Lower bounds for smith's rule in stochastic machine scheduling

Authors:
Caroline Jagtenberg;Uwe Schwiegelshohn;Marc Uetz
Affiliations:
Utrecht University, Dept. of Mathematics, Utrecht, The Netherlands;TU Dortmund, Robotics Research Institute, Dortmund, Germany;University of Twente, Dept. of Applied Mathematics, Enschede, The Netherlands
Venue:
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Year:
2010

Citing 6
Cited 1

Worst case bound of an LRF schedule for the mean weighted flow-time problem

SIAM Journal on Computing
Sequencing Tasks with Exponential Service Times to Minimize the Expected Flow Time or Makespan

Journal of the ACM (JACM)
Approximation in stochastic scheduling: the power of LP-based priority policies

Journal of the ACM (JACM)
A PTAS for Minimizing the Total Weighted Completion Time on Identical Parallel Machines

Mathematics of Operations Research
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
When greediness fails: examples from stochastic scheduling

Operations Research Letters

Analysis of computer job control under uncertainty

Journal of Computer and Systems Sciences International

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the problem to minimize the weighted sum of completion times in nonpreemptive parallel machine scheduling. In a landmark paper from 1986, Kawaguchi and Kyan [5] showed that scheduling the jobs according to the WSPT rule -also known as Smith's rule-has a performance guarantee of 1/2 (1 + √2) ≈ 1.207. They also gave an instance to show that this bound is tight. We consider the stochastic variant of this problem in which the processing times are exponentially distributed random variables. We show, somehow counterintuitively, that the performance guarantee of the WSEPT rule, the stochastic analogue of WSPT, is not better than 1.243. This constitutes the first lower bound for WSEPT in this setting, and in particular, it sheds new light on the fundamental differences between deterministic and stochastic scheduling problems.