基于公平原则的应急物资分配模型与算法

灾害发生后,灾区第一时间的自救和互救对于救灾工作至关重要.本文考虑自然灾害发生后,外界的救灾物资没有到达受灾地区的这段时间内,灾区的各个地区基于相互救援的应急物资分配问题.在考虑地区之间物资分配公平性的基础上,本文建立了一个双目标优化模型,模型的目标函数是最大化地区的物资的满足量,以及最小化最大运送时间.进一步地,本文提出了一个改进的差分进化算法求解该双目标优化模型,计算结果从计算时间和解的质量两个方面验证了算法的有效性;同时,本文通过一组例子验证了公平性约束的合理性.最后,本文通过一组算例分析,验证了改进的差分进化算法对大规模问题的有效性,说明救灾物资的最大允许运输时间和地区间合作的关系.论文的研究成果对基于属地管理的灾区自救和互救决策具有重要的理论和实践指导价值.

The model and algorithm for emergency supplies distribution based on fairness

Self-aid and mutual aid for affected areas immediately after disasters is essential in the rescue work. Emergency supplies distribution problem which considers the mutual aid among the affected areas is researched in this paper. The problem occurs in the period when the supplies cannot be transported to the affected areas immediately after natural disasters. A bi-objective optimization model with fairness constraint is constructed, with the first objective maximize delivery supplies and the second objective minimizing the maximum transport time among the affected areas. Besides, an improved differential evolution algorithm is proposed to solve the optimization model. And experimental results show the proposed algorithm is effective in the computation time and the quality of the solution. At the same time, the reasonability of the fairness is verified. Finally, the improved differential evolution algorithm is suitable for large scale problems and the relationship between the allowed transport time of relief supplies and area cooperation frequency is analyzed. This work has an important significance in theoretical and practical of attribution principles based self-aid and mutual aid management in natural disaster.