本文主要是介绍数学规划学习之配送中心选址问题，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！
学习了数学规划，现在把做的题目进行总结——配送选址问题
某省共有92个城市，城市位置、标号，公路交通网数据见附件1。
某企业在该省标号前20位的城市建立了直销中心，各直销中心负责所在城市的销售，销售量见附件1。该企业欲在该省设立一个配送中心负责给直销中心配送产品，配送中心建设成本为30万元。每吨公里运费2元，每吨产品的销售利润为300元。
试建立数学模型分析研究下面的问题：
（1）为了降低运输成本，配送中心应选在哪个城市？
（2）请为该企业制定一个成本最小的5年产品配送计划：应设立几个配送中心、各设在何处？
（3）如果该企业考虑重新为20个直销中心选址，请给出最佳的5年产品销售、配送计划。
（4）假定没有直销中心城市的客户按就近的原则购买产品，请重新考虑问题（3）。
（1）对于第一个问题，首先考虑题目，降低运输成本，在配送中心费用相同的情况下，考虑最小的公里数，因此，把此题归为最短路径问题。
首先，对于最短路径问题，最常用的就是floyd算法和dijkstra算法，在学习的过程中，已经对这两种算法有所理解，在mydijkstra算法中需要知道邻接矩阵然后要明确自己需要从哪个值到另一个值的最短路径。
对于dijkstra有：
function [mydistance,mypath]=mydijkstra(a,sb,db);
% 输入：a—邻接矩阵，a（i，j)是指i到j之间的距离，可以是有向的
% sb—起点的标号, db—终点的标号
% 输出：mydistance—最短路的距离, mypath—最短路的路径
n=size(a,1); %n取a的行数，即顶点个数
visited(1:n) = 0;visited(sb)=1;%记录顶点是否得到标号
distance(1:n) = inf; distance(sb) = 0; %起点到各顶点距离的初始化u=sb; %u为最新的P标号顶点
parent(1:n) = 0; %前驱顶点的初始化
for i = 1: n-1id=find(visited==0); %查找未标号的顶点for v = id if a(u, v) + distance(u) < distance(v)distance(v) = distance(u) + a(u, v); %修改标号值 parent(v) = u; end endtemp=distance;temp(visited==1)=inf; %已标号点的距离换成无穷[t, u] = min(temp); %找标号值最小的顶点 visited(u) = 1; %标记已经标号的顶点end
mypath = [];
if parent(db) ~= 0 %如果存在路!t = db; mypath = [db];while t ~= sbp = parent(t);mypath = [p mypath];t = p; end
end
mydistance = distance(db);而对于floyd可以知道，在floyd算法中并不需要要从哪到哪的要求，只需要算出邻接矩阵即可。
对于floyd算法有：
function [dist,mypath,path]=floyd2(a);
% 输入：a—邻接矩阵，元素(aij)是顶点i到j之间的直达距离，可以是有向的% 输出：dist—最短路的距离；% mypath—最短路的路径
n=size(a,1); path=zeros(n);
for k=1:nfor i=1:nfor j=1:nif a(i,j)>a(i,k)+a(k,j)a(i,j)=a(i,k)+a(k,j);path(i,j)=k;endendend
end
dist=a;for g=1:nfor h=1:ngg=g;while path(gg,h)~=0&&path(path(gg,h),h)~=0 path(g,h)=path(path(gg,h),h);gg=path(gg,h); endend
end
for i=1:length(a)for j=1:length(a)
parent=path(i,:); %从起点i到终点j的最短路上各顶点的前驱顶点
parent(parent==0)=i; %path中的分量为0，表示该顶点的前驱是起点
mypath{i,j}=[j]; t=j;
while t~=ip=parent(t); mypath{i,j}=[p,mypath{i,j}];t=p;
endend
end在对于第一个问题中，可以知道应该算出每个点与点之间的距离，但在计算距离的时候，应该要筛选出sheet2中，有点点并没有相互连接的地方，在matlab编程中，可以使用find等函数进行筛选。
然后因为是练习数学规划，在此，下面是lingo程序的第一个问题的解答。
此时的程序为：
model:sets:nodesr/n1..n92/:xu;!xu为每个城市的需求量,问题1、2中只需考虑前20个城市;nodesc/m1..m92/:y,cost;!y为城市是否为配送中心的0-1变量;links(nodesr,nodesc): dist,x;!x(i,j)为判定第j个城市作为配送中心是否为第i个直销中心配送货物的0-1变量;
endsets!目标函数;min=z;
z=@sum(nodesr(I)|I#LE#20:@sum(nodesc(J): dist(I,J)*x(I,J)*xu(I)))*2;!约束条件;
@for(nodesr(I)|I#LE#20:@sum(nodesc(J): x(I,J))=1);!每个直销中心的需求都得到满足;
@sum(nodesc(J):y(J))=1; !只设置1个直销中心;
