Online scheduling of weighted equal-length jobs with hard deadlines on parallel machines

We consider the problem of scheduling a maximum profit selection of equal length jobs on m identical machines. Jobs arrive online over time and the goal is to determine a non-preemptive schedule which maximizes the total profit of the scheduled jobs. Let the common processing requirement of the jobs be p > 0. For each job ji, i = 1, . . . , n we are given a release time ri (at which the job becomes known) and a deadline ri + p+ δi. If the job is scheduled and completed before the deadline, a profit of wi is earned. Upon arrival of a new job, an online algorithm must decide whether to accept the job or not. In case of acceptance, the online algorithms must provide a feasible starting date for the job. Competitive analysis has become a standard way of measuring the quality of online algorithms. For a maximization problem, an online algorithm is called ccompetitive, if on every input instance it achieves at least a 1/c-fraction of the optimal (“offline”) profit. We give lower bounds for the competitivity of online algorithms and propose algorithms which match this lower bound up to a constant factor.