Network flow approaches to pre-emptive open-shop scheduling problems with time-windows

This paper deals with pre-emptive open-shop scheduling problems with time-windows. Network flow procedures to check feasibility and a max-flow parametrical algorithm to minimize the makespan are introduced. Also, computational complexities are evaluated for these feasibility and optimization algorithms. The proposed method is a strongly polynomial algorithm to minimize the makespan of the pre-emptive open-shop scheduling problems with time-windows strictly respected. Finally, the applications of the proposed algorithms are illustrated with numerical examples.