A New Hybrid Multi-Objective Scheduling Model for Hierarchical Hub and Flexible Flow Shop Problems

Technologies and lifestyles have been increasingly geared toward consumerism in recent years. Accordingly, it is both the price and the delivery time that matter most to the ultimate customers of commercial enterprises. Consequently, the importance of having an optimal delivery time is becoming increasingly evident these days. Scheduling can be used to optimize supply chains and production systems in this manner, which is one practical method for lowering costs and boosting productivity. This paper suggests a multi-objective scheduling model for hierarchical hub structures (HHS) with three levels of service. The factory and customers hub (second level) and central are on the first level in which the factory has a Flexible Flow Shop (FFS) environment. The noncentral hub (third level) is responsible for the delivery of products made in the factory to customers. Customer nodes and factories are connected separately to the second level, and the non-central hubs are connected to the third level. The model's objective is to minimize transportation and production costs and product arrival times. To validate and evaluate the model, small instances have been solved and analyzed in detail with the weighted sum and e-constraint methods. Consequently, based on the ideal mean distance (MID) metric, the two methods were compared for the designed instances. As NP-hardness causes the previously proposed methods to solve large-scale problems to be time-consuming, a meta-heuristic method was developed to solve the large-scale problem