Dynamic Pricing with Financial Milestones: Feedback-Form Policies

Management Science, Forthcoming

Columbia Business School Research Paper No. 12-8

42 Pages Posted: 12 Jan 2012  

Omar Besbes

Columbia Business School - Decision Risk and Operations

Costis Maglaras

Columbia Business School - Decision Risk and Operations

Date Written: November 30, 2011

Abstract

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 multi-unit, residential real estate developments, where intermediate milestone constraints play an important role in their financing and construction.

Keywords: Revenue management, dynamic pricing, market uncertainty, estimation, feedback, real estate, asymptotic analysis

Suggested Citation

Besbes, Omar and Maglaras, Costis, Dynamic Pricing with Financial Milestones: Feedback-Form Policies (November 30, 2011). Management Science, Forthcoming; Columbia Business School Research Paper No. 12-8. Available at SSRN: https://ssrn.com/abstract=1983308

Omar Besbes (Contact Author)

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Costis Maglaras

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

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