Online unbounded batch scheduling on parallel machines with delivery times

We consider the online unbounded batch scheduling problems on m identical machines subject to release dates and delivery times. Jobs arrive over time and the characteristics of jobs are unknown until their arrival times. Jobs can be processed in a common batch and the batch capacity is unbounded. On...

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Published inJournal of combinatorial optimization Vol. 29; no. 1; pp. 228 - 236
Main Authors Liu, Peihai, Lu, Xiwen
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.01.2015
Subjects
Combinatorics
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Delivery times
Scheduling
Online algorithm
Competitive ratio
Batch machines
Online AccessGet full text
ISSN1382-6905
1573-2886
DOI10.1007/s10878-014-9706-4

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Abstract We consider the online unbounded batch scheduling problems on m identical machines subject to release dates and delivery times. Jobs arrive over time and the characteristics of jobs are unknown until their arrival times. Jobs can be processed in a common batch and the batch capacity is unbounded. Once the processing of a job is completed it is independently delivered to the destination. The objective is to minimize the time by which all jobs have been delivered. For each job J j , its processing time and delivery time are denoted by p j and q j , respectively. We first consider a restricted model: the jobs have agreeable processing and delivery times, i.e., for any two jobs J i and J j p i > p j implies q i ≥ q j . For the restrict case, we provide a best possible online algorithm with competitive ratio 1 + α m , where α m > 0 is determined by α m 2 + m α m = 1 . Then we present an online algorithm with a competitive ratio of 1 + 2 / ⌊ m ⌋ for the general case.
AbstractList We consider the online unbounded batch scheduling problems on m identical machines subject to release dates and delivery times. Jobs arrive over time and the characteristics of jobs are unknown until their arrival times. Jobs can be processed in a common batch and the batch capacity is unbounded. Once the processing of a job is completed it is independently delivered to the destination. The objective is to minimize the time by which all jobs have been delivered. For each job J j , its processing time and delivery time are denoted by p j and q j , respectively. We first consider a restricted model: the jobs have agreeable processing and delivery times, i.e., for any two jobs J i and J j p i > p j implies q i ≥ q j . For the restrict case, we provide a best possible online algorithm with competitive ratio 1 + α m , where α m > 0 is determined by α m 2 + m α m = 1 . Then we present an online algorithm with a competitive ratio of 1 + 2 / ⌊ m ⌋ for the general case.
Author Liu, Peihai
Lu, Xiwen
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Issue 1
Keywords Delivery times
Scheduling
Online algorithm
Competitive ratio
Batch machines
Language English
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Snippet We consider the online unbounded batch scheduling problems on m identical machines subject to release dates and delivery times. Jobs arrive over time and the...
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SubjectTerms Combinatorics
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Title Online unbounded batch scheduling on parallel machines with delivery times
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