A multi-objective three-level hierarchical hub location-queue problem with congestion and reliability under uncertainty: A case study

. This study investigates a three-level hierarchical hub problem considering numerous features, such as congestion and reliability. This relates to ground and air hubs as high layers in this hierarchical network. A four-objective model is presented; it lowers the number of routes, network-related costs, and hub queue waiting times while raising the network’s route reliability. Due to the impact of service time on customer satisfaction in this issue, a time frame that a penalty is assigned for the amount of delay is considered. Both the airport and the ground are hub facilities in this regard. M/M/C/K queue systems are those found in the airport and ground hubs. Due to the multi-objective nature of the problem, the LP-metric and goal attainment (GA) approaches are used to resolve it and verify multiple samples with varying weight values provided by the decision-maker. The results from the above-mentioned methods are ranked using a simple additive weighting (SAW) method. A few parameters are treated as fuzzy numbers to make the model more realistic, and the Jimenez’s model and chance-constrained programming are used to present the findings. Considering numerous weights for each objective function and solving two methods, Pareto solutions are obtained.