Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14567
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Main Title: Approximation in stochastic scheduling: The power of LP-based priority policies
Author(s): Möhring, Rolf H.
Schulz, Andreas S.
Uetz, Marc
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15794
http://dx.doi.org/10.14279/depositonce-14567
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: We consider the problem to minimize the total weighted completion time of a set of jobs with individual release dates which have to be scheduled on identical parallel machines. Job processing times are not known in advance, they are realized on-line according to given probability distributions. The aim is to find a scheduling policy that minimizes the objective in expectation. Motivated by the success of LP-based approaches to deterministic scheduling, we present a polyhedral relaxation of the performance space of stochastic parallel machine scheduling. This relaxation extends earlier relaxations that have been used, among others, by Hall, Schulz, Shmoys, and Wein (1997) in the deterministic setting. We then derive constant performance guarantees for priority policies which are guided by optimum LP solutions, and thereby generalize previous results from deterministic scheduling. In the absence of release dates, the LP-based analysis also yields an additive performance guarantee for the WSEPT rule which implies both a worst-case performance ratio and a result on its asymptotic optimality, thus complementing previous work by Weiss (1990). The corresponding LP lower bound generalizes a previous lower bound from deterministic scheduling due to Eastman, Even, and Isaacs (1964), and exhibits a relation between parallel machine problems and corresponding problems with only one fast single machine. Finally, we show that all employed LPs can be solved in polynomial time by purely combinatorial algorithms.
Subject(s): stochastic scheduling
approximation
worst-case performance
priority policy
LP-relaxation
WSEPT rule
asymptotic optimality
Issue Date: 1998
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 1998, 595
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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