The no-wait flowshop scheduling problem with hard due date constraints is critical to operations in many industries, such as plastic, chemical, and pharmaceutical manufacturing. However, to date, there is a lack of effective optimization algorithms for this NP-hard problem. This paper develops a new mixed integer linear programming (MILP) model and a two-phase enumeration algorithm to improve the best-so-far exact methods for solving this problem with the objective of minimizing the makespan. A comprehensive computational experiment is performed to compare the performances of the discussed exact methods. The computational results demonstrate that the proposed MILP model and the two-phase enumeration algorithm significantly outperform the best-so-far optimization methods, and the (sub-) optimal solutions to several unsolved instances from the literature are reported.