Heuristical methods for the relaxed two-dimensional rectangle scheduling problem

We are dealing with a problem of one-resource-constrained scheduling: How can a number of n tasks be distributed on the time-interval [0, m] so that the maximum of the amount of the resource used be minimum. There are two special cases: the scheduling of identical parallel machines, and the bin-packing problem. We apply two earlier methods and introduce a new heuristics. Upper bounds and numerical aspects are also investigated. The results show that in many cases the new method is better than the previously existing ones.