×

zbMATH — the first resource for mathematics

Dynamic pricing of inventory/capacity with infrequent price changes. (English) Zbl 1116.90009
Summary: We consider a problem of dynamically pricing a single product sold by a monopolist over a short time period. If demand characteristics change throughout the period, it becomes attractive for the company to adjust price continuously to respond to such changes (i.e., price-discriminate intertemporally). However, in practice there is typically a limit on the number of times the price can be adjusted due to the high costs associated with frequent price changes. If that is the case, instead of a continuous pricing rule the company might want to establish a piece-wise constant pricing policy in order to limit the number of price adjustments. Such a pricing policy, which involves optimal choice of prices and timing of price changes, is the focus of this paper. We analyze the pricing problem with a limited number of price changes in a dynamic, deterministic environment in which demand depends on the current price and time, and there is a capacity/inventory constraint that may be set optimally ahead of the selling season. The arrival rate can evolve in time arbitrarily, allowing us to model situations in which prices decrease, increase, or neither. We consider several plausible scenarios where pricing and/or timing of price changes are endogenized. Various notions of complementarity (single-crossing property, supermodularity and total positivity) are explored to derive structural results: conditions sufficient for the uniqueness of the solution and the monotonicity of prices throughout the sales period. Furthermore, we characterize the impact of the capacity constraint on the optimal prices and the timing of price changes and provide several other comparative statics results. Additional insights are obtained directly from the solutions of various special cases.

MSC:
90B05 Inventory, storage, reservoirs
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Y. Aviv, A. Pazgal, A partially observed Markov decision process for dynamic pricing, Working Paper, Washington University, St. Louis, 2004. · Zbl 1232.91238
[2] Y. Aviv, A. Pazgal, Optimal pricing of seasonal products in the presence of forward-looking consumers, Working Paper, Washington University, St. Louis, 2003.
[3] Bertsekas, D.P., Nonlinear programming, (1999), Athena Scientific · Zbl 0935.90037
[4] Bitran, G.; Caldentey, R., Commissioned paper: an overview of pricing models for revenue management, Manufacturing and service operations management, 5, 203-229, (2003)
[5] Bitran, G.R.; Mondschein, S.V., Periodic pricing of seasonal products in retailing, Management science, 43, 64-79, (1997) · Zbl 0888.90026
[6] Brynjolfsson, E.; Smith, M., Frictionless commerce? A comparison of Internet and conventional retailers, Management science, 46, 563-585, (1999)
[7] Bulow, J.I., Durable-goods monopolists, Journal of political economy, 90, 314-332, (1982)
[8] Chan, L.M.A.; Shen, M.; Simchi-Levi, D.; Swann, J., Coordinating pricing, inventory, and production: A taxonomy and review, ()
[9] Coase, R.H., Durability and monopoly, Journal of law and economics, 15, 143-159, (1972)
[10] Eliashberg, J.; Steinberg, R., Marketing-production decisions in an industrial channel of distribution, Management science, 33, 981-1000, (1987) · Zbl 0626.90031
[11] Elmaghraby, W.; Kesinocak, P., Dynamic pricing in the presence of inventory considerations: research overview, current practices, and future directions, Management science, 49, 1287-1309, (2003) · Zbl 1232.90042
[12] Federgruen, A.; Heching, A., Combined pricing and inventory control under uncertainty, Operations research, 47, 454-475, (1999) · Zbl 0979.90004
[13] Feng, Y.; Gallego, G., Optimal starting times for end-of-season sales and optimal stopping times for promotional fares, Management science, 46, 1371-1391, (1995) · Zbl 0859.90024
[14] Feng, Y.; Gallego, G., Perishable asset revenue management with Markovian time dependent demand intensities, Management science, 46, 941-956, (2000) · Zbl 1231.91271
[15] G. Gallego, A demand model for yield management, Technical report, Columbia University, 1996.
[16] Gallego, G.; van Ryzin, G., Optimal dynamic pricing of inventories with stochastic demand over finite horizons, Management science, 40, 999-1020, (1994) · Zbl 0816.90054
[17] D. Gupta, A.V. Hill, T. Bouzdine-Chameeva, A pricing model for clearing end of season retail inventory, Working Paper, University of Minnesota, 2002. · Zbl 1085.90003
[18] Karlin, S., Total positivity, (1968), Stanford University Press Stanford, CA · Zbl 0219.47030
[19] Kunreuther, H.; Schrage, L., Joint pricing and inventory decisions for constant priced items, Management science, 19, 732-738, (1973) · Zbl 0255.90010
[20] Levi, D.; Bergen, M.; Dutta, S.; Venable, R., The magnitude of menu costs: direct evidence from large US supermarket chains, Quarterly journal of economics, 112, 791-825, (1997)
[21] Levi, D.; Dutta, S.; Bergen, M.; Venable, R., Price adjustment at multiproduct retailers, Managerial and decision economics, 19, 81-120, (1998)
[22] Levinthal, D.A.; Purohit, D., Durable goods and product obsolescence, Marketing science, 8, 35-56, (1989)
[23] Lilien, G.L.; Kotler, P.; Moorthy, K.S., Marketing models, (1992), Prentice Hall New Jersey
[24] McGill, J.I.; van Ryzin, G., Revenue management: research overview and prospects, Transportation science, 33, 233-256, (1999) · Zbl 1002.90032
[25] Milgrom, P.; Shannon, C., Monotone comparative statics, Econometrica, 62, 157-180, (1994) · Zbl 0789.90010
[26] S. Netessine, R. Shumsky, Revenue management games, Management Science, forthcoming. Available from: <http://www.netessine.com>. · Zbl 1232.91089
[27] Rajan, A.; Rakesh; Steinberg, R., Dynamic pricing and ordering decisions by a monopolist, Management science, 38, 240-262, (1992) · Zbl 0763.90016
[28] Rao, V.R., Pricing models in marketing, ()
[29] Smith, S.A.; Achabal, D.D., Clearance pricing and inventory policies for retail chains, Management science, 44, 285-300, (1998) · Zbl 0989.90098
[30] Topkis, D.M., Supermodularity and complementarity, (1998), Princeton University Press Princeton, NJ
[31] Varian, H., Price discrimination, ()
[32] X. Xu, W.J. Hopp, Dynamic pricing and inventory control with demand substitution: The value of pricing flexibility, Working Paper, Northwestern University, 2004.
[33] M.J. Zbaracki, M. Ritson, D. Levy, S. Dutta, M. Bergen, The managerial and customer dimensions of the cost of price adjustment: Direct evidence from industrial markets, Working Paper, University of Pennsylvania, 2000.
[34] Zhao, W.; Zheng, Y.-S., Optimal dynamic pricing for perishable assets with nonhomogeneous demand, Management science, 46, 375-388, (2000) · Zbl 1231.91106
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.