Single‐machine scheduling to minimize maximumtardiness with minimum number of tardy jobs

Abstract

This paper develops a branch and bound algorithm for solving the single‐machine schedulingproblem with the objective of minimizing the maximum tardiness of any job, subjectto the constraint that the total number of tardy jobs is minimum. The algorithm uses a newlower bounding scheme, which is based on due date relaxation. Various dominance rules areused in the algorithm to limit the size of the search tree. Results of extensive computationaltests show that the proposed branch and bound algorithm is effective in solving problemswith up to 1000 jobs.