In this paper, an open-shop scheduling problem with stochastic process times is considered. The objective function is to minimize the weighted sum of earliness and tardiness costs. This type of objective function, in addition to the optimal schedule, puts forward the issue of finding optimal values of start times of jobs. In scheduling problems with stochastic process times, unlike the deterministic variants, it is not possible to determine the schedule before the random variables are realized. Whenever a machine becomes available (for example finishes processing some jobs) a job should be selected to be passed on it from the set of available jobs. This selection process is carried out in real-time. We have devised a simulation-optimization algorithm which calculates the distribution functions of the completion times of jobs via central limit theorem. These distribution functions are used for cost estimation in the real-time job selecting process. In other words, whenever some jobs are competing for a free machine, a pair wise cost competition is raised among them and the winner is passed on the free machine. Moreover, the distribution function of the completion time of each job is also used to adjust its start time. Finally, some test problems are generated and solved by our algorithm. The results demonstrate that our algorithm, even without adjusting the start times, outperforms the algorithm which acts randomly in the real-time job selecting process.
