Optimal Control Policy of a Production and Inventory System for Deteriorating Items in Segmented Market

Market segmentation is an essential element of marketing in industrialized countries. Goods can no longer be produced and sold without considering customer needs and recognized the heterogeneity of these needs. In this paper, we use market segmentation approach in single product inventory system with deteriorating items. The objective is to make use of optimal control theory to solve the production –inventory problem and develop an optimal production policy that maximize the total profit associated with inventory and production rate in segmented market. First, we consider a single production and inventory problem with multi-destination demand that vary from segment to segment. Further, we described a single source production –multi destination demand and inventory problem under the assumption that firm may choose independently the inventory directed to each segment. Both the problems are discussed and solved using Pontryagin Maximum principle.