Chen & Chen  constructed the production planning model that was based on three assumptions: (1) the demand occurs in the future time and is a random variable, (2) there are two stages in the production process, (3) the unit production cost is a linear function of production in the unit time. Then, the optimal production rates is derived so as to maximize the profit.
The aim of this article is to extend the model under (1) the leadtime between the production process is considered, (2) the object is cost minimization. And then, the phenomenon of optimal solution is discussed.
Journal of statistics & management systems 2(1), pp.23-40