Two machine flow shop scheduling problem with no wait in process: Controllable machine speeds

The paper considers a two machine flow shop scheduling problem with no wait in process. The objective is to find the optimal values of machine speeds and to determine the time-optimal schedule. There are two machines, A and B, and a set of n jobs each consisting of two operations. The first operation of each job is to be processed on machine A and the second on machine B. For each feasible schedule, the second operation of each job starts at the same time the first operation of this job is completed (the no wait condition). Machine speeds are supposed to be controllable and should be selected in order to minimize a certain penalty function. The objective function depends on both profits resulting from the reduction of the makespan and expenditures for increasing the machine speeds. An O(n³) algorithm is described to solve the problem.