Scheduling of Unit-time Jobs with Distinct Due Windows on Parallel Processors

Abstract

Problems of scheduling n unit-time jobs on m identical parallel processors are studied, in which for each job a distinct due window is given in advance. If a job is completed within its due window, then it incurs no penalty. Otherwise, it incurs a job-dependent earliness or tardiness cost. For the problem in which earliness and tardiness costs depend on the distance between job completion time and the due window, the objective is to find a job schedule such that a sum or maximum of weighted costs associated with earliness and tardiness is minimized. For the problem with distance-independent costs, the objective is to find a schedule such that the total weighted number of early and tardy jobs is minimized. Properties of optimal solutions of these problems are established. It is proved that these problems can be reduced to min-sum and min-max assignment problems solvable in time O(n4).