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Single Machine Scheduling with Rejection: Minimizing Total Weighted Completion Time and Rejection Cost

Single Machine Scheduling with Rejection: Minimizing Total Weighted Completion Time and Rejection Cost

Atefeh Moghaddam, Lionel Amodeo, Farouk Yalaoui, Behrooz Karimi
Copyright: © 2012 |Volume: 3 |Issue: 2 |Pages: 20
ISSN: 1942-3594|EISSN: 1942-3608|EISBN13: 9781466610729|DOI: 10.4018/jaec.2012040103
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MLA

Moghaddam, Atefeh, et al. "Single Machine Scheduling with Rejection: Minimizing Total Weighted Completion Time and Rejection Cost." IJAEC vol.3, no.2 2012: pp.42-61. http://doi.org/10.4018/jaec.2012040103

APA

Moghaddam, A., Amodeo, L., Yalaoui, F., & Karimi, B. (2012). Single Machine Scheduling with Rejection: Minimizing Total Weighted Completion Time and Rejection Cost. International Journal of Applied Evolutionary Computation (IJAEC), 3(2), 42-61. http://doi.org/10.4018/jaec.2012040103

Chicago

Moghaddam, Atefeh, et al. "Single Machine Scheduling with Rejection: Minimizing Total Weighted Completion Time and Rejection Cost," International Journal of Applied Evolutionary Computation (IJAEC) 3, no.2: 42-61. http://doi.org/10.4018/jaec.2012040103

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Abstract

In this paper, the authors consider a single machine scheduling problem with rejection. In traditional research, it is assumed all jobs must be processed. However, in the real-world situation, certain jobs can be rejected. In this study, the jobs can be either accepted and scheduled or be rejected at the cost of a penalty. Two objective functions are considered simultaneously: (1) minimization of the sum of weighted completion times for the accepted jobs, and (2) minimization of the sum of penalties for the rejected jobs. The authors apply two-phase method (TPM), which is a general technique to solve bi-objective combinatorial optimization problems, to find all supported and non-supported solutions for small-sized problems. The authors present a mathematical model for implementing both phases. On the other hand, three different bi-objective simulated annealing algorithms have also been developed to find a good estimation of Pareto-optimal solutions for large-sized problems. Finally the authors discuss the results obtained from each of these algorithms.

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