Stochastic regional-based profit-maximizing hub location problem: a sustainable overview

Climate change is one of the most important concerns globally, and countries need to improve their transportation infrastructure to handle flows with the least air pollution. In specific cities and regions, carbon emissions may cause in future many issues for people and societies. Although transportation hubs are very helpful in the reduction of transportation costs, they may cause an increase in carbon emissions in some regions, leading to long-term environmental problems. In this study, a model is developed for the profit-maximizing hub location problem that incorporates three pillars of sustainability. The proposed model is not only designed to maximize profit but also to control carbon emissions using a carbon cap policy and to reduce differences in emissions between regions with consideration of population density. This scheme will lead to achieving a sustainable transportation network. A two-stage stochastic programming approach is employed to cope with demand uncertainty. An enhanced sampling based on the self-organizing map method was utilized to cluster scenarios that lead to dealing with small-sized problems. Furthermore, classical Benders decomposition, Pareto-optimal cut Benders decomposition, and L-shaped algorithms are employed to solve the proposed models more efficiently. The proposed models are analyzed using the well-known Turkish Network (TR) data set. Computational results demonstrate that the proposed models help to achieve sustainability. Factors of sustainability such as environmental and social can be achieved by slightly reducing the amount of profit in the economic factor. Furthermore, results show that the L-shaped algorithm with a multi-cut scheme outperforms the commercial solver, classical Benders decomposition, and Pareto-optimal cut Benders decomposition algorithms in large-size instances.