https://hal-utt.archives-ouvertes.fr/hal-02507770Moghaddam, AtefehAtefehMoghaddamLOSI - Laboratoire d'Optimisation des Systèmes Industriels - ICD - Institut Charles Delaunay - UTT - Université de Technologie de Troyes - CNRS - Centre National de la Recherche ScientifiqueAmodeo, LionelLionelAmodeoLOSI - Laboratoire d'Optimisation des Systèmes Industriels - ICD - Institut Charles Delaunay - UTT - Université de Technologie de Troyes - CNRS - Centre National de la Recherche ScientifiqueYalaoui, FaroukFaroukYalaouiLOSI - Laboratoire d'Optimisation des Systèmes Industriels - ICD - Institut Charles Delaunay - UTT - Université de Technologie de Troyes - CNRS - Centre National de la Recherche ScientifiqueKarimi, BehroozBehroozKarimiAUT - Amirkabir University of TechnologySingle Machine Scheduling with Rejection: Minimizing Total Weighted Completion Time and Rejection CostHAL CCSD2012[INFO.INFO-RO] Computer Science [cs]/Operations Research [cs.RO][MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Gavrysiak, Daniel2020-03-13 15:02:222022-06-26 01:39:002020-03-13 15:02:22enJournal articles10.4018/jaec.20120401031In 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.