Dynamic Pricing with Financial Milestones: Feedback-Form Policies

• Published in: Management science Vol. 58; no. 9; pp. 1715 - 1731
• Main Authors: Besbes, Omar, Maglaras, Costis
• Format: Journal Article
• Language: English
• Published: Hanover, MD INFORMS 01-09-2012; Institute for Operations Research and the Management Sciences
• Subjects: Applied sciences; asymptotic analysis; Asymptotic methods; Demand models; Determinism; dynamic pricing; estimation; Exact sciences and technology; feedback; Financing methods; Firm modelling; Fixed prices; Heuristics; Management science; Market prices; market uncertainty; Methods; Operational research and scientific management; Operational research. Management science; Optimal policy; Optimal solutions; Planning methods; Pricing; Pricing policies; Real estate; Real estate developments; Revenue; Revenue management; Sales; Selling; Studies; Unit pricing; United States; Optimal policy; Income; real estate; Feedback regulation; asymptotic analysis; Return rate; Real time; Set constraint; Modeling; estimation; market uncertainty; Uncertain system; Financial policy; Sales; Feedback; Financing; Pricing; Asymptotic approximation; Dynamic programming; Tariffication; revenue management; dynamic pricing
• ISSN: 0025-1909; 1526-5501
• DOI: 10.1287/mnsc.1110.1513

We study a seller that starts with an initial inventory of goods, has a target horizon over which to sell the goods, and is subject to a set of financial
milestone
constraints on the revenues and sales that need to be achieved at different time points along the sales horizon. We characterize the revenue maximizing dynamic pricing policy for the seller and highlight the effect of revenue and sales milestones on its structure. The optimal policy can be written in feedback form, where the price at each point in time is selected so as to track the most stringent among all future milestones. Building on that observation, we propose a discrete-review policy that aims to dynamically track the appropriate milestone constraint and show that this simple and practical policy is near optimal in settings with large initial capacity and long sales horizons even in settings with no advance demand model information. One motivating application comes from the sales of new multiunit, residential real estate developments, where intermediate milestone constraints play an important role in their financing and construction.
This paper was accepted by Gérard P. Cachon, stochastic models and simulation.