Scheduling one-part-type serial manufacturing system under periodic demand: a solvable case

The paper studies one-part type, multiple-stage production system with periodic demands. A buffer of infinite capacity is placed after each machine. Inventory flow through buffers is controlled by machine production rates. The objective is to find a cyclic production rate, which minimizes all inventory-related expenses over an infinite planning horizon. With the aid of the maximum principle, optimal production policies are derived and the continuous-time scheduling problem is reduced to a discrete timing problem. As a result, a polynomial-time algorithm is suggested to calculate the optimal production rate. A numerical example is used to illustrate the algorithm.