A Probabilistic Mathematical Programming model for Locating Virtual Hubs in Airline Transportation Network under a M/M/C/K Queuing Model

In this study, a probabilistic mathematical programming model for locating virtual hubs in an airline transportation network in a dynamic environment and taking into account the capacity constraints for the original and virtual hubs is considered. The aim is to determine the optimal locations for establishment of the virtual hubs from among the candidate locations and design an optimal virtual hub network for allocation of the demand flow between the nodes to each hub along the planning horizon, so that the sum of transportation costs on different routes and the virtual hub location costs, along the planning horizon is minimized. In here, capacity constraints are applied to the model using an M/M/C/K queue model. Also, the demand at the relevant nodes are considered nondeterministic and scenario-based. The proposed problem is formulated as a nonlinear robust optimization mathematical programming model and solved by the LINGO optimization software. The effectiveness of the proposed model and its sensitivity to various parameters are investigated using a well-known CAB data set.