A two-machine flowshop maximum tardiness scheduling problem with a learning effect

The primary objective of this paper is to study a two-machine flowshop scheduling problem with a learning effect where the goal is to find a sequence that minimizes the maximum tardiness. We employ a branch-and-bound method and a simulated annealing (SA) method to search for the optimal solution and a near-optimal solution, respectively. Computational results, using Fisher's (Math Program 11:229-251 1971) framework, show that the mean and maximum number of nodes for the branch-and-bound algorithm decrease when the learning effect is stronger, the value of the tardiness factor is smaller, or the value of the due date range is larger. In addition, comparisons between the SA method and the earliest due date first (EDD) rule are provided for large-job sizes. Results indicate that the percentage of time that the SA solution outperforms the EDD solution decreases as the job size increases and the learning effect becomes greater. Additionally, the SA solution is never worse than the EDD solution.