Batch scheduling of simple linear deteriorating jobs on a single machine to minimize makespan

We consider a scheduling problem in which n jobs are to be processed on a single machine. The jobs are processed in batches and the processing time of each job is a simple linear function of its waiting time, i.e., the time between the start of the processing of the batch to which the job belongs an...

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Bibliographic Details
Published in:European journal of operational research Vol. 202; no. 1; pp. 90 - 98
Main Authors: Ji, Min, Cheng, T.C.E.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.04.2010
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
Applied sciences
Approximation
Batch scheduling
Batch scheduling Makespan Computational complexity FPTAS
Computational complexity
Dynamic programming
Exact sciences and technology
FPTAS
Inventory control, production control. Distribution
Job shops
Linear programming
Makespan
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization algorithms
Production scheduling
Queuing theory. Traffic theory
Scheduling, sequencing
Studies
Makespan
FPTAS
Batch scheduling
Computational complexity
Growth rate
Optimal algorithm
Polynomial approximation
Linear time
Processing time
Approximation algorithm
Batch processing
Waiting time
Precedence constraint
Polynomial time
Minimum time
Deterioration
NP hard problem
Batch process
Batch production
Dynamic programming
Single machine
Completion time
Execution time
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:We consider a scheduling problem in which n jobs are to be processed on a single machine. The jobs are processed in batches and the processing time of each job is a simple linear function of its waiting time, i.e., the time between the start of the processing of the batch to which the job belongs and the start of the processing of the job. The objective is to minimize the makespan, i.e., the completion time of the last job. We first show that the problem is strongly NP-hard. Then we show that, if the number of batches is B, the problem remains strongly NP-hard when B ⩽ U for a variable U ⩾ 2 or B ⩾ U for any constant U ⩾ 2 . For the case of B ⩽ U , we present a dynamic programming algorithm that runs in pseudo-polynomial time and a fully polynomial time approximation scheme (FPTAS) for any constant U ⩾ 2 . Furthermore, we provide an optimal linear time algorithm for the special case where the jobs are subject to a linear precedence constraint, which subsumes the case where all the job growth rates are equal.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2009.05.021