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• This work studies an integrated distributed flow shop scheduling and distribution problem. • A mixed integer programming model is given to describe this problem mathematically. • An enhanced brain storm optimization algorithm is designed. • Optimal solutions are obtained by using mathematical programming solvers. • State-of-the-art results are acquired by the designed approach. Production and distribution are two essential activities in supply chain management. Currently, integrated production and distribution problems receive much attention because decision-makers devote to improving the operation efficiency of both stages and try to achieve an optimal solution. This work proposes an integrated distributed production and distribution problem with consideration of time windows, in which a set of jobs (i.e., customer orders) needs to be assigned among factories and the jobs are processed on flow shop environments at their associated factories. Then, the completed jobs are delivered by capacitated vehicles to customers in different regions while satisfying given time windows as much as possible. Accordingly, to optimally solve the proposed problem, a mixed integer programming model with minimizing total weighted earliness and tardiness has been established. For the optimization task, an enhanced brain storm optimization algorithm with some particular strategies is designed to handle the considered problem. To assess the performance of the proposed optimization method, several experiments by adopting a set of benchmark test problems are performed, and state-of-the-art optimizers are chosen for comparisons. The obtained optimization results exhibit that the designed algorithm significantly outperforms its rivals and can be considered as an excellent optimizer for solving the studied problem. Besides, compared with the CPLEX solver, the designed optimizer also performs much better for solving large-size problems. [ABSTRACT FROM AUTHOR]