Single .machine Total Weighted Tardiness with Release Dates Single Machine Total Weighted Tardiness with Release Dates

The single machine total weighted tardiness with release dates problem is known to be strongly NP-hard. With a new lower bounding scheme and a new upper bounding scheme, we get an efficient branch and bound algorithm. In the paper, we first introduce the history of the problem and its computational complexity. Second, the lower bounding schemes and the upper bounding schemes are described in detail. We also present all the dominance rules used in the branch and bound algorithm to solve the problem. In the dominance rules part, we describe the labeling scheme and suggest a data structure for a dominance rule. Finally, we implement the branch and bound algorithm in C++ for the problem with all the techniques introduced above. We present numerical results produced by the program. Using the same instance generating scheme and the test instances from Dr. Jouglet, our results show that this branch and bound method outperforms the previous approaches specialized for the problem.