Optimal production and setup control of a dynamic two-product manufacturing system: Analytical solution

This paper deals with the optimal control of a one-machine two-product manufacturing system with setup changes, operating in a continuous time dynamic environment. The system is deterministic. A known constant setup time is incurred when production is switched from one product to the other. Each product or part has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a feedback control problem. The objective is to minimize the sum total of backlog and inventory costs incurred over a finite horizon. The optimal solution provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels). For the steady state, the optimal cyclic schedule is determined. To solve the transient case, the systemʹs state space is partitioned into mutually exclusive regions, such that, with each region the optimal control policy is determined analytically.