SCHEDULING WITH RELEASE TIMES AND DEADLINES ON A MINIMUM NUMBER OF MACHINES

摘要

In this paper we study the SRDM problem motivated by a variety of practical applications. We are given n jobs with integer release times, deadlines, and processing times. The goal is to find a non-preemptive schedule such that all jobs meet their deadlines and the number of machines needed to process all jobs is minimum. If all jobs have equal release times and equal deadlines, SRDM is the classical bin packing problem, which is NP-complete. The slack of a job is the difference between its release time and the last possible time it may be started while still meeting its deadline. We show that instances consisting of jobs with slack at most one can be solved efficiently. We close the resulting gap by showing that the problem already becomes NP-complete if slacks up to 2 are allowed. Additionally, we consider several variants of the SRDM problem and provide exact and approximation algorithms.