Scheduling on identical machines : how good is LPT in an on-line setting?

We consider a parallel machine scheduling problem where jobs arrive over time. A set of independent jobs has to be scheduled on m identical machines, where preemption is not allowed and the number of jobs is unknown in advance. Each job becomes available at its release date, which is not known in advance, and its processing time becomes known at its arrival. We deal with the problem of minimizing the makespan, which is the time by which all jobs have been finished. We propose and analyze the following on-line algorithm: At any time a machine becomes availabe for processing, schedule an available job with the largest processing time. We prove that this algorithm has a performance guarantee of , and that this bound is tight. Furthermore, we show that any on-line algorithm will have a performance bound of at least 1.3473. This bound is improved to (5 - v5)/2˜1.3820 for M = 2

On-line scheduling of two-machine open shops where jobs arrive over time

We investigate the problem of on-line scheduling two-machine open shops with the objective of minimizing the makespan.Jobs arrive independently over time, and the existence of a job is not known until its arrival. In the clairvoyant on-line model, the processing requirement of every job becomes fully known at the arrival of the job, while inthe non-clairvoyant on-line model, this processing requirement is notknown until the job is processed and completed.In both models, scheduling of a job is irrevocable. We study the two-machine open shop problem for both models in the preemptive and in the non-preemptive version. For each of the four variants, we provide an algorithm that is best possible with respect to the worst-case performance. In the clairvoyant on-line model, the best worst-case performance ratios are 5/4 (preemptive) and 3/2 (non-preemptive), and in the non-clairvoyant on-line model, they are 3/2 (preemptive and non-preemptive)

Multiprocessor Jobs, Preemptive Schedules, and One-Competitive Online Algorithms

We study online preemptive makespan minimization on m parallel machines, where the (multiprocessor) jobs arrive over time and have widths from some fixed set W ¿ {1,2,…,m}. For every number m of machines we concisely characterize all the sets W for which there is a 1-competitive fully online algorithm and all the sets W for which there is a 1-competitive nearly online algorithm

Combinatorial Online Optimization in Real Time

Optimization is the task of finding an optimum solution to a given problem. When the decision variables are discrete we speak of a combinatorial optimization problem. Such a problem is online when decisions have to be made before all data of the problem are known. And we speak of a real-time online problem when online decisions have to be computed within very tight time bounds. This paper surveys the are of combinatorial online and real-time optimization, it discusses, in particular, the concepts with which online and real-time algorithms can be analyzed