Optimal production policy for multi-product with inventory-level-dependent demand in segmented market

Market segmentation has emerged as the primary means by which firms achieve optimal production policy. In this paper, we use market segmentation approach in multi-product inventory system with inventory-level-dependent demand. The objective is to make use of optimal control theory to solve the inventory-production problem and develop an optimal production policy that minimizes the total cost 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 describe a single source production and multi destination inventory and demand problem under the assumption that firm may choose independently the inventory directed to each segment. The optimal control is applied to study and solve the proposed problem.