Optimizing Supply Chain Coordination through Cross-Functional Integration: A Dynamic Model Using Optimal Control Theory

Abstract

This paper is concerned with the cross-functional coordination of certain internal and external processes in a supply chain to balance supply with customer demand. Activities need to be synchronized in order to avoid issues such as delays in delivery and unnecessary inventory of raw material or of finished products. This can be achieved by integrating the purchasing, logistics, and production processes together. We propose a dynamic model and employ optimal control theory to obtain the optimal raw material supply rate, the optimal transfer rate of the raw material for production, and the optimal production rate. Some managerial insights are obtained through numerical examples and sensitivity analyses. Among the insights gained is that the approach is well suited for medium to long range planning horizon, when raw material and end product deterioration are high, and when the initial gaps between the inventory levels and their respective goals are the smallest.