Improved interval indexed formulation based heuristic algorithm for scheduling problem

Scheduling problems in manufacturing systems and industrial engineering are very complex. If the scale of a problem exceeds a certain threshold, the problem is difficult to solve by traditional or formal optimization approaches. In this paper, scheduling problem is modeled with interval indexed formulation. In the model, intervals formation are very important to the efficiency of the algorithm. We proposed two methods for improving the intervals. First method is increasing time limit approach and the second one is long-short time limit approach. We test our algorithm on a kind of NP-hard problem-single machine total weighted tardiness problem. The results give a validation that the approach we presented have promising to be used to some traditional hard problems, especially, to single machine schuduling problem.