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1、introduction 在确定各疫区药品和疫苗的总需求量后，我们需要一个有效的运输分配双重网络模型，及时 地实现最优分配。 整个运输网络可以分为医疗中心网络和以医疗中心为核心的临时发热门诊 子网络。 我们现在的任务是将药品从2 个国际机场分运到各地区的医疗中心，再由医疗中心 根据当地的用药需求动态分配到临时发热门诊，运输过程中综合考虑药品的送达率、疫苗的 时效性、用药动态需求、运输成本等因素。 After pinpointing the total amount of vaccines and other medicaments for each district, we need to b
2、uild a network to ship and distribute these medicines optimally. The whole network is divided as a central network that comprises medical centers and subnetworks within each medical center. By doing so, the problem is transformed as first distributing medicines from 2 airports to central network s e
3、ach medical center and then allocating medicines in each subnetwork of each medical center. 问题分析： 从宏观上来看，疫苗、药品的来源可能有塞拉利昂本地医药公司生产，也有国际 支援。 考虑到该国本身医学研发水平、医药生产技术落后，我们有理由假设治疗埃博拉的疫 苗和药品全部由国际支援，药品统一送到指定的枢纽。现在的问题是如何将现有的药品根据 需求量选择最优方案送达各医疗中心。在疫情蔓延的情况下，我们需要将药品在最短时间内 送达医疗中心， 其次再考虑在相同时间的情况下优先选择低成本运输。那么问题则转化为一
4、个简单的多目标线性规划问题，即在一个简单的应急运输网络中，从多种运输方案中选 择最佳方案 , 使药品运输时间最短 , 并且运输费用最低。 2 个优化目标分层次实现 优化，首先满足时间约束，其次满足成本约束。 Problem Analysis: We assume that all medicines for Ebola are donated from international assistance and are first shipped to certain locations. Our task is devising a distribution model that can op
5、timally distribute these medicines to each medical center and meet their demand. Considering that the epidemic is spreading, we should try to minimize the shipment time. In addition, we need to reduce cost associated with such shipment. Therefore, the problem is effectively a multi-objective linear
6、programming problem, i.e., building a scheme that can result in minimum time and cost. We thus take two steps to optimize the problem where the shipment time constraint and the cost constraint are considered sequentially. 1 / 10 模型建立： 设 E=E1，E2， 为药品需求点的集合， Ej 的资源需求量为 ej ，S=s;s;s;药物 供给点的集合， S处可供给的药品量
7、为Sj，且 ji es;从 Si到 EJ的运输单位成 本为 Cij；从 Si到 Ej 的最短时间为tij ；从 Si向 Ej的物资运数量为Xij。设 立两 级 优 化 指 标 , 上 层 是 效 益 性 指 标 , 采 用 “ 应 急时间最短 ” 下层 是 耗 费性指 标 , 采用“ 总成本最低” 。 考虑药品的运送量对运送最短时间有一定影响，在此引入函数 gij=xijtheta. 其中 theta 为运送量对时间的影响因子。构造最短时间为上层目标函数y1=maxgt, 最低运输成本为下层目标函数y2=heCX;由此，药品运输系统的双层规划模型为： Building the model: L
8、et 12 E ,E ,.,E n Ebe the set of medical centers that demands medicines for Ebola. The demanded medicine quantity of j Eis j e. Similarly, let 1,2 S S ,.,S n Sbe the set of locations where medicines are first stored. The medicine quatity of i Sis i s. It is not hard to imagine that ji es. Further, w
9、e define ij c, ij tand ij xas the shipment cost, shipment time and shipped medicine quantity from i Sto j Erespectively. Adopting a two layer optimization index where the upper layer deals with minimizing shipment time and the lower layer concerns about reducing shipment cost. Given that the shipped
10、 quantity will influence the shipment time, we define ijij gxwhere is a factor for modeling the influence. Constructing 1 maxgt ijij yas the upper layer s objective function and 2 , ijij i j yc xas the lower layer s objective function. Then, the double-layer programming model is shown as below: 1 2
11、1 1 miny 0,i1,.,m; j1,.,n miny ,i1,.,m . ., j1,.,n 0,i1,.,m; j1,.,n ij n iji j m iji i ij t xs st stxe x 2 / 10 模型的求解： 借助 Matlab 通过简单的遍历即可求出最佳方案。但考虑到塞拉利昂本身交通并不发达，可 能某些地方不能直接到达，或最短时间过长，实际中不可行， 因此我们必须加上新的限制条 件。处理过程如下： Step1 对 Tij（i=1， ,m;j=1, ,m）进行排序，取出不相等的数值；取出互不相等的数值，记 为 ，令 k=1. step2 把应急时间大于T，的运输线路
12、的运费设为无穷大，其余路线运费保持不变，求解在 该条件限制下的可行方案。 Step3 若该限制条件下有解，则停止，当前解为最优解；否则令K=K+1 ，转入 STEP2重新求 解。 通过以上双层规划模型，我们可以根据实际的交通路况求解出向医疗中心运输药品的最佳方 案。 Solving the Model: Using the enumeration provided by MATLAB, we can obtain the proposed optimal distribution scheme. However, the transportation infrastructure in Sie
13、rra Leone is underdeveloped. Some shipment routes are therefore infeasible. Also, some shipment time may be exceedingly large. We therefore add some new constraints to the problem, as outlined below: Step 1: Sort ij t（i=1， ,m;j=1, ,m） and extract those that are different. These extracted shipment ti
14、me are denoted as 12 . r tttand let k equals 1. Step 2: Set a time threshold k t; let the shipment cost be a very large number for routes whose shipment time exceed T. Step 3: If there exists solutions, the programming stops and the solution is the optimal solution; otherwise, let k=k+1 and return t
15、o Step 2. Adopting the above two-layer programming model, we can devise an optimal medicine distribution scheme that takes real transportation feasibility into account. 子网优化配送模型：based on Time Space Network Mode 问题分析：医疗中心固定分布于塞拉利昂的几个行政区（主网结构固定），而以医疗中心为 核心的临时发热门诊子网络存在以下几方面的不同： 1.当疫情爆发时，在疫区附近的临时发热门诊会随疫
16、情趋势严重而增多，也就是子网络的 需求点是随时间动态变化的。 2.临时发热门诊医疗条件差，不能像医疗中心一样将疫苗长时间低温保存，从医疗中心送 3 / 10 出到各发热门诊后，在常温下只能短时间保存，因此必须定时定量输送，才能保证疫苗 的有效使用。 3门诊接收患者的数量是不断变化的，各临时发热门诊预报的药品需求量也存在误差。 因此对于医疗中心到临时发热门诊的子网络运输模型仅采用这种一次决策运输方案，效果显 然是不理想的。 Distribution scheme in subnetworks As mentioned above, distribution in subnetworks concerns about each medical center optimally distributes its received medicines to its different departments. Compared
