Sustainable hub location under uncertainty

This paper addresses the sustainable design of hub networks under uncertainty in the context of less-than-truckload transportation, taking into account factors related to carbon pricing. The problem is modeled to maximize profits in a stochastic demand environment, where a portion of the demand may remain unserved depending on the trade-off between profits, costs, and carbon emissions. The model explicitly incorporates a carbon tax into the objective function, along with transportation and hub operation costs. To ensure compliance with the carbon cap, a constraint is incorporated to limit the emissions across the entire transportation network. The carbon emission on each arc of the network is modeled using a generic convex function that depends on the total demand routed on the arc which is then approximated by a piecewise linear function to derive a mixed-integer stochastic formulation. A Benders-decomposition-based algorithm coupled with a sample average approximation scheme is developed to solve the stochastic model. The algorithm is enhanced with acceleration techniques to solve large-scale instances. Extensive computational experiments are conducted to evaluate the efficiency of the proposed algorithm and also to analyze the impact of incorporating carbon pricing factors on optimal hub networks. Computational results provide insights into sustainable hub network designs.