A BB&R algorithm for minimizing total tardiness on a single machine with sequence dependent setup times

This paper presents a Branch, Bound, and Remember (BB&R) exact algorithm using the Cyclic Best First Search (CBFS) exploration strategy for solving the ${1|ST_{sd}|\sum T_{i}}$ scheduling problem, a single machine scheduling problem with sequence dependent setup times where the objective is to find a schedule with minimum total tardiness. The BB&R algorithm incorporates memory-based dominance rules to reduce the solution search space. The algorithm creates schedules in the reverse direction for problems where fewer than half the jobs are expected to be tardy. In addition, a branch and bound algorithm is used to efficiently compute tighter lower bounds for the problem. This paper also presents a counterexample for a previously reported exact algorithm in Luo and Chu (Appl Math Comput 183(1):575–588, 2006) and Luo et?al. (Int J Prod Res 44(17):3367–3378, 2006). Computational experiments demonstrate that the algorithm is two orders of magnitude faster than the fastest exact algorithm that has appeared in the literature. Computational experiments on two sets of benchmark problems demonstrate that the CBFS search exploration strategy can be used as an effective heuristic on problems that are too large to solve to optimality.