Minimizing total completion time in a two-machine flow shop with deteriorating jobs

This paper considers a two-machine flow shop scheduling problem with deteriorating jobs. By a deteriorating job, we mean that the processing time of a job is an increasing function of its execution start time. A simple linear deterioration function is assumed. The objective is to find a sequence that minimizes total completion time. Optimal solutions 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. A heuristic algorithm is also proposed to overcome the inefficiency of the branch-and-bound algorithm. Computational results show that the proposed heuristic algorithm performs effectively and efficiently.