An efficient scheduling algorithm using the Simulated Annealing (SA) method is proposed, In an actual large scheduling problem, the number of schedules searched within a reasonable time is restricted, because calculation of the starting times of jobs requires a long computation time when the problem has various types of constraints. In the proposed algorithm, two types of improvements are proposed to reduce the computation time of a scheduling algorithm: One is to reject, at an early stage of the starting time calculation, those schedules that have little possibility of being accepted in the simulated annealing method. The other is to reject unpromising schedules stochastically using the data related to the production sequence of jobs-not after the calculation of the starting times of jobs hut at the step of generating a new production sequence of jobs, Thus, compared with the algorithm which selects a new production sequence randomly, better schedules can be derived in shorter computation time. The developed algorithm has been applied to a practical scheduling problem at a resin production plant, and it has become clear that this algorithm can generate significantly better schedules with a much shorter computation time.