Reliable hub-and-spoke network design problems under uncertainty through multi-objective programming

HLP (hub location problem) tries to find locations of hub facilities and assignment of nodes to extended facilities. Hubs are facilities to collect, arrange, and distribute commodities in telecommunication networks, cargo delivery systems, etc. Hubs are very crucial and their inaccessibility impresses on network whole levels. In this paper, first, total reliability of the network is defined based on considering the reliability values of nubs and arcs. Then, a reliable hub-and-spoke network design problem under uncertainty is introduced through the multi - objective programming method in which the parameters are random fuzzy variables. Indeed, we are making effort to either maximize the average reliability or minimize total cost. Then, the proposed reliable multi - objective hub-and-spoke network design problem under uncertainty is solved by a new method using Zimmermann fuzzy multi - objective programming and random fuzzy chance-constrained programming based on possibility theory. Finally, some benchmark problems are solved as numerical examples to clarify the described method and show its efficiency.