Branch-and-Bound Method to solve the Pm, hj1||ΣCi problem

In this paper, we consider the parallel-machine scheduling problem with a maintenance scheduled period on each machine, to minimize the sum of completion times of jobs. We propose a branch-and-bound method to solve this problem. We define a new separation scheme for this method and we compare it with the first scheme that we preconized for this method at the beginning. Dominance properties, upper and lower bounds are described. A performance study, propped up by experimental tests, shows an important reduction of the search space and a better convergence delay by using the new separation scheme