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 d dimensional region 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.
INFORMS Journal on Computing 16(2). p198-208. 2004