@for(nodesc(J):@for(nodesr(I)|I#LE#20:x(I,J)<=y(J)));!反映x和y的对应关系,其实这儿可以写成'=';
@for(nodesc(J):x(J,J)=y(J)); !j恰好同时为直销中心和配送中心;
@for(links:@bin(x));
@for(nodesc:@bin(y));
data:
dist= 0.0000000e+000 1.8987490e+001 3.8838842e+001 4.5352167e+001 9.3742889e+001 9.5375178e+001 1.1500349e+002 9.0226247e+001 9.2254378e+001 1.4649568e+002 1.9087929e+002 2.2236153e+002 2.2001753e+002 1.6028474e+002 1.4249318e+002 9.2868122e+001 3.5912053e+001 2.5645722e+001 1.7583464e+001 5.2631990e+001 1.9293439e+002 2.1096215e+002 2.2501753e+002 2.2893203e+002 2.1090427e+002 1.8187929e+002 1.8931232e+002 1.9001160e+002 1.9515806e+002 1.2083445e+002 1.1281154e+002 1.0360174e+002 9.8502720e+001 9.7279316e+001 8.8011738e+001 9.0823632e+001 9.5922652e+001 5.8809349e+001 5.5809349e+001 3.8131680e+001 4.4412053e+001 2.6063196e+001 1.8000938e+001 2.8474323e+001 8.1303534e+001 8.0925709e+001 1.0830311e+002 1.1850115e+002 8.8742889e+001 8.6067321e+001 8.2259434e+001 8.0655768e+001 8.2034685e+001 5.9231176e+001 5.1497831e+001 7.6413127e+001 6.4033709e+001 7.1533709e+001 7.9343959e+001 6.2744611e+001 9.7457721e+001 4.8852167e+001 3.5044403e+001 2.5989018e+001 2.3599092e+001 2.0436814e+001 1.6194173e+001 1.2071068e+001 5.0000000e+000 1.0385165e+001 1.1403124e+001 1.6403124e+001 1.0296111e+001 6.2649820e+000 9.3005376e+000 1.2836072e+001 1.6403124e+001 6.4031242e+000 1.3111328e+001 1.7583464e+001 3.2353926e+001 3.6439214e+001 3.1030887e+001 4.0879744e+001 4.8159854e+001 5.6237542e+001 5.1942002e+001 4.7910873e+001 4.3879744e+001 4.5171338e+001 4.9914755e+001 6.9939739e+0011.8987490e+001 0.0000000e+000 2.1116536e+001 5.6850675e+001 7.8337113e+001 9.8420771e+001 9.7281187e+001 7.2503941e+001 7.4532072e+001 1.2877337e+002 1.7315698e+002 2.0463922e+002 2.0103004e+002 1.4129725e+002 1.2477088e+002 7.3880632e+001 2.5911116e+001 4.3847598e+001 3.6570954e+001 7.0833867e+001 1.7394690e+002 1.9197466e+002 2.0603004e+002 2.1120972e+002 1.9318197e+002 1.6415698e+002 1.7159002e+002 1.7228930e+002 1.7743576e+002 1.0311214e+002 9.5089235e+001 8.5879433e+001 8.0780413e+001 7.9557010e+001 7.0289431e+001 7.1836142e+001 7.6935162e+001 3.9821859e+001 3.6821859e+001 1.9144190e+001 3.4411116e+001 1.6062258e+001 8.0000000e+000 9.4868330e+000 6.3581228e+001 6.3203403e+001 9.2897333e+001 1.0309537e+002 7.3337113e+001 8.3281962e+001 7.9474076e+001 7.5172913e+001 6.6628909e+001 4.3825401e+001 3.3775525e+001 7.9415554e+001 7.5532217e+001 8.3032217e+001 8.2389552e+001 7.4243119e+001 1.0895623e+002 6.0350675e+001 4.6542911e+001 