Two-machine flowshop scheduling to minimize mean flow time under linear deterioration

In many real production situations, jobs take longer times if they start later. This phenomenon is known as deteriorating jobs. In this paper, linear deterioration is discussed in a two-machine flowshop where the objective is to minimize the mean flow time. A branch-and-bound algorithm and several heuristic algorithms are provided to search for the optimal solution and the near-optimal solutions, respectively. Computational results are presented to evaluate the performance of the proposed algorithms. In addition, the impact of the deterioration rate is investigated.