A new lower bound for minimising the total completion time in a two-machine flow shop under release dates

In this paper, we describe a mixed integer linear programming (MILP) formulation used to model the two-machine flow shop scheduling problem subject to release dates. This MILP formulation is based on the Positional and Assignment Variables(PAVF). The results of the linear relaxation bound derived from the later mathematical formulation shows the performance of this new bound compared with the best known lower bound recently presented for the studied problem.