Consider the problem Fm||Cmax. Assume that the schedule does allow one job to pass another while they are waiting for processing on a machine.
(a) Show that there always exists an optimal schedule that does not require sequence changes between machines 1 and 2 and between machines m − 1 and m. (Hint: By contradiction. Suppose the optimal schedule requires a sequence change between machines 1 and 2. Modify the schedule in such a way that there is no sequence change and the makespan remains the same.)
Please provide a theoretical proof, not a numerical example