A branch-and-bound algorithm for minimising the number of tardy jobs in a two-machine flow-shop problem with release dates

This article considers the two-machine flow-shop scheduling problem with the objective of minimising the number of tardy jobs in which jobs have release dates. Since the problem under consideration is an NP-hard problem, a branch-and-bound (B&B) algorithm is viable to solve the problem exactly. A heuristic algorithm as an upper bound, some lower bounds and several efficient dominance properties are used to speed up the elimination process of the B&B algorithm. For the evaluation of the performance of the proposed algorithm, computational experiments are performed on test problems and results are displayed. The experimental results show that the proposed B&B algorithm can solve problems with up to 28 jobs in timely manner, and the average percentage gap of the heuristic solutions is about 10%.