A Lagrangian relaxation approach to the mixed-product assembly line sequencing problem: A case study of a door-lock company in Taiwan

In mixed-product assembly line sequencing, the production resources required for the assembly lines should be scheduled to minimize the overall cost and meet customer demand. In this paper, we study an assembly line sequencing problem for the door-lock industry in Taiwan and develop an integer programming formulation with realistic constraints. The complex solution space makes the resulting program difficult to solve using commercial optimization packages. Therefore, a heuristic based on the Lagrangian relaxation principle is developed to solve this problem efficiently. We evaluate the efficiency of the developed Lagrangian relaxation heuristic by comparing its solutions with those obtained using a commercial optimization package: the computational results show that the developed heuristic solves the real-world problem faster than the optimization package by almost 15 times in CPU time at a comparable solution quality.