The Continuous Assignment Problem and Its Application to Preemptive and Non-Preemptive Scheduling with Irregular Cost Functions

It is with the aim of solving scheduling problems with irregular cost functions that this paper focuses on the continuous assignment problem. It consists in partitioning a region of R into subregions of prescribed volumes so that the total cost is minimized. The dual problem of the continuous assignment problem is an unconstrained maximisation of a non-smooth concave function. The preemptive variant of the scheduling problem with irregular cost functions corresponds to the one-dimensional continuous assignment problem and a lower bound for the non-preemptive variant can be derived. It is computationally tested in a branch-and-bound algorithm.