3.7487526e+001 3.1656574e+001 2.8494297e+001 2.4251656e+001 2.1058558e+001 1.3987490e+001 8.6023253e+000 2.0390614e+001 1.6062258e+001 2.4124515e+001 2.5252472e+001 2.5586250e+001 2.9121784e+001 3.3593920e+001 2.5390614e+001 3.2098818e+001 3.6570954e+001 5.0555802e+001 5.4641090e+001 4.9232763e+001 5.9081621e+001 6.6361731e+001 7.4439418e+001 7.0143879e+001 6.6112750e+001 6.2081621e+001 6.3373215e+001 6.8116631e+001 8.0727959e+0013.8838842e+001 2.1116536e+001 0.0000000e+000 4.0433852e+001 5.7220577e+001 7.7304235e+001 7.6164651e+001 5.1387404e+001 5.3415536e+001 1.0765683e+002 1.5204044e+002 1.8352268e+002 1.8740507e+002 1.2767227e+002 1.0365434e+002 6.0255658e+001 4.7027652e+001 5.8949096e+001 4.1942567e+001 8.5935365e+001 1.6032193e+002 1.7834968e+002 1.9240507e+002 1.9009319e+002 1.7206543e+002 1.4304044e+002 1.5047348e+002 1.5117276e+002 1.5631922e+002 8.1995603e+001 7.3972698e+001 6.4762897e+001 5.9663877e+001 5.8440474e+001 4.9172895e+001 5.4172895e+001 5.9271915e+001 6.0938396e+001 5.7938396e+001 4.0260726e+001 5.5527652e+001 3.7178794e+001 2.9116536e+001 1.1629703e+001 4.2464691e+001 4.2086867e+001 7.1780797e+001 8.1978836e+001 5.2220577e+001 6.2165426e+001 5.8357539e+001 5.4056377e+001 4.5512373e+001 2.2708865e+001 1.2658989e+001 5.8299017e+001 5.9115393e+001 6.6615393e+001 6.1273015e+001 5.7826296e+001 9.2539406e+001 4.3933852e+001 3.0126088e+001 2.1070703e+001 1.5239751e+001 1.8402028e+001 2.2644669e+001 2.6767775e+001 3.3838842e+001 2.9718862e+001 4.0241967e+001 3.7178794e+001 4.5241052e+001 4.5103824e+001 3.1157107e+001 2.7621573e+001 3.2093709e+001 4.2093709e+001 4.6414702e+001 5.0886838e+001 6.5657300e+001 6.9742588e+001 6.4334261e+001 7.4183119e+001 8.1463229e+001 8.9540916e+001 8.5245377e+001 8.1214248e+001 7.7183119e+001 7.8474713e+001 8.3218129e+001 1.0184450e+0024.5352167e+001 5.6850675e+001 4.0433852e+001 0.0000000e+000 4.9200435e+001 5.0023011e+001 7.6566903e+001 8.3272828e+001 8.9866681e+001 1.4410798e+002 1.8849159e+002 2.1997383e+002 2.0981794e+002 1.5008515e+002 1.1475067e+002 8.2668530e+001 7.4705246e+001 6.3843619e+001 4.6837089e+001 6.7988800e+001 1.8273480e+002 2.0076256e+002 2.1481794e+002 2.2654433e+002 2.0851657e+002 1.7949159e+002 1.8692462e+002 1.6226909e+002 1.5535338e+002 8.1029762e+001 9.9673358e+001 8.7968658e+001 9.1549301e+001 9.4891619e+001 8.5624041e+001 8.0624041e+001 8.5723060e+001 4.8609758e+001 4.5609758e+001 6.3287427e+001 8.3205246e+001 6.4856389e+001 5.6794131e+001 4.7363843e+001 7.9972291e+001 