A new Lagrangian Relaxation based method to improve schedule quality

Lagrangian Relaxation (LR) bas been used for manufacturing scheduling with good results. For practical applications, the method, however, may suffer from slow convergence, and may not be able to generate good results within a required CPU time. To improve convergence and solution quality, a new augmented LR method is presented in this paper where additional penalty terms associated with constraint violation is added to the objective function. To overcome the inseparability difficulty caused by the penalty term, a surrogate subgradient direction is used to update the multipliers and to guarantee solvability and convergence. Numerical testing results demonstrate that compared with the standard LR method, the augmented LR method is computationally efficient, and generates good schedules with reduced cost.