Properties of a sequencing problem for a mixed model assembly line with conveyor stoppages

The concept of Autonomation in the Toyota production system admits workers to stop the conveyor whenever they fail to complete the operations within their work stations in a mixed-model assembly line. Therefore, the conveyor stoppage becomes a crucial criterion in sequencing problems for mixed-model assembly lines in the Toyota production system. In this paper, we consider a goal of minimizing a total conveyor stoppage time. A sequencing problem with this goal is formulated. Several useful properties, such as, the computational complexity of the sequencing problem, necessary and sufficient conditions that a conveyor stoppage occurs, lower and upper bounds of the objective function, and sufficient conditions for the optimality of a solution, are characterized. Based on the properties, a heuristic algorithm is designed. A numerical example is given to illustrate the methodology.