7.3972291e+001 6.3760655e+001 7.3958694e+001 5.0555808e+001 4.0715154e+001 3.6907267e+001 3.5303601e+001 4.3847605e+001 3.4494537e+001 4.4544413e+001 3.1060960e+001 1.8681542e+001 2.6181542e+001 3.3991791e+001 1.7392444e+001 5.2105554e+001 3.5000000e+000 1.0307764e+001 1.9363149e+001 2.5194101e+001 2.8356379e+001 3.2599019e+001 3.6722125e+001 4.3793193e+001 4.9178358e+001 5.0196317e+001 5.5196317e+001 5.5648278e+001 5.1617149e+001 3.6051630e+001 3.2516096e+001 3.6988232e+001 4.6988232e+001 5.1309225e+001 5.5781361e+001 7.0551823e+001 7.4637111e+001 6.9228784e+001 7.0796774e+001 6.3516664e+001 7.1594352e+001 8.1859032e+001 7.7827903e+001 7.3796774e+001 7.7332308e+001 8.0869284e+001 1.0089427e+0029.3742889e+001 7.8337113e+001 5.7220577e+001 4.9200435e+001 0.0000000e+000 2.9426289e+001 2.7366468e+001 3.5356854e+001 4.6954268e+001 1.0041606e+002 1.4479967e+002 1.7628191e+002 1.8655062e+002 1.2969629e+002 6.5550234e+001 6.2279671e+001 1.0424823e+002 1.1223434e+002 9.5227811e+001 1.1703955e+002 1.6234594e+002 1.7749524e+002 1.9155062e+002 1.8285241e+002 1.6482466e+002 1.3579967e+002 1.4323271e+002 1.1306865e+002 1.0615294e+002 3.1829327e+001 5.0472922e+001 3.8768223e+001 4.3633327e+001 5.1199700e+001 5.1196908e+001 5.6196908e+001 5.7780281e+001 9.4211191e+001 9.1211191e+001 9.7481303e+001 1.1274823e+002 9.4399371e+001 8.6337113e+001 6.8850280e+001 5.0657392e+001 4.4657392e+001 1.4560220e+001 2.4758259e+001 5.0000000e+000 8.4852814e+000 1.2293168e+001 1.6594331e+001 1.1708204e+001 3.4511712e+001 4.4561588e+001 2.0836971e+001 3.0518894e+001 2.3018894e+001 1.5208644e+001 3.8658304e+001 5.3758259e+001 5.2550748e+001 5.8698486e+001 6.7753871e+001 7.2460328e+001 7.5622605e+001 7.9865246e+001 8.3988352e+001 9.1059419e+001 8.6939439e+001 9.7462544e+001 9.4399371e+001 1.0246163e+002 1.0000787e+002 8.4442351e+001 8.0906817e+001 8.5378953e+001 9.5378953e+001 9.9699947e+001 1.0417208e+002 1.1894254e+002 1.2302783e+002 1.1761951e+002 1.1984752e+002 1.1256741e+002 1.2064510e+002 1.3090978e+002 1.2687865e+002 1.2284752e+002 1.2638306e+002 1.2992003e+002 1.4994502e+0029.5375178e+001 9.8420771e+001 7.7304235e+001 5.0023011e+001 2.9426289e+001 0.0000000e+000 2.7672317e+001 3.5662703e+001 4.7260117e+001 1.0072191e+002 1.4510552e+002 1.7658776e+002 1.8685647e+002 1.3000213e+002 6.5856083e+001 6.2585520e+001 1.2433189e+002 1.1386663e+002 9.6860100e+001 1.1786212e+002 1.6265179e+002 1.7780109e+002 1.9185647e+002 1.8315826e+002 1.6513050e+002 1.3610552e+002 