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

Document Type : Article


1 Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

2 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran


This study presents a four-objective model for a three-level hierarchical hub problem, in which nodes are connected to ground hubs in a star-like pattern at the lowest level of a hierarchy of demand, and ground hubs are connected to airport hubs at the next level up. This model finds 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, a time frame is considered, in which a penalty is assigned for the amount of delay. Both the airport and the ground are hub facilities in this regard. M/M/C/K queue systems are those found in airport and ground hubs. This problem aims to locate the predetermined hubs and assign nodes to the network. Due to the multi-objective model, 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 forgoing approaches are ranked using the simple additive weighting (SAW) method. A few parameters are treated as fuzzy numbers to make the model more realistic, and the Jimenez model and chance-constrained programming are used to present the findings.


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