Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan
We consider the problem of scheduling n deteriorating jobs with release dates on a single batching machine. Each job’s processing time is an increasing simple linear function of its starting time. The machine can process up to b jobs simultaneously as a batch. The objective is to minimize the maximu...
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| Veröffentlicht in: | European journal of operational research Jg. 210; H. 3; S. 482 - 488 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Amsterdam
Elsevier B.V
01.05.2011
Elsevier Elsevier Sequoia S.A |
| Schriftenreihe: | European Journal of Operational Research |
| Schlagworte: | |
| ISSN: | 0377-2217, 1872-6860 |
| Online-Zugang: | Volltext |
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| Abstract | We consider the problem of scheduling
n deteriorating jobs with release dates on a single batching machine. Each job’s processing time is an increasing simple linear function of its starting time. The machine can process up to
b jobs simultaneously as a batch. The objective is to minimize the maximum completion time, i.e., makespan. For the unbounded model, i.e.,
b
=
∞, we obtain an
O(
n
log
n) dynamic programming algorithm. For the bounded model, i.e.,
b
<
n, we first show that the problem is binary NP-hard even if there are only two distinct release dates. Then we present
O(
nb) and
O((
nb/
h)
h
) algorithms for the case where the job processing order is predetermined in advance and for the case where there are
h,
h
⩾
2, distinct deteriorating rates, respectively. Furthermore, we provide a fully polynomial-time approximation scheme for the case where the number of distinct release dates is a constant. |
|---|---|
| AbstractList | We consider the problem of scheduling
n deteriorating jobs with release dates on a single batching machine. Each job’s processing time is an increasing simple linear function of its starting time. The machine can process up to
b jobs simultaneously as a batch. The objective is to minimize the maximum completion time, i.e., makespan. For the unbounded model, i.e.,
b
=
∞, we obtain an
O(
n
log
n) dynamic programming algorithm. For the bounded model, i.e.,
b
<
n, we first show that the problem is binary NP-hard even if there are only two distinct release dates. Then we present
O(
nb) and
O((
nb/
h)
h
) algorithms for the case where the job processing order is predetermined in advance and for the case where there are
h,
h
⩾
2, distinct deteriorating rates, respectively. Furthermore, we provide a fully polynomial-time approximation scheme for the case where the number of distinct release dates is a constant. We consider the problem of scheduling n deteriorating jobs with release dates on a single batching machine. Each job's processing time is an increasing simple linear function of its starting time. The machine can process up to b jobs simultaneously as a batch. The objective is to minimize the maximum completion time, i.e., makespan. For the unbounded model, i.e., b = [infinity], we obtain an O(n log n) dynamic programming algorithm. For the bounded model, i.e., b < n, we first show that the problem is binary NP-hard even if there are only two distinct release dates. Then we present O(nb) and O((nb/h)h) algorithms for the case where the job processing order is predetermined in advance and for the case where there are h, h [greater-or-equal, slanted] 2, distinct deteriorating rates, respectively. Furthermore, we provide a fully polynomial-time approximation scheme for the case where the number of distinct release dates is a constant. We consider the problem of scheduling n deteriorating jobs with release dates on a single batching machine. Each job's processing time is an increasing simple linear function of its starting time. The machine can process up to b jobs simultaneously as a batch. The objective is to minimize the maximum completion time, i.e., makespan. For the unbounded model, i.e., b = [infinity], we obtain an O(n log n) dynamic programming algorithm. For the bounded model, i.e., b < n, we first show that the problem is binary NP-hard even if there are only two distinct release dates. Then we present O(nb) and O((nb/h) super()h algorithms for the case where the job processing order is predetermined in advance and for the case where there are h, h [inline image] 2, distinct deteriorating rates, respectively. Furthermore, we provide a fully polynomial-time approximation scheme for the case where the number of distinct release dates is a constant. We consider the problem of scheduling n deteriorating jobs with release dates on a single batching machine. Each job's processing time is an increasing simple linear function of its starting time. The machine can process up to b jobs simultaneously as a batch. The objective is to minimize the maximum completion time, i.e., makespan. For the unbounded model, i.e., b = ∞, we obtain an O(n log n) dynamic programming algorithm. For the bounded model, i.e., b < n, we first show that the problem is binary NP-hard even if there are only two distinct release dates. Then we present O(nb) and O((nb/h)^h) algorithms for the case where the job processing order is predetermined in advance and for the case where there are h, h ≥ 2, distinct deteriorating rates, respectively. Furthermore, we provide a fully polynomial-time approximation scheme for the case where the number of distinct release dates is a constant. [PUBLICATION ABSTRACT] |
| Author | Yuan, Jinjiang Cheng, T.C.E. Li, Shisheng Ng, C.T. |
| Author_xml | – sequence: 1 givenname: Shisheng surname: Li fullname: Li, Shisheng organization: Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, People’s Republic of China – sequence: 2 givenname: C.T. surname: Ng fullname: Ng, C.T. email: lgtctng@polyu.edu.hk organization: Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People’s Republic of China – sequence: 3 givenname: T.C.E. surname: Cheng fullname: Cheng, T.C.E. organization: Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People’s Republic of China – sequence: 4 givenname: Jinjiang surname: Yuan fullname: Yuan, Jinjiang organization: Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, People’s Republic of China |
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| Keywords | Batching Scheduling Dynamic programming Release dates Deterioration Task scheduling Processing time Makespan Approximation algorithm Modeling Batch scheduling Workload Batchwise NP hard problem Batch process Batch production Single machine Completion time Execution time |
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n deteriorating jobs with release dates on a single batching machine. Each job’s processing time is an increasing simple... We consider the problem of scheduling n deteriorating jobs with release dates on a single batching machine. Each job's processing time is an increasing simple... |
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| SubjectTerms | Algorithms Applied sciences Approximation Batching Deterioration Dynamic programming Exact sciences and technology Infinity Inventory control, production control. Distribution Job shops Mathematical analysis Mathematical models Mathematical programming Operational research Operational research and scientific management Operational research. Management science Optimization algorithms Production scheduling Release dates Scheduling Scheduling Batching Deterioration Release dates Dynamic programming Scheduling, sequencing Studies |
| Title | Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan |
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