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Recent years have seen a great deal of attention in energy conservation for production and manufacturing activities, particularly for energy-intensive industries. One of the useful strategies in reducing unnecessary energy consumption is to schedule these activities by considering both energy-driven and time-oriented criteria. This scheduling model can make an interaction between the energy consumption and the production cost to realize an efficient and sustainable production process. In this regard, the customers' expectation for due date is another important factor for decision-makers to control the delay in delivery. Making these decisions is extremely difficult due to uncertain circumstances to extract the accurate information of facilities and jobs in advance. Aforementioned issues in the context of urgent need for energy-conservation as well as the advent of globalized and multi-factory manufacture motivate our attempts to address a stochastic multi-objective distributed permutation flow shop scheduling problem by considering total tardiness constraint via minimizing the makespan and the total energy consumption. Due to the uncertainty of the proposed problem, a chance-constrain approach is used to describe decision-makers' awareness for the total tardiness, and accordingly, a chance-constrained programming model is utilized to formulate this problem. As a complicated optimization problem, a new multi-objective brain storm optimization algorithm incorporating stochastic simulation approach is specifically designed to better solve problem. A comparative study based on a set of benchmark test problems as well as two classical and popular algorithms is provided. The experimental results demonstrate that the proposed algorithm shows a very competitive performance in dealing with the investigated problem. [ABSTRACT FROM AUTHOR]

• 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]