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

Atefeh Moghaddam, Lionel Amodeo, Farouk Yalaoui and Behrooz Karimi
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Atefeh Moghaddam: University of Technology of Troyes, France
Lionel Amodeo: University of Technology of Troyes, France
Farouk Yalaoui: University of Technology of Troyes, France
Behrooz Karimi: Amirkabir University of Technology, Iran

International Journal of Applied Evolutionary Computation (IJAEC), 2012, vol. 3, issue 2, 42-61

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:igg:jaec00:v:3:y:2012:i:2:p:42-61

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