Branch-and-bound and simulated annealing algorithms for a two-agent scheduling problem

We consider a two-agent scheduling problem on a two-machine flowshop setting, where the objective is to minimize the total tardiness of the first agent with the restriction that the number of tardy jobs of the second agent is zero. It is reported in the literature that the complexity of even two-machine flowshop problem, where both agents wish to complete their jobs as soon as possible, is shown NP-hard. Motivated by the limitation and suggestions, this paper proposes a branch-and-bound algorithm and a simulated annealing heuristic algorithm to search for the optimal solution and near-optimal solutions, respectively. Computational results are also presented to evaluate the performance of the proposed algorithms.