Effective neighbourhood functions for the flexible job shop problem

The flexible job shop problem is an extension of the classical job shop scheduling problem which allows an operation to be performed by one machine out of a set of machines. The problem is to assign each operation to a machine (routing problem) and to order the operations on the machines (sequencing problem), such that the maximal completion time (makespan) of all operations is minimized. To solve the flexible job shop problem approximately, we use local search techniques and present two neighbourhood functions (Nopt1, Nopt2). Nopt2 is proved to be optimum connected. Nopt1 does not distinguish between routing or sequencing an operation. In both cases, a neighbour of a solution is obtained by moving an operation which affects the makespan. Our main contribution is a reduction of the set of possible neighbours to a subset for which it can be proved that it always contains the neighbour with the lowest makespan. An efficent approach to compute such a subset of feasible neighbours is presented. A tabu search procedure is proposed and an extensive computational study is provided. We show that our procedure outperforms previous approaches.