Efficient meta-heuristics based on various dominance criteria for a single-machine bi-criteria scheduling problem with rejection

•A bi-objective single machine production scheduling problem with rejection has been studied.•Different efficient meta-heuristics have been developed.•Various dominance concepts such as Lorenz, S-CDAS and modified S-CDAS have been coupled with GA and SA.•Improving algorithms’ efficiency by defining new dominance concept has been shown.•Many real manufacturing systems with limited machine capacity and out-sourcing can be modeled by the studied configuration.

In this paper, we try to fill in the gap between theory and practice in production scheduling by defining a new term as “rejection” and treating the corresponding scheduling problem with multi-objective optimization approach. We study a bi-objective single machine scheduling problem with rejection. At the beginning of scheduling time horizon, scheduler needs to decide which job shall be rejected due to the resource constraints regarding two objective functions: minimization of total weighted completion time of accepted jobs and total rejection penalty of rejected jobs. We develop different algorithms to find the best estimation of Pareto-optimal front for this problem. In order to improve the quality of the solutions, on the one hand, and facilitate the process of selecting best solution for the final decision maker, on the other hand, we integrate various dominance criteria into our proposed algorithms. Finally we compare the performance of those methods by testing on a large set of instances and highlight the advantages and weak points of each one.