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Parallel machine scheduling with job assignment restrictions

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  • Celia A. Glass
  • Hans Kellerer

Abstract

In the classical multiprocessor scheduling problem independent jobs must be assigned to parallel, identical machines with the objective of minimizing the makespan. This article explores the effect of assignment restrictions on the jobs for multiprocessor scheduling problems. This means that each job can only be processed on a specific subset of the machines. Particular attention is given to the case of processing times restricted to one of two values, 1 and λ, differing by at most 2. A matching based polynomial time ε‐approximation algorithm is developed that has a performance ratio tending to $2-{1 \over 1+\lambda}$ . This algorithm is shown to have the best possible performance, tending to 3/2, for processing times 1 and 2. For the special case of nested processing sets, i.e., when the sets of machines upon which individual jobs may be assigned are non‐overlapping, the behavior of list scheduling algorithms is explored. Finally, for assignment restrictions determined by just one characteristic of the machines, such as disc storage or memory constraint in the case of high performance computing, we contribute an algorithm that provides a 3/2 worst case bound and runs in time linear in the number of jobs. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007

Suggested Citation

  • Celia A. Glass & Hans Kellerer, 2007. "Parallel machine scheduling with job assignment restrictions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(3), pages 250-257, April.
    • Handle: RePEc:wly:navres:v:54:y:2007:i:3:p:250-257
    DOI: 10.1002/nav.20202
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    Cited by:

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    2. Mallik Angalakudati & Siddharth Balwani & Jorge Calzada & Bikram Chatterjee & Georgia Perakis & Nicolas Raad & Joline Uichanco, 2014. "Business Analytics for Flexible Resource Allocation Under Random Emergencies," Management Science, INFORMS, vol. 60(6), pages 1552-1573, June.
    3. Jinwen Ou & Joseph Y.‐T. Leung & Chung‐Lun Li, 2008. "Scheduling parallel machines with inclusive processing set restrictions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 328-338, June.
    4. Kangbok Lee & Byung‐Cheon Choi & Joseph Y‐T. Leung & Michael L. Pinedo & Dirk Briskorn, 2012. "Minimizing the total weighted delivery time in container transportation scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(3‐4), pages 266-277, April.
    5. Jinwen Ou & Xueling Zhong & Xiangtong Qi, 2016. "Scheduling parallel machines with inclusive processing set restrictions and job rejection," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(8), pages 667-681, December.
    6. Huiqiao Su & Michael Pinedo & Guohua Wan, 2017. "Parallel machine scheduling with eligibility constraints: A composite dispatching rule to minimize total weighted tardiness," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(3), pages 249-267, April.

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