The flexible blocking job shop with transfer and set-up times

The Flexible Blocking Job Shop (FBJS) considered here is a job shop scheduling problem characterized by the availability of alternative machines for each operation and the absence of buffers. The latter implies that a job, after completing an operation, has to remain on the machine until its next operation starts. Additional features are sequence-dependent transfer and set-up times, the first for passing a job from a machine to the next, the second for change-over on a machine from an operation to the next. The objective is to assign machines and schedule the operations in order to minimize the makespan. We give a problem formulation in a disjunctive graph and develop a heuristic local search approach. A feasible neighborhood is constructed, where typically a critical operation is moved (keeping or changing its machine) together with some other operations whose moves are implied. For this purpose, we develop the theoretical framework of job insertion with local flexibility, based on earlier work of Groflin and Klinkert on insertion. A tabu search that consistently generates feasible neighbor solutions is then proposed and tested on a larger test set. Numerical results support the validity of our approach and establish first benchmarks for the FBJS.