Mixed-model assembly line scheduling using the Lagrangian relaxation technique

The increasing market demand for product variety forces manufacturers to design mixed-model assembly lines on which different product models can be switched back and forth and mixed together with little changeover costs. This paper describes the design and implementation of an optimization-based scheduling algorithm for mixed-model compressor assembly lines at Toshiba with complicated component supply requirements. A separable integer optimization formulation is obtained by treating compressor lots going through a properly balanced line as undergoing a single operation, and the scheduling goal is to delivery products just in time while avoiding possible component shortage. The problem is solved by using Lagrangian Relaxation (LR). Several generic defects of LR leading to slow algorithm convergence are identified based on geometrical insights, and are overcome by perturbing/changing problem parameters. Numerical testing shows that nearoptimal schedules are efficiently obtained, convergence is significantly improved, and the method is effective for practical problems. The system is currently under deployment at Toshiba.