Optimal Scheduling of a Flexible Manufacturing System: A Stochastic Control Problem for a System with Jump Markov Disturbances

摘要

Consider a Flexible Manufacturing System (FMS) which consists of m machines, and manufactures p part types. Suppose that each part requires unit of time at each machine. Suppose now that each machine jumps from a working state to a failed state, and back to a working state, according to a continuous time, finite state, Markov Chain, and that all machines do so independently. Then the entire FMS also behaves as a finite state Markov Chain with states F1,F2, ...,F2m. Let (qij) be the transition rates. Suppose now that there is a constant demand rate vector for the various parts. Then x sub i denotes the inventory of the part types, it is our goal is to keep x close to zero.