Lagrangian relaxation for complex job shop scheduling

Market competition forces manufactures to schedule their resources efficiently for on-time order delivery and low inventory. However, for companies such as textile and steel-making companies, optimizing schedules is difficult because of the NP-hard nature of the problem and the complex product structures: assemblies, disassemblies and couplings across orders. To address the difficulties, this paper extends the Lagrangian relaxation approach through selectively relaxing precedence constraints. The solution oscillation is identified and alleviated by adding auxiliary penalty and by nonlinear approximation. Furthermore, the normalized surrogate subgradient method is developed to accelerate the convergence of Lagrangian multipliers to obtain good solutions in computational efficient manner. Testing results demonstrate that better schedules are obtained when solution oscillation is alleviated. The newly developed normalized method significantly improves traditional methods