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To address the shortage of relief in disaster areas during the early stages after an earthquake, a location-routing problem (LRP) was studied from the perspective of fairness. A multi-objective model for the fair LRP was developed by lexicographic order object optimal method in consideration of the urgent window constraints, partial road damage, multimodal relief delivery, disaster severity, and vulnerability of each demand node when its demand is not satisfied. The goals of this model are to minimize (1) the maximum loss of demand node, (2) the total loss of demand node, and (3) the maximum time required for the demand node to receive relief. A hybrid heuristic algorithm was proposed to solve the model. Finally, the utility and fairness of the model and algorithm were demonstrated by a case study during the first day after the great Wenchuan earthquake in China.

Taking carbon emissions into account in decision-making on distribution network operations contributes to achieving the goal of promoting energy conservation and emissions reduction. The focus of this paper is to research multicapacity hierarchical location-routing robust optimization in distribution network design under carbon trading policies. First, this problem is described as a mixed integer nonlinear programming model. Then, based on strong duality theory, the nonlinear model is transformed into a linear robust equivalent model. Finally, GUROBI software is used for numerical calculation and analysis. The results suggest the following: carbon trading policies have a carbon abatement effect; with a decrease in the carbon emissions cap and an increase in carbon trading prices, carbon emissions undergo a ladder-like downward trend; uncertain fluctuations in freight units will influence the optimal decision-making patterns of enterprises; and making more vehicles available will reduce carbon emissions. The government should set a reasonable carbon emissions cap according to market conditions. Enterprises could adopt robust control parameters on the basis of their decision-making preferences and consider the impact of carbon trading policy in formulating and adjusting an optimal decision-making scheme. INDEX TERMS Carbon emissions, carbon trading, green location-routing problem, robust optimization.

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