With the emergence of advanced manufacturing and Industry 4.0 technologies, there is a growing interest in coordinating the production and distribution in supply chain management. This paper addresses the production and distribution problems with sequence dependent setup time for multiple customers in flow shop environments. In this complex decision-making problem, an efficient scheduling approach is required to optimize the trade-off between the total cost of tardiness and batch delivery. To achieve this, three new metaheuristic algorithms such as Differential Evolution with different mutation strategy variation and a Moth Flame Optimization, and Lévy-Flight Moth Flame Optimization algorithm are proposed and presented. In addition, a design-of-experiment method is used to identify the best possible parameters for the proposed approaches for the problem under study. The proposed algorithms are validated on a set of problem instances. The variants of differential evolution performed better than the other compared algorithms and this demonstrates the effectiveness of the proposed approach. The algorithms are also validated using an industrial case study. © 2021 Elsevier Ltd