The analysis of optimal control model in matching problem between manufacturing and marketing

A mathematical model is developed and presented to solve the optimal control problem in matching between manufacturing and marketing when the market demand possesses the property of linearity. The main purpose of this paper is to investigate the optimal choice between production rate which may affect the inventory level and the optimal sales rate at each time through different pricing strategies so as to achieve the maximum profit for a given planning horizon. The results demonstrated that the relative size of the output yielded by minimizing average cost and yielded by maximizing profit at constant-zero inventory can determine the optimal production rate and sales rate. Furthermore, the optimal inventory policy can be determined to be a constant-zero inventory policy or constant-positive inventory policy, or mixed inventory policy, according to the value of optimal production rate.