Computer-aided formulation and optimal control of an integrated production system for competitive products

An integrated production, inventory and advertising system has been formulated based on control engineering principles. In this system, the customer's demand is satisfied from stock, which in turn is replenished from production facilities. But sales reflect the advertising effort, present as well as past. The past effort has been considered as a delay with an assumed delay period. The problem is formulated as a state and observation model. Out of this an augmented model of state and parameters is formed. The parameters describing the model are estimated from MAP discrete filter algorithm. It is shown that sales of product 1 or product 2 at (k + l)th period is effected by sales and advertising of product 1 or product 2 at the kth period, and also by sales and advertising of product 2 or product 1 at (k-θ)th period, where 6 is the delay.