Sustainable multi-period hub location under uncertainty

In hub-and-spoke systems, hub location and allocation decisions depend on some parameters, such as transportation demand. When demand is time-dependent, a function can be estimated that reflects demand changes over time. In real-world conditions, due to the lack of knowledge and the nature of transportation demand, the coefficients of this function cannot be determined precisely. In this case, these coefficients are considered as uncertain parameters. In this paper, we propose a multi-objective mixed-integer nonlinear programming model for a sustainable multi-period hub location problem when demand changes are based on a linear function of time, and the coefficients of this function are fuzzy parameters. In the proposed model, it is possible to increase the capacity of hubs and hub links and transfer the capacity between hubs through modules. Also, the model determines the best timing for implementing the decisions. The objectives include minimizing system costs, minimizing emissions, and maximizing job opportunities related to sustainability aspects. We linearize the model and present a crisp counterpart formulation. Then, the computational results and sensitivity analysis are presented. Results show that the cost of designing the hub network with economic and social considerations is higher than the cost of designing the network with economic and environmental considerations. Ignoring the uncertainty in the problem can lead to non-optimal solutions. Also, the impact of increasing the number of hubs on reducing emissions after a threshold is marginal. We also introduce some valid inequalities to strengthen the formulation. The results indicate the acceptable performance of valid inequalities.