On the optimal number of machines operated by a single worker

An optimal design problem is considered for man-machine systems, where a group of numerically controlled (NC) machines is operated by a single worker. The processing time at each machine and the service time by the worker are assumed to be random variables. The decision variable is the number of machines in the group and the optimal criterion is to minimize the cost for producing a product. It is found that the minimum-cost number of machines, N_c, is the lower bound on the optimal numbers of machines under other important criteria. We present the upper and lower bounds on N_cs for the systems where the coefficients of variations of the service- and processing-time distributions are less than 1. Moreover, it is shown that the bounds are tight for such systems.