Multi-objective hub network design under uncertainty considering congestion: An M/M/c/K queue system

•We provide a bi-objective hub location model to minimize the cost and maximum the travel time.•We consider multi-capacity levels for hub nodes.•We design a multi-modal hub location network.•We model the congestion at hubs as an M/M/c/K queue system.•We develop efficient meta-heuristics to obtain near-optimal Pareto solutions.

Hub location problems have applications in a variety of fields including cargo delivery systems and telecommunication network design. Hub location problems deal with locating a set of hub nodes and allocating non-hub nodes to the located hubs. This paper presents a new bi-objective model for a multi-modal hub location problem under uncertainty considering congestion in the hubs. The objective functions attempt to minimize the total transportation cost as well as minimize the maximum transportation time between each pair of Origin-Destination (O-D) nodes in the network. To cope with the computational complexity of the problem, a well-known meta-heuristic algorithm, namely differential evolution (DE), is developed to obtain near-optimal Pareto solutions. Furthermore, several computational experiments and sensitivity analyses are provided to demonstrate the efficiency and applicability of the presented model and solution algorithm. Finally, the conclusion is presented.