On the optimal control of a manufacturing firm

Abstract

Various existing models of the optimal control of production rates of manufacturing firms are discussed. A new model is derived by considering the combined effects of: the inventory level of the firm, the shipment sent from the firm, the shipment rate, the Orders received by the firm, the demand rate, the rate of change of the demand rate, the production rate, the advertising expenditure, and the level of unfilled Orders. Further, a new version of shortage cost is introduced. The well-known Pontryagin maximum principle and transversality condition are used to obtain the optimal production rate and the optimal advertising expenditure. A numerical example is given for Illustration.