This paper deals with a sequencing problem for a mixed-model assembly line in a Just-In-Time production system. The line is stopped, whenever workers fail to complete their operations within their stations. The problem is to minimize a total cost consisting of idle times of workers and stopping times of the line. A branch-and-bound algorithm is devised for the problem. Moreover, an approximate algorithm based on simulated annealing is develored to solve real scale sequencinm problems. An optimal solution computed by the branch-and-bound algorithm is used to tune values of several parameters of the approximate algorithm. Its application to an actual assembly line demonstrates its efficiency.