Optimization of production planning problem with continuously distributed time-lags

This paper considers a production and inventory problem in which the utility or potential of an item gradually reduces with the passage of time, such as grain, photographic film and electronic component. The aim of this paper is to determine the production rate of the decaying item in a way that minimizes the current value of total cost using optimal control theory. For the model developed, a computational procedure of finding an optimal solution is developed. The steady-state solution and the properties of the optimal solution for the case of constant rate of decay are discussed.