An Optimal control approach to marketing‐production planning

The problem of finding an optimal advertising and production policy in a firm is analysed using a recently proposed model of a marketing-production system and it is shown that the optimal control problem underlying the proposed model is a partially singular control problem.

Abstract

Abstract The problem of finding an optimal advertising and production policy in a firm is analysed using a recently proposed model of a marketing‐production system. First, it is shown that the optimal control problem underlying the proposed model is a partially singular control problem. Then, a reverse‐time parametric solution procedure is designed to determine the optimal advertising and production policy for the proposed model. Finally, it is shown that the results derived from the new model are applicable to problems of capacity expansion in a firm.