An improved Lagrangian relaxation approach for solving job shop scheduling problems

An approach to the job shop scheduling problem that uses an auxiliary problem formulation to reduce solution oscillation is presented. A demonstration using actual factory data shows that the auxiliary formulation can generate near-optimal schedules in reasonable computation time and can provide a lower bound to evaluate schedule quality. In the auxiliary problem formulation, quadratic penalties are directly included in the objective function for the purpose of restricting operation movement in the time horizon. This is necessary since operation precedence constraints often lead to solution oscillation from iteration to iteration in the relaxed problem. Although solution oscillation is not completely eliminated, results indicate that the auxiliary objective function reduces the magnitude of solution oscillation, making an augmented Lagrangian approach unnecessary. In addition, the relaxed problem is directly decomposed into operation-level subproblems