The planning of a manufacturing system: a dynamic model

The paper studies a dynamical model of a manufacturing process taking into account: the purchase of raw materials; the scheduling of production; the planning of sales. We particularly deal with the planning of the production rate and of sales. The basic hypotheses are: the orders of each finished product are known over a given period of time T; the inventory levels are the state variables of the process; the control variables are the purchase, productiqn and sale rates. The goal of the ‘controller’ is to determine a policy which allows him to minimize at the time T the ‘capital’. As ‘capital’ we consider both the financial means and the technological resources employed in the process. Bilateral constraints in state and control variables have been introduced in our model. The Maximum Principle has been used to formulate the problem and to obtain a solution.