1.4353855e+002 1.1337450e+002 1.0645879e+002 3.2135176e+001 5.0778771e+001 3.9074071e+001 4.3939176e+001 5.1505549e+001 5.1502757e+001 5.6502757e+001 5.8086130e+001 9.4517040e+001 9.1517040e+001 1.0919471e+002 1.3283189e+002 1.1448303e+002 1.0642077e+002 8.8933938e+001 5.0963241e+001 4.4963241e+001 1.4866069e+001 2.5064108e+001 3.3194889e+001 2.2754582e+001 1.8946695e+001 2.3247858e+001 3.1791862e+001 5.4595370e+001 6.4645246e+001 2.7490499e+001 3.1341469e+001 2.3841469e+001 1.6031220e+001 3.9480880e+001 5.4064108e+001 5.3373324e+001 6.0330775e+001 6.9386160e+001 7.5217112e+001 7.8379390e+001 8.2622030e+001 8.6745136e+001 9.3816204e+001 9.9201369e+001 1.0021933e+002 1.0521933e+002 1.0567129e+002 1.0164016e+002 8.6074640e+001 8.2539107e+001 8.7011243e+001 9.7011243e+001 1.0133224e+002 1.0580437e+002 1.2057483e+002 1.2466012e+002 1.1925179e+002 1.2067010e+002 1.1338999e+002 1.2146768e+002 1.3173236e+002 1.2770123e+002 1.2367010e+002 1.2720563e+002 1.3074261e+002 1.5076759e+0021.1500349e+002 9.7281187e+001 7.6164651e+001 7.6566903e+001 2.7366468e+001 2.7672317e+001 0.0000000e+000 2.4777246e+001 2.9092085e+001 7.3283506e+001 1.1766712e+002 1.4914936e+002 1.5941807e+002 1.0901221e+002 3.8183766e+001 4.1595595e+001 1.1508414e+002 1.3511375e+002 1.1810722e+002 1.4440602e+002 1.4166187e+002 1.5036268e+002 1.6441807e+002 1.5571986e+002 1.3769210e+002 1.0866712e+002 1.1610015e+002 8.5702184e+001 8.0154569e+001 5.8309519e+000 2.3106454e+001 1.1401754e+001 1.6500774e+001 2.4067147e+001 3.3334725e+001 3.5512832e+001 3.0413813e+001 7.3527115e+001 7.0527115e+001 8.8204784e+001 1.1360516e+002 1.1334344e+002 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1.0642113e+002 1.3217973e+002 1.4237776e+002 1.1261951e+002 1.0994394e+002 1.0613605e+002 1.0453238e+002 1.0591130e+002 8.3107793e+001 7.6993250e+001 1.0028974e+002 8.7910326e+001 9.5410326e+001 1.0322058e+002 8.6621228e+001 1.2133434e+002 7.2728784e+001 5.8921020e+001 4.9865635e+001 4.9094510e+001 4.5932233e+001 4.7225060e+001 4.3101954e+001 3.6030887e+001 4.1416051e+001 3.5242654e+001 3.3170505e+001 2.5108248e+001 2.9139377e+001 4.0248222e+001 3.6712688e+001 3.2240552e+001 2.4627762e+001 1.7919559e+001 1.3447423e+001 1.0433265e+001 5.4083269e+000 0.0000000e+000 9.8488578e+000 1.7128968e+001 2.5206655e+001 2.0911116e+001 1.6879987e+001 1.2848858e+001 1.4140452e+001 1.8883868e+001 3.8908852e+0014.0879744e+001 5.9081621e+001 7.4183119e+001 7.0796774e+001 1.1984752e+002 1.2067010e+002 1.4721399e+002 1.2557052e+002 