Dynamic Pricing with Periodic Review and a Finite set of Prices with Cancellation

Document Type : Research Paper


Industrial Eng. Dept., Sharif University of Technology, Tehran, Iran


In this paper, three dynamic pricing models are developed and analyzed. We assume a limited number of a particular asset is offered for sale over a period of time. This asset is perishable and can be an inventory or a manufacturing capacity. During each period, the seller sets a price for this asset. This price is selected from a predetermined discrete set. The maximum amount which a customer is willing to pay is called "reservation price". Different customers have different reservation prices. The distribution function of the reservation prices for all potential customers is known. Demands arrive according to a nonhomogeneous Poisson process. To maximize the expected revenue, the price of this asset is controlled periodically, as sales evolve. Demand cancellation is also considered. Furthermore, we study the effect of cancellation as well as setting a sale limit for each period. The analysis of the models indicates that their properties are different from those of the basic models studied previously. By randomly generated examples, we show that the properties of “Inventory Monotonocity” and “Time Monotonocity” do not hold in our models, while these properties hold for continuous price review models.


Main Subjects

[1] Bitran G.R., Mondschein S.V. (1995), An Application of Yield Management to the Hotel Industry
Considering Multiple Day Stays; Operations Research 43; 427-443.
[2] Bitran G.R., Mondschein S.V. (1997), Periodic pricing of seasonal products in retailing; Management
Science 43; 64-79.
[3] Bitran G.R., Caldentey R. (2003), An overview of pricing models for Revenue Management;
Manufacturing and Service Operations Management 5; 203-230.
[4] Brumelle S.L., McGill J.I. (1993), Airline Seat Allocation with Multiple Nested Fare Classes;
Operations Research 41; 127–137.
[5] Chatwin R.E. (2000), Optimal Dynamic Pricing of Perishable Products with Stochastic Demand and a
Finite Set of Prices; European Journal of Operational Research 125; 149-174.
[6] Elmaghraby W., Keskinocak P. (2003), Dynamic Pricing in the Presence of Inventory Considerations;
Management Science.49; 1287-1309.
[7] 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.
[8] 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.
[9] Gallego G., Van Ryzin G.J. (1994), Optimal dynamic pricing of inventories with stochastic demand
over finite horizon, Management Science 40; 999-1020.
[10] Kincaid W.M., Darling D.A. (1963), An inventory pricing problem; Journal of Mathematical Analysis
and Applications 7(2); 183-208.
[11] Littlewood K. (1972), Forecasting and Control of Passenger Bookings; AGIFORS Symposium
Proceedings 12; Nathanya, Israel.
[12] Robinson L.W. (1995), Optimal and Approximate Control Policies for Airline Booking with
Sequential Nonmonotonic Fare Classes; Operations Research 43; 252-263.
[13] Ross S.M. (1970), Applied probability models with optimization applications; Holden Day, Inc.; San
[14] Subramanian J., Autenbacher C.J.L, Stidham S.J. (1999), Yield Management with Overbooking,
Cancellations and No Shows; Transportation Science 33(2); 147-167.
[15] Zhao W., Zheng Y.S. (2000), Optimal Dynamic Pricing for Perishable Assets with Nonhomogeneous
Demand; Management Science 46; 375-388.
Volume 3, Issue 3 - Serial Number 3
November 2009
Pages 213-226
  • Receive Date: 04 March 2008
  • Revise Date: 16 August 2008
  • Accept Date: 19 February 2009
  • First Publish Date: 01 November 2009