A theoretical development for the total tardiness problem and its application in branch and bound algorithms

This paper deals with the single machine total tardiness problem, and proves that if the job sequences produced by two heuristics, named as Time Forward and Time Backward algorithms, have the same starting and ending job subsequences, then there exists an optimal job sequence with the starting and ending job subsequences. The computation experiments show that there is a significant improvement of the running time of a branch and bound algorithm with the incorporation of the new property.