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Here, we investigate the classical p-median location problem on a network in which the vertex weights and the distances between vertices are uncertain. We propose a programming model for the uncertain p-median location problem with tail value at risk objective. Then, we show that it is NP-hard. Therefore, a novel hybrid modified binary particle swarm optimization algorithm is presented to obtain the approximate optimal solution of the proposed model. The algorithm contains the tail value at risk simulation and the expected value simulation. Finally, by computational experiments, the algorithm is illustrated to be efficient.

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The hub location and revenue management problem are two research topics in the field of network design and transportation. The hub location model designs the structure of the transportation network, while the revenue management model allocates network capacity to different customer categories according to their price sensitivity. Revenue management determines which products to sell to which customers and at what price. On the other hand, due to the limited number of aircraft seats, the revenue management problem has been widely used in the aviation industry. In this study, a robust optimization model is developed for the hub location and revenue management problem. For this purpose, a real-world case study with a central hub and six airports is presented and solved using CPLEX solver in GAMS software. Finally, a sensitivity analysis was performed on the key parameters of the problem, and their effect on the objective functions of the problem was investigated. Results show that the proposed model achieved the feasible solution in reasonable time for real case problem by exact method.