为了兼顾应急物资配送的效率与公平，在考虑应急物资分类与分批配送的基础上，建立了效率目标与公平目标相结合的多周期应急物资分批配送模型。效率目标计算了规划周期内所有车辆的运输成本，公平目标通过各周期惩罚成本最小化实现物资在受灾点间的均衡分配。设计了针对多目标优化模型求解Pareto解集的计算方法，通过算例验证了求解方法的可行性。结果表明：通过观察Pareto前沿，追求物资的分配公平会增加救援车辆的出车次数和配送批次，考虑运输成本时车辆会采用集中配送策略。
In emergency management and related fields, it's still a challenging research subject that how to respond post-disaster emergency requirements quickly to reduce losses of disaster through the efficient emergency logistics system. Based on principle of Humanitarian relief, the distribution and delivery strategies of post-disaster emergency logistics need to ensure both the maximization of the number of benefited victims and equal opportunity for every victim to be rescued. Otherwise, the result of inequity rescues will produce certain social costs. Depending on differences between characteristics of post-disaster supplies, demand can be divided into one-time demand and cyclical demand, which have different requirements for distribution strategies. In this paper, a multicycle and multi-item batch distribution model of emergency supplies is built to combine the efficiency target and the equity target, based on considering classification of emergency materials and uncertainty of supplies, in order to give consideration to both the minimization of emergency materials' distribution costs and the maximization of the equity target. The efficiency target achieves effective use of relief supplies by minimizing distribution costs which are produced in the material distribution part in the planning cycle; the equity target minimizes social costs which are produced by unsatisfied demands in the planning cycle, for achieving equilibrium assignment of supplies between affected nodes. Besides, two-phase algorithm is designed to solve the Pareto disaggregation of multi-objective optimization model. The first step is the search of feasible path set,according to the vehicle capacity constraints and single-cycle travel time constraints.In the second step,based on the theory of ε-constraint optimization method, multi-objective optimization problem is converted into a series of single-objective optimization problem,and the optimal solution for each single-objective optimization problem is seemed, thereby obtaining the Pareto disaggregation of the model. At last, the rationality of the model and the feasibility of the solution are verified through designing reasonable examples and solving. The results indicate that the cycle distribution strategy to achieve batch distribution can (1) ensure that all affected nodes could receive the first batch of key relief supplies in a short time;(2) reduce social costs arising from allocation inequality and distribution delays;(3) improve the equity of the distribution and allocation of emergency supplies. In addition, calculating the Pareto front for policy-makers can provide a variety of decision-making schemes, and help decision makers intuitively understand the relationship between the efficiency target and the equity target, thereby developing effective distribution strategies according to the specific circumstances.
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