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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Bibliographic Details
Published in:European journal of operational research Vol. 210; no. 3; pp. 482 - 488
Main Authors: Li, Shisheng, Ng, C.T., Cheng, T.C.E., Yuan, Jinjiang
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.05.2011
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
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
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
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary: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.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2010.11.021