In this paper, a stochastic group shop scheduling problem with a due date related objective is studied. The group shop scheduling problem provides a general formulation including two other shop scheduling problems, the job shop and the open shop. Both job release dates and processing times are assumed to be random variables with known distributions. Moreover, earliness and tardiness of jobs are penalized at different rates. The objective is to minimize the expected maximum completion cost among all jobs. A lower bound on the objective function is proposed, and then, a hybrid approach following a simulation optimization procedure is developed to deal with the problem. An ant colony optimization algorithm is employed to construct good feasible solutions, while a discrete event simulation model is used to estimate the performance of each constructed solution that, taking into account its lower bound, may improve the best solution found so far. The proposed approach is then evaluated through computational experiments.
