OPTIMAL PRODUCTION AND SETUP CONTROL OF A DYNAMIC 2-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 ti me 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 tim e and constant demand rate, as well as an infinite supply of raw mater ial. The problem is formulated as a feedback control problem. The obje ctive is to minimize the sum total of backlog and inventory costs incu rred 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, th e optimal cyclic schedule is determined. To solve the transient case, the system's state space is partitioned into mutually exclusive region s, such that, with each region the optimal control policy is determine d analytically.