Two-stage stochastic and robust green location-routing problem

As urbanization increases, low–pollution freight delivery is crucial, while customer demand is often uncertain. For these reasons, this paper introduces a new mixed-integer mathematical model for the two-stage stochastic green location-routing problem, in which the customer demands are uncertain, and speed, travel time, and fuel consumption are considered. The strategic decisions related to the location represent the first stage of decision-making, while the tactical decisions related to allocation, routing, and speed determination are made in the second stage. The model minimizes fixed operating costs and reduces CO2 emissions and fuel consumption. The robust model includes a hybrid heuristic algorithm based on Lagrangean relaxation and Benders decomposition algorithms. To evaluate the convergence rate and solution quality, the method is applied to random test instances generated in the literature. Finally, to investigate the performance of the algorithm, a sensitivity analysis regarding several variables is performed. The results show that low and high speeds increase the fuel consumption and air pollution, while using more than one depot reduces them, yet the overall cost increases. The outcomes support transportation planners in achieving long-term sustainability goals.