Single machine total tardiness problem: exact and heuristic algorithms based on Beta-sequence and decomposition theorems

The primary concern of this thesis is to analyze single machine total tardiness problem and to develop both an exact algorithm and a heuristic algorithm. The analysis of the literature reveals that exact algorithms are limited to 100 jobs. We enlarge this limit considerably by basing our algorithms on the ¡3- Sequence and decomposition theorems from the recent literature. With our algorithm, we exactly solve 200 job problems in low CPU time, and we also solved 120 out of 160 test problems with 500 jobs. In addition we develop a heuristic based on our exact algorithm which results in optimum solutions in 30% of test problems and stays with 9% of the optimal in all test runs.