Optimal Configurations of General Job Shops

In this paper we study the problem of minimizing the expected number of jobs in a single class general open queueing network model of a job shop. This problem was originally posed by Buzacott and Shanthikumar [2] and solved by them for a special case. We extend their work in this paper. We derive feasibility conditions that simplify the analysis of the problem. We show that the optimal configuration can be completely characterized when both the utilizations of the machine centers are high and there are a large number of servers at each machine center. We also derive conditions under which the optimization problem reduces to solving a concave or a convex program and provide conditions under which the uniform flow line and the symmetric job shop (or variants of these) are optimal configurations for the job shop.