A branch-and-bound algorithm for solving a two-machine flow shop problem with deteriorating jobs

In this paper we consider a two-machine flow shop scheduling problem with deteriorating jobs. By a deteriorating job we mean that the job's processing time is an increasing function of its starting time. We model job deterioration as a function that is proportional to a linear function of time. The objective is to find a sequence that minimizes the total completion time of the jobs. For the general case, we derive several dominance properties, some lower bounds, and an initial upper bound by using a heuristic algorithm, and apply them to speed up the elimination process of a branch-and-bound algorithm developed to solve the problem.