A Preemptive Single-machine Scheduling Problem with Controllable Processing Times and a Late Work Criterion

In classical scheduling problems, jobs are usually assumed to be non-preemptive with constant processing times. In many practical cases, however, restrictions on preemption can be released by outsourcing and the job processing times are controllable by allocating additional resources to the job operations. In this paper, we consider a single-machine scheduling problem with preemption such that each job processing time can be reduced linearly by using additional resource. The objective is to minimize the sum of total late work and total compression cost. We show that the problem can be solved in polynomial time.