The two-machine flowshop scheduling problems with total tardiness

This paper considers the criterion of minimizing total job tardiness in the two-machine flowshop system. The conditions that determine which of a pair of adjacent jobs in a sequence should precede the other to minimize total job tardiness are derived. A branch-and-bound solution procedure to reach an optimal solution to the problem is developed. A simple and computationally efficient heuristic is also presented. Moreover, an illustrative example together with the computational characteristics of the algorithm and the heuristic is provided.