In the two-machine no-wait flowshop scheduling problem, a quick algorithm for makespan minimization and its
complexity are presented. The properties of the permutation schedule in the two-machine no-wait flowshop are analyzed. It
is proved that the feasible solutions of the two-machine no-wait flowshop scheduling problem must exist in the permutation
schedules, and the optimal solution of the two-machine no-wait flowshop scheduling problem can be found in permutation
schedules. Finally, the complexity of the two-machine flowshop scheduling problem with both regular jobs and no-wait jobs
is studied, and provide the theoretical base for further exploring the two machine no-wait flowshop scheduling problem.