A joint dynamic pricing and advertising model of perishable products

Abstract

Advertising and dynamic pricing play key roles in maximizing profit of a firm. In this paper a joint dynamic pricing and advertising problem for perishable products is investigated, where the time-varying demand rate is decreasing in sales price and increasing in goodwill. A dynamic optimization model is proposed to maximize total profit by setting a joint pricing and advertising policy under the constraint of a limited advertising capacity. By solving the dynamic optimization problem on the basis of Pontryagin’s maximum principle, the analytical solutions of the optimal joint dynamic pricing and advertising policy are obtained. Additionally, to highlight the advantage of the joint dynamic strategy, the case of the optimal advertising with static pricing policy is considered. Numerical examples are presented to illustrate the validness of the theoretical results, and some managerial implications for the pricing and advertising of the perishable products are provided.

Keywords:

• perishable products
• advertising
• dynamic pricing
• pontryagin’s maximum principle

Acknowledgements

This work was supported by the National Nature Science Foundation of China Nos. 61473204, 71371133 and the Program for New Century Excellent Talents in Universities of China (NCET-11-0377), and China Scholarship Council.