兼顾公平与效率的多目标应急物资分配问题研究

Multi-Objective Emergency Resources Allocation with Fairness and Efficiency Considerations

大规模灾害发生初期,首批应急物资往往供不应求,物资分配决策者需要在追求效率的同时兼顾公平。针对该问题,构建以总加权嫉妒值最小为公平目标,以总物流成本最小为效率目标,以比例公平为约束条件的多目标数学优化模型;设计改进的快速非支配排序遗传算法,求解冲突多目标的帕累托前沿,并给出帕累托前沿解的选择策略。案例分析表明,模型和算法能有效解决供小于求情况下的应急物资公平分配问题,揭示了最小嫉妒公平与比例公平的悖反关系,以及资源的短缺程度从客观上决定了应急物资分配的总体公平程度。

Because the first batch of emergency resources cannot meet all the needs from the disaster areas in the initial stage of a large-scale disaster,decision makers should consider both fairness and efficiency.A multi-objective mathematical optimization model with the minimum total weighted envy value as the fairness goal,the minimum total logistics cost as the efficiency goal,and the proportional fairness as constraints is established.An improved fast non-dominated sorting genetic algorithm is proposed to find Pareto frontier of the model,and a Pareto frontier solution selection strategy is presented.The numerical results verify the effectiveness of the model and algorithm,and reveal the tradeoff between the minimum envy fairness and the proportional fairness,and show that the degree of shortage of resources objectively determines the overall fairness degree.