Single-machine scheduling with trade-off between number of tardy jobs and compression cost

We consider a single-machine scheduling problem, in which the job processing times are controllable or compressible. The performance criteria are the compression cost and the number of tardy jobs. For the problem, where no tardy jobs are allowed and the objective is to minimize the total compression...

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Bibliographic Details
Published in:Journal of scheduling Vol. 10; no. 4-5; pp. 303 - 310
Main Authors: He, Yong, Wei, Qi, Cheng, T. C. E.
Format: Journal Article
Language:English
Published: New York Springer Nature B.V 01.10.2007
Subjects:
Algorithms
Costs
Employment
Job shops
Linear programming
Scheduling
Studies
ISSN:1094-6136, 1099-1425
Online Access:Get full text
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Summary:We consider a single-machine scheduling problem, in which the job processing times are controllable or compressible. The performance criteria are the compression cost and the number of tardy jobs. For the problem, where no tardy jobs are allowed and the objective is to minimize the total compression cost, we present a strongly polynomial time algorithm. For the problem to construct the trade-off curve between the number of tardy jobs and the maximum compression cost, we present a polynomial time algorithm. Furthermore, we extend the problem to the case of discrete controllable processing times, where the processing time of a job can only take one of several given discrete values. We show that even some special cases of the discrete controllable version with the objective of minimizing the total compression cost are NP-hard, but the general case is solvable in pseudo-polynomial time. Moreover, we present a strongly polynomial time algorithm to construct the trade-off curve between the number of tardy jobs and the maximum compression cost for the discrete controllable version. [PUBLICATION ABSTRACT]
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ISSN:1094-6136
1099-1425
DOI:10.1007/s10951-007-0027-7