The problem considered in this article is a generalization of the familiar makespan problem, in which n jobs are allocated among m parallel processors, so as to minimize the maximum time (or cost) on any processor. The present problem is more general, in that the authors allow the processors to have (a) different initial costs, (b) different utilization levels before new costs are incurred, and (c) different rates of cost increase. A heuristic adapted from the bin-packing problem is shown to provide solutions which are close to optimal as the number of iterations is allowed to increase. Computational testing, over a large number of randomly generated problem instances, suggests that heuristic errors are, on average, very small.
