Makespan Minimization on Three-Machine Flow shop with deteriorating jobs

In this study, we consider a permutation flow shop scheduling problem on a three-machine with deteriorating jobs (a deteriorating job means that the job’s processing time is an increasing function of its starting time) so as to minimize the makespan. We model job deterioration as a function that is proportional to a linear function of time. For some special cases, we prove that the problem can be solved in polynomial time. We develop branch-and-bound and heuristic procedures for the general case. Computational experiments for the branch-and-bound algorithm and heuristic algorithm are presented.