The continuous assignment problem and its application to preemptive and non-preemptive scheduling with irregular cost functions
Résumé
This paper focuses on the continuous assignment problem with the eventual aim to solve scheduling problems with irregular cost functions. It consists of partitioning a region of Rd into subregions of prescribed volumes so that the total cost is minimized. The dual problem of the continuous assignment problem is an unconstrained maximization 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.