Minimizing maximum tardiness and number of tardy jobs on parallel machines subject to minimum flow-time

This paper considers the problems of scheduling jobs on parallel identical machines where an optimal schedule is defined as one that gives the smallest maximum tardiness (or the minimum number of tardy jobs) among the set of schedules with optimal total flow-time (the sum of the completion times of all jobs). We show that these problems are unary NP-Hard, develop lower bounds for these two secondary criteria problems, and describe heuristic algorithms for their solution. Results of a computational study show that the proposed heuristic algorithms are quite effective and efficient in solving these hierarchical criteria scheduling problems.