Minimizing tardy jobs in a two-stage hybrid flowshop

We consider the two-stage hybrid flowshop problem with the objective of minimizing the total number of tardy jobs. Since this problem is strongly NP-hard, several heuristic algorithms are developed to find optimal or near optimal schedule for the case when the first stage contains only one machine and the second stage contains m identical parallel machines. Results of computational tests in solving problems up to 100 jobs are reported and directions for future research are provided.