Scheduling jobs to minimize total cost

The problem of preemptively scheduling a set of independent jobs with release times and deadlines to a set of parallel identical processors is a well-known scheduling problem. In this paper, we extend this famous problem by adding the consideration that the processing requirement of each job is not a fixed quantity but is a linear function of cost. We assume that the more cost we pay, the less processing requirement there is. Under this new assumption, our goal is to use the minimum cost to complete all jobs subject to their processing conditions. Two polynomial algorithms are developed for this new variant of scheduling problem.