Integrated Capacity Planning and Production Control of an Assembly Manufacturing System

For an assembly manufacturing system, its capacity planning problem and production control problem are usually considered separately. However, production capacity cannot exert its maximum productivity without employing optimal production control; and optimal production control may not satisfy the demand without sufficient production capacity. Therefore, it is important to jointly optimize capacity planning and production control. First, the mathematical formulation of integrated production control and capacity planning problem for an assembly manufacturing system with multiple upstream production lines and one downstream assembly line is proposed in this paper. Second, we develop a method to obtain the marginal probability distribution of the inventory level in the assembly system, which can be employed to calculate the average production cost under an approximate optimal production control policy. Since optimal control policy is subject to production capacity (i.e., machine number), we employ the integer programming method to optimize the machine number (i.e., production capacity), which consequently influences the control policy. Numerical experiments are conducted to verify the correctness of the method of calculating steady-state probability distribution, and the effectiveness of the algorithm of integrated optimization of production control and production capacity.