Minimizing total completion time in a two-machine flowshop with a learning effect

In many situations, a worker's ability improves as a result of repeating the same or similar tasks; this phenomenon is known as the “learning effect”. In this paper, the learning effect is considered in a two-machine flowshop. The objective is to find a sequence that minimizes the total completion time. Several dominance properties and the lower bounds are derived to speed up the elimination process of the branch-and-bound algorithm. A heuristic algorithm is also proposed to overcome the inefficiency of the branch-and-bound algorithm. In the simulation, the proposed heuristic algorithm is shown to perform consistently than the previous one.