Variable neighborhood search for the single machine scheduling problem to minimize the total early work

In this paper, the single machine scheduling problem to minimize the total early work is studied. The aim of this problem is to minimize the total amount of processing performed on the jobs before their due dates. We have proposed a better implementation of the existing dynamic programming method and thus solved large problems in an exact way. In particular, we can currently resolve instances of sizes 10,000 exactly instead of 200 with a pseudo-polynomial dynamic programming algorithm. Since the considered problem was proven to be NP-hard, a heuristic based on the Variable Neighborhood Search (VNS) method is proposed to solve larger instances. Computational experiments show that both methods are efficient.