The two-machine flowshop total completion time problem: Improved lower bounds and a branch-and-bound algorithm

This paper presents a branch-and-bound algorithm for the two-machine flowshop scheduling problem with the objective of minimizing the sum of completion times. The main feature of the branch-and-bound algorithm is a new lower bounding scheme that is based on a network formulation of the problem. With extensive computational tests, we demonstrate that the branch-and-bound algorithm can solve problems with up to 60 (45) jobs, where processing times are uniformly distributed in the [1, 10] ([1, 100]) range.