On the efficiency of imbalance in a class of manufacturing systems

In this paper, the problem of simultaneously allocating servers and loadings of stations in a class of manufacturing systems modelled as network of queues is considered. The throughput function of the closed network of queues is demonstrated as a Schur convex function of server allocation, that is, increasing the server allocation vector under majorization increases the performance in the shop in terms of the throughput. It also reduces the congestion in the open network of queues in terms of reducing the total number of jobs in the sense of likelihood ratio ordering. These are the extensions of the numerical result of Green and Guha in the service system with independent M/M/c systems to the network of queues. The results can be used to support production planning in certain manufacturing systems. [In Korean.]