Optimal control of a revenue management system with dynamic pricing facing linear demand

被引:21
作者
Chou, Fee-Seng
Parlar, Mahmut [1 ]
机构
[1] McMaster Univ, DeGroote Sch Business, Hamilton, ON L8S 4M4, Canada
[2] Natl Univ Singapore, Dept Decis Sci, Singapore 117591, Singapore
关键词
optimal control; quadratic programming; dynamic pricing; revenue management;
D O I
10.1002/oca.785
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
This paper considers a dynamic pricing problem over a finite horizon where demand for a product is a time-varying linear function of price. It is assumed that at the start of the horizon there is a fixed amount of the product available. The decision problem is to determine the optimal price at each time period in order to maximize the total revenue generated from the sale of the product. In order to obtain structural results we formulate the decision problem as an optimal control problem and solve it using Pontryagin's principle. For those problems which are not easily solvable when formulated as an optimal control problem, we present a simple convergent algorithm based on Pontryagin's principle that involves solving a sequence of very small quadratic programming (QP) problems. We also consider the case where the initial inventory of the product is a decision variable. We then analyse the two-product version of the problem where the linear demand functions are defined in the sense of Bertrand and we again solve the problem using Pontryagin's principle. A special case of the optimal control problem is solved by transforming it into a linear complementarity problem. For the two-product problem we again present a simple algorithm that involves solving a sequence of small QP problems and also consider the case where the initial inventory levels are decision variables. Copyright (C) 2006 John Wiley & Sons, Ltd.
引用
收藏
页码:323 / 347
页数:25
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