On-line scheduling in the presence of overload
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Speed is as powerful as clairvoyance
Journal of the ACM (JACM)
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
How to schedule when you have to buy your energy
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Energy-efficient due date scheduling
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
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We consider several online scheduling problems that arise when customers request make-to-order products from a company. At the time of the order, the company must quote a due date to the customer. To satisfy the customer, the company must produce the good by the due date. The company must have an online algorithm with two components: The first component sets the due dates, and the second component schedules the resulting jobs with the goal of meeting the due dates. The most basic quality of service measure for a job is the quoted lead time, which is the difference between the due date and the release time. We first consider the basic problem of minimizing the average quoted lead time. We show that there is a (1 + ε)-speed O(log k/ε)-competitive algorithm for this problem (here k is the ratio of the maximum work of a job to the minimum work of a job), and that this algorithm is essentially optimally competitive. This result extends to the case that each job has a weight and the objective is weighted quoted lead time. We then introduce the following general setting: there is a nonincreasing profit function pi(t) associated with each job Ji. If the customer for job Ji is quoted a due date of di, then the profit obtained from completing this job by its due date is pi(di). We consider the objective of maximizing profits. We show that if the company must finish each job by its due date, then there is no O(1)-speed poly-log-competitive algorithm. However, if the company can miss the due date of a job, at the cost of forgoing the profits from that job, then we show that there is a (1+ ε)-speed O(1 + 1/ε)-competitive algorithm, and that this algorithm is essentially optimally competitive.