Lagrangian relaxation-based lower bound for the two-machine flow shop with synchronized periodic maintenance

In this work, we present a Lagrangian relaxation approach to generate a new lower bound for the two-machine flow shop scheduling problem under synchronized and periodic maintenance activities. The word synchronized is used to specify that the maintenance starts at the same time on both machines. The problem is denoted as F2/nr — pm/Cmax. First, we investigate a time-indexed formulation for the problem. Then, a lower bound was proposed using Lagrangian relaxation. Computational study shows satisfactory results.