Optimal Control Policy to Production and Inventory System with Promotion Effort Dependent Demand in Segmented Market

Abstract

With the increase in competition in the market, it becomes imperative for the interaction between marketing and production of a firm in the segmented market. This paper considers the problem of finding an optimal promotion and production strategy, where the consumer demand rate depends on dffierentiated and mass promotion efforts. Differentiated promotions can reach each segment independently and mass promotion reaches with a fixed segment-spectrum. Under reasonable conditions, two optimal control problems are formulated. The first one considers a single source inventory and multi-segmented demand problem. In the second, a multi-segmented inventory and demand problem is considered where it is assumed that the firm chooses an inventory directed to each segment. The solution to both problems is obtained by using Pontryagin's maximum principle. Numerical examples are provided to illustrate the applicability of proposed problems. The discretized version of the problem is formulated and solved with some numeric data.