Asymptotic analysis of manufacturing systems

A manufacturing facility is considered in which there are m identical machines that are equally capable of producing n distinct part types. The production must be scheduled to meet a deterministic demand. However, the machines are subject to a Markovian breakdown and repair process. The paper simplifies the problem by using the hierarchical structure that is inherent in this model. Thus, it is assumed that the time scale in which the machine breakdown and repair process is occurring is much shorter than the time scale in which the costs are being evaluated. That is, both the holding cost function and the discount rate are small, and the demand is nearly constant. A general limiting procedure is presented for manufacturing systems in the presence of an hierarchy between the time scales of certain events. This procedure is described in an example with two parts and two machines. Also, a convergence rate is obtained for a simpler problem