Polynomial time approximation schemes for general multiprocessor job shop scheduling

We study preemptive and non-preemptive versions of the general multiprocessor job shop scheduling problem: Given a set of n tasks each consisting of at most μ ordered operations that can be processed on different (possibly all) subsets of m machines with different processing times, compute a schedul...

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Bibliographic Details
Published in:Journal of algorithms Vol. 45; no. 2; pp. 167 - 191
Main Authors: Jansen, Klaus, Porkolab, Lorant
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 01.11.2002
Elsevier
Subjects:
Applied sciences
Computer science; control theory; systems
Computer systems performance. Reliability
Exact sciences and technology
Operational research and scientific management
Operational research. Management science
Scheduling, sequencing
Software
Polynomial
Minimum
Scheme
Polynomial approximation
Job shop
Processing time
Process
Makespan
Approximation algorithm
Machine
Result
Numerical approximation
Multiprocessor
Accuracy
Development
Shift
Order
Linear programming
Scheduling
Algorithm
Flow
Polynomial time
Optimal solution
Schedule
Models
Problem
ISSN:0196-6774, 1090-2678
Online Access:Get full text
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Summary:We study preemptive and non-preemptive versions of the general multiprocessor job shop scheduling problem: Given a set of n tasks each consisting of at most μ ordered operations that can be processed on different (possibly all) subsets of m machines with different processing times, compute a schedule (preemptive or non-preemptive, depending on the model) with minimum makespan where operations belonging to the same task have to be scheduled according to the specified order. We propose algorithms for both preemptive and non-preemptive variants of this problem that compute approximate solutions of any positive ϵ accuracy and run in O( n) time for any fixed values of m, μ, and  ϵ. These results include (as special cases) many recent developments on polynomial time approximation schemes for scheduling jobs on unrelated machines, multiprocessor tasks, and classical open, flow and job shops.
ISSN:0196-6774
1090-2678
DOI:10.1016/S0196-6774(02)00248-1