This paper considers a stochastic job-shop scheduling problem. Many real world scheduling problems address probabilistic behavior in process times, due dates or other parameters. A job-shop scheduling problem was considered with stochastic process times and possible machine breakdowns. Distribution functions of process times are supposed to be known. Also, life times of machines are assumed to be exponentially distributed. In stochastic scheduling problems, unlike the deterministic variants, the solution cannot be fully determined a priori. In other words, every time a machine becomes available, a job has to be chosen to be passed on it from all the jobs that are waiting in line. The objective usually would be minimization of some measure consisting total tardiness and earliness. A solution to such a problem consists of two parts: 1.A strategy (rule) to choose one job from the jobs that are waiting in line 2.Near optimal values of start times of jobs A heuristic rule based was devised on the famous central limit theorem to choose the job that should be passed on the freed machine. Also, an extensive simulation was used and a special push-forward technique to optimize start times and evaluate our solution method.
