Sequencing problem for a mixed-model assembly line in the Toyota production system

The paper discusses a sequencing problem of a mixed-model assembly line in the Toyota Motor Corporation production system, which is well known as the Just-in-Time production system. Whenever a worker in the assembly line finds that he might fail to complete his operations within the work zone, he pushes a button to call an auxiliary worker who assists him in the operations. If he can complete the operations within his work zone with the help of the auxiliary worker, the line does not stop. Otherwise, the line stops. In the Toyota production system, it is very important to keep a constant rate of usage of every part used by the assembly line. Hence, there are two goals for the sequencing problem in the Toyota production system. The paper provides a new formulation for the sequencing problem with two goals. It considers the goal of keeping the constant rate of part usage as a constraint of the sequencing problem, and it formulates a sequencing problem of minimizing the total line stoppage time with auxiliary workers and the constraints for keeping the constant rate of part usage. Since this problem is NP-hard and the size of the practical problems at Toyota are huge, a two-phase approximation algorithm is proposed. Numerical examples show that the proposed algorithm is efficient and can find a good suboptimal solution.