Steady State Solution of Optimal Production Control of a Dynamic Four-Product Manufacturing System with Setup Costs and Setup Time

Abstract

The steady state solution of optimal control of a one-machine four-product manufacturing system with setup changes, operating in a continuous time dynamic environment is considered here. The system is deterministic. When production is switched from one product to the other, a known constant setup time and a setup cost are incurred. Each product 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 aim is to minimize the total backlog, inventory and setup 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).