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 setup 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 costs of setup, production, and surplus. The decision 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 problem in which the machine´s stochastic availability is replaced by its equilibrium mean availability. Methods of constructing asymptotic optimal decisions for the original problem from optimal or near-optimal decisions for the limiting problem are given