A mixed integer programming approach for the single machine problem with unequal release dates

In this paper, we consider the problem of scheduling on a one-machine, a set of operations subject to unequal release dates with respect to the total completion time. This problem is known to be NPNP-hard in the strong sense. We propose an algorithm based on a Mixed Integer Linear Programming. This algorithm includes the implementation of a preprocessing procedure together with the consideration of valid inequalities. A computer simulation to measure the performance of the algorithm shows that our proposed method outperforms state-of-the-art branch-and-bound algorithms.