Scheduling equal-length jobs with arbitrary sizes on uniform parallel batch machines

We consider the problem of scheduling jobs with equal lengths and arbitrary sizes on uniform parallel batch machines with different capacities. Each machine can only process the jobs whose sizes are not larger than its capacity. Several jobs can be processed as a batch simultaneously on a machine, a...

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Published inOpen mathematics (Warsaw, Poland) Vol. 21; no. 1; pp. 228 - 249
Main Authors Xin, Xiao, Khan, Muhammad Ijaz, Li, Shuguang
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter 28.02.2023
De Gruyter Poland
Subjects
68Q25
90B35
Algorithms
Approximation
equal job lengths
job sizes
makespan
Mathematical analysis
Scheduling
uniform parallel batch machines
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Abstract We consider the problem of scheduling jobs with equal lengths and arbitrary sizes on uniform parallel batch machines with different capacities. Each machine can only process the jobs whose sizes are not larger than its capacity. Several jobs can be processed as a batch simultaneously on a machine, as long as their total size does not exceed the machine’s capacity. The objective is to minimize makespan. Under a divisibility constraint, we obtain two efficient exact algorithms. For the general problem, we obtain an efficient 2-approximation algorithm. Previous work has shown that the problem cannot be approximated to within an approximation ratio better than 2, unless P = NP, even when all machines have identical speeds and capacities.
AbstractList We consider the problem of scheduling jobs with equal lengths and arbitrary sizes on uniform parallel batch machines with different capacities. Each machine can only process the jobs whose sizes are not larger than its capacity. Several jobs can be processed as a batch simultaneously on a machine, as long as their total size does not exceed the machine’s capacity. The objective is to minimize makespan. Under a divisibility constraint, we obtain two efficient exact algorithms. For the general problem, we obtain an efficient 2-approximation algorithm. Previous work has shown that the problem cannot be approximated to within an approximation ratio better than 2, unless P = NP, even when all machines have identical speeds and capacities.
We consider the problem of scheduling jobs with equal lengths and arbitrary sizes on uniform parallel batch machines with different capacities. Each machine can only process the jobs whose sizes are not larger than its capacity. Several jobs can be processed as a batch simultaneously on a machine, as long as their total size does not exceed the machine’s capacity. The objective is to minimize makespan. Under a divisibility constraint, we obtain two efficient exact algorithms. For the general problem, we obtain an efficient 2-approximation algorithm. Previous work has shown that the problem cannot be approximated to within an approximation ratio better than 2, unless P = NP, even when all machines have identical speeds and capacities.
Author Xin, Xiao
Khan, Muhammad Ijaz
Li, Shuguang
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  fullname: Xin, Xiao
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  organization: Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China
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  surname: Li
  fullname: Li, Shuguang
  email: sgliytu@hotmail.com
  organization: College of Computer Science and Technology, Shandong Technology and Business University, Yantai 264005, China
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SubjectTerms 68Q25
90B35
Algorithms
Approximation
equal job lengths
job sizes
makespan
Mathematical analysis
Scheduling
uniform parallel batch machines
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Title Scheduling equal-length jobs with arbitrary sizes on uniform parallel batch machines
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