Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher.
Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?
Some links on this page may take you to nonfederal websites. Their policies may differ from this site.

null (Ed.)Abstract We consider a natural generalization of classical scheduling problems to a setting in which using a time unit for processing a job causes some timedependent cost, the timeofuse tariff, which must be paid in addition to the standard scheduling cost. We focus on preemptive singlemachine scheduling and two classical scheduling cost functions, the sum of (weighted) completion times and the maximum completion time, that is, the makespan. While these problems are easy to solve in the classical scheduling setting, they are considerably more complex when timeofuse tariffs must be considered. We contribute optimal polynomialtime algorithms and best possible approximation algorithms. For the problem of minimizing the total (weighted) completion time on a single machine, we present a polynomialtime algorithm that computes for any given sequence of jobs an optimal schedule, i.e., the optimal set of time slots to be used for preemptively scheduling jobs according to the given sequence. This result is based on dynamic programming using a subtle analysis of the structure of optimal solutions and a potential function argument. With this algorithm, we solve the unweighted problem optimally in polynomial time. For the more general problem, in which jobs may have individual weights, we develop a polynomialtime approximation scheme (PTAS) based on a dual scheduling approach introduced for scheduling on a machine of varying speed. As the weighted problem is strongly NPhard, our PTAS is the best possible approximation we can hope for. For preemptive scheduling to minimize the makespan, we show that there is a comparably simple optimal algorithm with polynomial running time. This is true even in a certain generalized model with unrelated machines.more » « less

Abstract We study a fundamental online job admission problem where jobs with deadlines arrive online over time at their release dates, and the task is to determine a preemptive singleserver schedule which maximizes the number of jobs that complete on time. To circumvent known impossibility results, we make a standard slackness assumption by which the feasible time window for scheduling a job is at least $$1+\varepsilon $$ 1 + ε times its processing time, for some $$\varepsilon >0$$ ε > 0 . We quantify the impact that different provider commitment requirements have on the performance of online algorithms. Our main contribution is one universal algorithmic framework for online job admission both with and without commitments. Without commitment, our algorithm with a competitive ratio of $$\mathcal {O}(1/\varepsilon )$$ O ( 1 / ε ) is the best possible (deterministic) for this problem. For commitment models, we give the first nontrivial performance bounds. If the commitment decisions must be made before a job’s slack becomes less than a $$\delta $$ δ fraction of its size, we prove a competitive ratio of $$\mathcal {O}(\varepsilon /((\varepsilon \delta )\delta ^2))$$ O ( ε / ( ( ε  δ ) δ 2 ) ) , for $$0<\delta <\varepsilon $$ 0 < δ < ε . When a provider must commit upon starting a job, our bound is $$\mathcal {O}(1/\varepsilon ^2)$$ O ( 1 / ε 2 ) . Finally, we observe that for scheduling with commitment the restriction to the “unweighted” throughput model is essential; if jobs have individual weights, we rule out competitive deterministic algorithms.more » « less