Optimal control of production and marketing systems with distributed time lags

This paper deals with the problem of production and advertising policy for a decaying item whose gradual loss of potential or utility is associated with the passage of time, such as grain, photographic film or electronic components. The delay effects of the advertisement on the sales rate are also considered in the problem. This leads to a control problem where the state equations are represented by integro-differential equations. The objective is to use optimal control theory to determine the production and advertising rates of the decay item which maximize the current value of net profit stream. For the model developed we present a computational procedure of finding the optimal policy and then carry out sensitivity analysis through an example problem. The properties of the optimal solution are discussed for the case of constant rate of delay effect.