Online Bi-Criteria Scheduling on Batch Machines with Machine Costs
We consider online scheduling with bi-criteria on parallel batch machines, where the batch capacity is unbounded. In this paper, online means that jobs’ arrival is over time. The objective is to minimize the maximum machine cost subject to the makespan being at its minimum. In unbounded parallel bat...
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| Published in | Mathematics (Basel) Vol. 7; no. 10; p. 960 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Basel
MDPI AG
01.10.2019
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| ISSN | 2227-7390 2227-7390 |
| DOI | 10.3390/math7100960 |
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| Abstract | We consider online scheduling with bi-criteria on parallel batch machines, where the batch capacity is unbounded. In this paper, online means that jobs’ arrival is over time. The objective is to minimize the maximum machine cost subject to the makespan being at its minimum. In unbounded parallel batch scheduling, a machine can process several jobs simultaneously as a batch. The processing time of a job and a batch is equal to 1. When job J j is processed on machine M i , it results cost c i j . We only consider two types of cost functions: c i j = a + c j and c i j = a · c j , where a is the fixed cost of machines and c j is the cost of job J j . The number of jobs is n and the number of machines is m. For this problem, we provide two online algorithms, which are showed to be the best possible with a competitive ratio of ( 1 + β m , ⌈ n m ⌉ ) , where β m is the positive root of the equation ( 1 + β m ) m + 1 = β m + 2 . |
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| AbstractList | We consider online scheduling with bi-criteria on parallel batch machines, where the batch capacity is unbounded. In this paper, online means that jobs’ arrival is over time. The objective is to minimize the maximum machine cost subject to the makespan being at its minimum. In unbounded parallel batch scheduling, a machine can process several jobs simultaneously as a batch. The processing time of a job and a batch is equal to 1. When job J j is processed on machine M i , it results cost c i j . We only consider two types of cost functions: c i j = a + c j and c i j = a · c j , where a is the fixed cost of machines and c j is the cost of job J j . The number of jobs is n and the number of machines is m. For this problem, we provide two online algorithms, which are showed to be the best possible with a competitive ratio of ( 1 + β m , ⌈ n m ⌉ ) , where β m is the positive root of the equation ( 1 + β m ) m + 1 = β m + 2 . We consider online scheduling with bi-criteria on parallel batch machines, where the batch capacity is unbounded. In this paper, online means that jobs’ arrival is over time. The objective is to minimize the maximum machine cost subject to the makespan being at its minimum. In unbounded parallel batch scheduling, a machine can process several jobs simultaneously as a batch. The processing time of a job and a batch is equal to 1. When job Jj is processed on machine Mi, it results cost cij. We only consider two types of cost functions: cij=a+cj and cij=a·cj, where a is the fixed cost of machines and cj is the cost of job Jj. The number of jobs is n and the number of machines is m. For this problem, we provide two online algorithms, which are showed to be the best possible with a competitive ratio of (1+βm,⌈nm⌉), where βm is the positive root of the equation (1+βm)m+1=βm+2. |
| Author | Chai, Xing Zhai, Weina Li, Wenhua |
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| Cites_doi | 10.1016/j.ipl.2009.08.008 10.1007/s10878-010-9298-6 10.1080/002075499192020 10.1007/s10878-017-0211-4 10.1080/07408170304378 10.1016/S0166-218X(00)00181-5 10.1080/07408179408966627 10.1016/j.ijpe.2014.07.027 10.1142/S021759591550030X 10.1007/s40305-014-0060-0 10.1080/07408179208964233 10.1080/00207720903428906 10.1007/s10878-015-9918-2 10.1002/(SICI)1099-1425(199806)1:1<31::AID-JOS4>3.0.CO;2-R 10.1007/s10878-007-9070-8 10.1016/j.ejor.2014.03.026 10.1007/s10951-009-0154-4 |
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| Snippet | We consider online scheduling with bi-criteria on parallel batch machines, where the batch capacity is unbounded. In this paper, online means that jobs’... We consider online scheduling with bi-criteria on parallel batch machines, where the batch capacity is unbounded. In this paper, online means that jobs'... |
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| SubjectTerms | Algorithms bi-criteria scheduling Competition competitive ratio Computer aided scheduling Cost function Costs Criteria Food science makespan maximum machine cost online algorithm Ratios Scheduling |
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| Title | Online Bi-Criteria Scheduling on Batch Machines with Machine Costs |
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