Bicriteria scheduling to minimize total late work and maximum tardiness with preemption

Abstract

We consider single-machine bicriteria scheduling of n jobs with preemption to minimize the total late work and maximum tardiness. Given the earliest due date order of the jobs in advance, we present an O(n)-time algorithm for the hierarchical scheduling problem and an O(nlogn)-time algorithm for the constrained scheduling problem. For the Pareto-scheduling problem, when all the processing times and due dates are integral, we construct the trade-off curve in O(nlognP) time, where P is the total processing time of the jobs.