A series-type multistage production system with random demand

We propose a mathematical model which considers the series-type product structure with n−1 predecessors. Our objective is to obtain the optimal production functions, in the planning horizon [0,T], based on the assumptions (1) that the cost of production unit is a linear function of production quantity in a time unit, (2) that sales of finished goods occur at the end of planning horizon, and (3) that product demand is a random variable. Then the phenomenon of optimal solution is discussed.