1.2759865e+002 1.8183995e+002 2.2622356e+002 2.5770580e+002 2.6011167e+002 2.0037887e+002 1.7783746e+002 1.3296225e+002 6.0506493e+001 1.5234023e+001 3.2240552e+001 1.1752246e+001 2.3302852e+002 2.5105628e+002 2.6511167e+002 2.6427630e+002 2.4624855e+002 2.1722356e+002 2.2465660e+002 2.2535588e+002 2.2600047e+002 1.5167685e+002 1.4815582e+002 1.3894602e+002 1.3384700e+002 1.3262359e+002 1.2335601e+002 1.2835601e+002 1.3345503e+002 9.8903480e+001 9.5903480e+001 7.8225811e+001 6.9006493e+001 5.9143879e+001 5.1081621e+001 6.8568454e+001 1.1664781e+002 1.1626999e+002 1.3440774e+002 1.4460578e+002 1.2120290e+002 1.1136224e+002 1.0755435e+002 1.0595069e+002 1.1449469e+002 9.2956651e+001 8.6842108e+001 1.0170805e+002 8.9328629e+001 9.6828629e+001 1.0463888e+002 8.1189218e+001 1.1590233e+002 6.7296774e+001 6.8769878e+001 5.9714492e+001 5.8943368e+001 5.5781090e+001 5.7073918e+001 5.2950812e+001 4.5879744e+001 5.1264909e+001 4.5091512e+001 4.3019363e+001 3.4957106e+001 3.8988234e+001 5.0097080e+001 4.6561546e+001 4.2089410e+001 3.4476620e+001 2.7768416e+001 2.3296280e+001 2.0282123e+001 1.5257185e+001 9.8488578e+000 0.0000000e+000 7.2801099e+000 1.5357797e+001 1.1062258e+001 7.0311289e+000 3.0000000e+000 6.5355339e+000 1.0072510e+001 3.0097495e+0014.8159854e+001 6.6361731e+001 8.1463229e+001 6.3516664e+001 1.1256741e+002 1.1338999e+002 1.3993388e+002 1.3285063e+002 1.3487876e+002 1.8912006e+002 2.3350367e+002 2.6498591e+002 2.6739178e+002 2.0765898e+002 1.7811765e+002 1.4024236e+002 6.7786603e+001 2.2514132e+001 3.9520662e+001 4.4721360e+000 2.4030863e+002 2.5833639e+002 2.7239178e+002 2.7155641e+002 2.5352866e+002 2.2450367e+002 2.3193671e+002 2.2563606e+002 2.1872036e+002 1.4439674e+002 1.5543593e+002 1.4622613e+002 1.4112711e+002 1.3990370e+002 1.3063612e+002 1.3563612e+002 1.4073514e+002 1.0618359e+002 1.0318359e+002 8.5505921e+001 7.6286603e+001 6.6423989e+001 5.8361731e+001 7.5848564e+001 1.2392792e+002 1.2355010e+002 1.2712763e+002 1.3732567e+002 1.1392279e+002 1.0408213e+002 1.0027424e+002 9.8670578e+001 1.0721458e+002 9.8011202e+001 9.4122218e+001 9.4427937e+001 8.2048519e+001 8.9548519e+001 9.7358768e+001 7.3909108e+001 1.0862222e+002 6.0016664e+001 7.3824428e+001 6.6994602e+001 6.6223478e+001 6.3061200e+001 6.4354028e+001 6.0230922e+001 5.3159854e+001 5.8545019e+001 5.2371622e+001 5.0299473e+001 4.2237215e+001 4.6268344e+001 5.7377190e+001 5.3841656e+001 4.9369520e+001 4.1756730e+001 3.5048526e+001 3.0576390e+001 2.7562232e+001 