¹University of Southampton, Southampton, UK

Correspondence: RCH Cheng, School of Mathematics, University of Southampton, Southampton S053 4TT, UK. E-mails: christine.currie@soton.ac.uk, r.c.h.cheng@maths.soton.ac.uk

Received February 2006; Accepted March 2007; Published online 23 May 2007.

Abstract

Competition has a huge influence on customer buying behaviour and will impact on the optimal price that companies should charge for goods or services. To date, many dynamic pricing models have not modelled competition explicitly. In this paper, we introduce pricing strategies that maximize revenue when selling an inventory of identical items by a fixed time and where there is a competing seller. The model used incorporates a probabilistic formulation of customer demand, which is influenced by the prices offered by the company and the competitor, and the time remaining until the end of the selling period. Calculus of variations is used to solve the problem and simple conditions are given that ensure the uniqueness of a solution. Illustrative examples are included. A practical implementation that uses dynamic updating is proposed and tested using simulated data, showing the effectiveness of the method.