The minimization of resource costs in scheduling independent tasks with fixed completion time

Abstract

We consider the problem of scheduling a set of independent tasks within a given time limit in order to minimize the cost of required resources. Tasks have different processing times and are non-preemptable (i.e. cannot be interrupted and restarted later). Each task requires a set of dedicated processors and some additional resources of different costs simultaneously available for its processing. Given a fixed set of processors and unlimited resources availability, the problem is to find the minimum resource cost schedule respecting the time constraint. We study this problem by means of a graph model which represents compatibilities between tasks, as that of finding the optimal reduction to an interval graph. Results show that dominant schedules correspond to a family of graphs which is contained in the constraints structure of the problem. Structural properties of the problem are discussed and solution algorithms are proposed.