2.2537295e+001 1.7128968e+001 7.2801099e+000 0.0000000e+000 8.0776872e+000 1.8342368e+001 1.4311239e+001 1.0280110e+001 1.3815644e+001 1.7352620e+001 3.7377604e+0015.6237542e+001 7.4439418e+001 8.9540916e+001 7.1594352e+001 1.2064510e+002 1.2146768e+002 1.4801157e+002 1.4092832e+002 1.4295645e+002 1.9719775e+002 2.4158136e+002 2.7306360e+002 2.7546946e+002 2.1573667e+002 1.8619533e+002 1.4832005e+002 7.0609351e+001 3.0591820e+001 4.7598349e+001 3.6055513e+000 2.4838632e+002 2.6641408e+002 2.8046946e+002 2.7963410e+002 2.6160635e+002 2.3258136e+002 2.4001440e+002 2.3371375e+002 2.2679804e+002 1.5247443e+002 1.6351361e+002 1.5430381e+002 1.4920479e+002 1.4798139e+002 1.3871381e+002 1.4371381e+002 1.4881283e+002 1.1426128e+002 1.1126128e+002 9.3583608e+001 7.8723980e+001 7.4501676e+001 6.6439418e+001 8.3926251e+001 1.3200561e+002 1.3162778e+002 1.3520532e+002 1.4540336e+002 1.2200047e+002 1.1215982e+002 1.0835193e+002 1.0674826e+002 1.1529227e+002 1.0608889e+002 1.0219990e+002 1.0250562e+002 9.0126206e+001 9.7626206e+001 1.0543646e+002 8.1986796e+001 1.1669991e+002 6.8094352e+001 8.1902116e+001 7.5072290e+001 7.4301165e+001 7.1138888e+001 7.2431715e+001 6.8308609e+001 6.1237542e+001 6.6622706e+001 6.0449309e+001 5.8377160e+001 5.0314903e+001 5.4346032e+001 6.5454877e+001 6.1919343e+001 5.7447207e+001 4.9834417e+001 4.3126213e+001 3.8654077e+001 3.0384981e+001 2.5360043e+001 2.5206655e+001 1.5357797e+001 8.0776872e+000 0.0000000e+000 1.1045361e+001 9.3407708e+000 1.3092384e+001 1.6627918e+001 1.2382152e+001 3.2407137e+0015.1942002e+001 7.0143879e+001 8.5245377e+001 8.1859032e+001 1.3090978e+002 1.3173236e+002 1.5827625e+002 1.3663278e+002 1.3866091e+002 1.9290221e+002 2.3728582e+002 2.6876806e+002 2.6898064e+002 2.0924784e+002 1.8889972e+002 1.4183122e+002 6.5579225e+001 2.6296280e+001 4.3302810e+001 1.4650912e+001 2.4189749e+002 2.5992525e+002 2.7398064e+002 2.7533856e+002 2.5731081e+002 2.2828582e+002 2.3571886e+002 2.3641814e+002 2.3706272e+002 1.6273911e+002 1.5921807e+002 1.5000827e+002 1.4490925e+002 1.4368585e+002 1.3441827e+002 1.3941827e+002 1.4451729e+002 1.0777245e+002 1.0696574e+002 8.9288068e+001 6.7694402e+001 7.0206137e+001 6.2143879e+001 7.9630712e+001 1.2771007e+002 1.2733224e+002 1.4547000e+002 1.5566804e+002 1.3226515e+002 1.2242450e+002 1.1861661e+002 1.1701295e+002 1.2555695e+002 1.0401891e+002 9.7904365e+001 1.1277030e+002 1.0039089e+002 1.0789089e+002 1.1570114e+002 9.2251476e+001 1.2696459e+002 7.8359032e+001 7.9832135e+001 