Generation of Production Cycles in Multiple Server Systems with Setup Times: The Case Study

The paper deals with the standard fluid model of multiproduct multiple-server production system where both setup times and costs are incurred whenever the server changes product. The ultimate objective is to minimize the long-run average cost per unit time. The paper follows the general approach to this problem that suggests to first determine optimal steady state system behavior and then to design a scheduling policy ensuring convergence to this steady state as time progresses. The second part of this program is treated. We propose a novel Puancare-type approach to generation of required production cycles in manufacturing systems. The approach is based on a new criterion for stability of equilibria of discrete-time invariant systems. Along with general discussion, a detailed presentation of the proposed method is given with respect to the popular model of a reentrant manufacturing system proposed by Kumar and Seidman.