Job-shop scheduling with processing alternatives

In this paper we study an extension of the job-shop scheduling problem where the job routings are directed acyclic graphs that can model partial orders of operations and that contain sets of alternative subgraphs consisting of several operations each. We develop two heuristic algorithms for our problem: a tabu search and a genetic algorithm. The two heuristics are based on two common subroutines: one to insert a set of operations into a partial schedule and another to improve a schedule with fixed routing alternatives. The first subroutine relies on an efficient operation insertion technique and the second one is a generalisation of standard methods for classical job-shop scheduling. We compare our heuristics on various test problems, including the special case MPM job-shop scheduling. Moreover, we report on the success of the two subroutines on open-shop instances.