Optimal and Near Optimal Control of a Two-Part-Type Stochastic Manufacturing System with Dynamic Setups

This paper deals with a manufacturing system consisting of a single machine subject to random failures and repairs. The machine can produce two types of parts. When the production is switched from one part type to the other a random setup time is incurred at a constant cost rate. The objective is to track the demand, while keeping the work-in-process as close as possible to zero, for both products. The problem is formulated as an optimal stochastic control. The optimal policy is obtained numerically by descretizing the continuous time continuous state optimality conditions using a Markov chain approximation technique. The discretized optimality conditions are shown to correspond to an infinite horizon, discrete time, discrete state dynamic programming problem. The optimal setup policy is shown to have two different structures depending on the parameters of the system. A heuristic policy is proposed to approximate the optimal setup policy. Simulation results show that the heuristic policy is a very good approximation for sufficiently reliable systems