A Relax-and-Solve Algorithm for the Ordered Flow-Shop Scheduling Problem

In the ordered flow-shop scheduling problem the processing times follow specific structures. We propose a relax-and-solve matheuristic for the ordered flow-shop problem to minimize the makespan, which is proven to be NP-hard. We compare the performance of our method and that of the state-of-the-art methods, and show that the proposed method is capable of reporting new best solutions for a large number of instances, and has the average gap of as low as 0.046% from the best known solutions.