Three-machine shop scheduling with partially ordered processing routes

This paper considers the problem of sequencing n jobs in a three-machine shop with the objective of minimising the maximum completion time. The shop consists of three machines, M-1, M-2, and M-3. A job is first processed on M-1 and then is assigned either the route (M-2, M-3) or the route (M-3, M-2). Thus, for our model the processing route is given by a partial order of machines, as opposed to the linear order of machines for a job shop, or to an arbitrary sequence of machines for an open shop. The main result is on O(n log n) time heuristic, which generates a schedule with the makespan that is at most 5/3 times the optimum value.