A robust optimization model for dynamic virtual hub location problem under uncertainty using an M/M/C/K queuing model: two metaheuristic algorithms

In a hub location problem, where an original hub is faced with shortage limitations, all or some routes passing through the original hub may be transferred to a virtual hub, in order to preserve a disconnection of the flow with minimal loss. In such a situation, reduction of congestion in the hubs plays a vital role in establishing the flow movement and avoiding traffic in the network. Here, a dynamic virtual hub location problem is investigated under conditions of uncertainty and presence of capacity constraints for the original and virtual hubs. The capacity constraints are applied to the model using an M/M/C/K queue. Moreover, the demand at the relevant points is considered to be nondeterministic and scenario-based. The problem is first formulated as an integrated probabilistic nonlinear mathematical model. The proposed model is then converted into a linear robust optimization model. The CPLEX optimization software package is used for solution of small samples. Two metaheuristic algorithms are introduced for large samples: a genetic algorithm and an imperialist competitive algorithm in a discrete space. The effectiveness of the proposed model is explored using the US well-known CAB data set. Several sample problems are also experimented to investigate the applicability of the model and the effectiveness of the algorithms. The results show appropriateness of the proposed mathematical model and the corresponding algorithms. The imperialist competitive algorithm turns to be more effective in terms of both the solution quality and the computing time.