On three-machine flow shop scheduling with deteriorating jobs

In this paper, we consider a three-machine permutation flow shop scheduling problem under simple linear deterioration. By a simple linear deterioration function, we mean that the processing time of a job is a simple linear function of its execution start time. The objective is to find a sequence that minimizes makespan. This problem is well known NP-hard. Optimal schedules are obtained for some special cases. For the general case, several dominance properties and two lower bounds are derived to speed up the elimination process of a branch-and-bound algorithm. Moreover, a heuristic algorithm is proposed to overcome the inefficiency of the branch-and-bound algorithm. Computational experiments on randomly generated problems is conducted to evaluate the branch-and-bound algorithm and heuristic algorithm. The analysis shows that the proposed heuristic algorithm performs effectively and efficiently.