This paper develops an enumeration algorithm for the no-wait flow shop scheduling problem with due date constraints. In this problem, waiting time is not allowed between successive operations of jobs. Plus, each job is accompanied by a due date which is dealt with as a hard constraint. The considered performance criterion is makespan. The problem is strongly NP-hard. In this research, a new modelling approach is developed for the problem. This new modelling technique and the resulting observations are incorporated into a new exact algorithm to solve the problem to optimality. To investigate the performance of the algorithm, a number of test problems are solved and the results are reported. Computational results demonstrate that the developed algorithm is significantly faster than the mathematical models.
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