Hierarchical Production and Setup Scheduling in Stochastic Manufacturing Systems

This paper is concerned with an asymptotic analysis of hierarchical production and setup scheduling in a stochastic manufacturing system consisting of a single failure-prone machine and facing constant demands for a number of products. At any given time the system can only produce one type of product, and the system requires a stop if production is to be switched from one type of product to another. A setup may involve setup time or setup cost or both. The objective of the problem is to minimize the total costs of setup, production, and surplus. The control variables are a sequence of setups and a production plan. An asymptotic analysis with respect to increasing rates of change in machine states gives rise to a deterministic limiting optimal control problem in which there is a control variable associated with each of the machine states and the production rate is obtain by weighting these controls with the stationary probabilities of the corresponding states. It is shown that the value function for the original problem converges to the value function of the limiting problem. Asymptotic optimal controls for the original problem from optimal or near-optimal controls for the limiting problem are constructed. A simple illustrative example is provided