 90-100. doi: 10.4236/ajor.2014.42009.
[1] Talluri, K.T. and van Ryzin, G.J. (2004) The Theory and Practice of Revenue Management. Springer Science + Business Media, Berlin. [2] Gallego, G. and van Ryzin, G. (1994) Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons. Management Science, 40, 999-1020. http://dx.doi.org10.1287/mnsc.40.8.999 [3] Bertsimas, D. and Perakis, G. (2006) Dynamic Pricing: A Learning Approach. Mathematical and Computational Models for Congestion Charging. Applied Optimization, 101, 45-79.
http://dx.doi.org/10.1007/0-387-29645-X_3 [4] Cope, E. (2006) Bayesian Strategies for Dynamic Pricing in E-Commerce. Naval Research Logistics, 54, 265-281.
http://dx.doi.org/10.1002/nav.20204 [5] Lobo, M.S. and Boyd, S. (2003) Pricing and Learning with Uncertain Demand.
http://www.stanford.edu/~boyd/papers/pdf/pric_learn_unc_dem.pdf [6] Gallego, G. and van Ryzin, G. (1997) A Multiproduct Dynamic Pricing Problem and its Applications to Network Yield Management. Operations Research, 45, 24-41. [7] Besbes, O. and Zeevi, A. (2006) Blind Nonparametric Revenue Management: Asymptotic Optimality of a Joint Learning and Pricing Method. Working Paper, Stanford Graduate School of Business. [8] Aviv, Y. and Pazgal, A. (2005) A Partially Observed Markov Decision Process for Dynamic Pricing. Management Science, 51, 1400-1416. http://dx.doi.org/10.1287/mnsc.1050.0393 [9] Araman, V.F. and Caldentey, R. (2009) Dynamic Pricing for Nonperishable Products with Demand Learning. Operations Research, 57, 1169-1188.http://dx.doi.org/10.1287/opre.1090.0725 [10] Lin, K.Y. (2006) Dynamic Pricing with Real-Time Demand Learning. European Journal of Operations Research, 174, 522-538. http://dx.doi.org/10.1016/j.ejor.2005.01.041 [11] Narahari, Y., Raju, C.V.L., Ravikumar, K. and Shah, S. (2005) Dynamic Pricing Models for Electronic Business. Sadhana, 30, 231-256. http://dx.doi.org/10.1007/BF02706246 [12] Farias, V.F. and Van Roy, B. (2010) Dynamic Pricing with a Prior on Market Response. Operations Research, 58, 1629. http://dx.doi.org/10.1287/opre.1090.0729 [13] DiMicco, J.M., Greenwald, A. and Maes, P. (2003) Learning Curve: A Simulation-Based Approach to Dynamic Pricing. Electronic Commerce Research, 3, 245-276.