7.0776750e+001 7.0005626e+001 6.6843348e+001 6.8136176e+001 6.4013070e+001 5.6942002e+001 6.2327167e+001 5.6153770e+001 5.4081621e+001 4.6019363e+001 5.0050492e+001 6.1159338e+001 5.7623804e+001 5.3151668e+001 4.5538878e+001 3.8830674e+001 3.4358538e+001 2.5354854e+001 2.0329916e+001 2.0911116e+001 1.1062258e+001 1.8342368e+001 1.1045361e+001 0.0000000e+000 4.0311289e+000 8.0622577e+000 1.1597792e+001 7.0725101e+000 2.1377558e+0014.7910873e+001 6.6112750e+001 8.1214248e+001 7.7827903e+001 1.2687865e+002 1.2770123e+002 1.5424512e+002 1.3260165e+002 1.3462978e+002 1.8887108e+002 2.3325469e+002 2.6473693e+002 2.6714279e+002 2.0741000e+002 1.8486859e+002 1.3999338e+002 6.1548096e+001 2.2265151e+001 3.9271681e+001 1.2946322e+001 2.4005965e+002 2.5808741e+002 2.7214279e+002 2.7130743e+002 2.5327968e+002 2.2425469e+002 2.3168773e+002 2.3238701e+002 2.3303159e+002 1.5870798e+002 1.5518695e+002 1.4597714e+002 1.4087812e+002 1.3965472e+002 1.3038714e+002 1.3538714e+002 1.4048616e+002 1.0593461e+002 1.0293461e+002 8.5256940e+001 6.9383209e+001 6.6175008e+001 5.8112750e+001 7.5599583e+001 1.2367894e+002 1.2330111e+002 1.4143887e+002 1.5163691e+002 1.2823402e+002 1.1839337e+002 1.1458548e+002 1.1298182e+002 1.2152582e+002 9.9987780e+001 9.3873237e+001 1.0873918e+002 9.6359757e+001 1.0385976e+002 1.1167001e+002 8.8220347e+001 1.2293346e+002 7.4327903e+001 7.5801006e+001 6.6745621e+001 6.5974497e+001 6.2812219e+001 6.4105047e+001 5.9981941e+001 5.2910873e+001 5.8296038e+001 5.2122641e+001 5.0050492e+001 4.1988234e+001 4.6019363e+001 5.7128209e+001 5.3592675e+001 4.9120539e+001 4.1507749e+001 3.4799545e+001 3.0327409e+001 2.1323725e+001 1.6298787e+001 1.6879987e+001 7.0311289e+000 1.4311239e+001 9.3407708e+000 4.0311289e+000 0.0000000e+000 4.0311289e+000 7.5666628e+000 3.0413813e+000 2.3066366e+0014.3879744e+001 6.2081621e+001 7.7183119e+001 7.3796774e+001 1.2284752e+002 1.2367010e+002 1.5021399e+002 1.2857052e+002 1.3059865e+002 1.8483995e+002 2.2922356e+002 2.6070580e+002 2.6311167e+002 2.0337887e+002 1.8083746e+002 1.3596225e+002 5.7516967e+001 1.8234023e+001 3.5240552e+001 9.4868330e+000 2.3602852e+002 2.5405628e+002 2.6811167e+002 2.6727630e+002 2.4924855e+002 2.2022356e+002 2.2765660e+002 2.2835588e+002 2.2900047e+002 1.5467685e+002 1.5115582e+002 1.4194602e+002 1.3684700e+002 1.3562359e+002 1.2635601e+002 1.3135601e+002 1.3645503e+002 1.0190348e+002 9.8903480e+001 8.1225811e+001 6.6016967e+001 6.2143879e+001 5.4081621e+001 7.1568454e+001 1.1964781e+002 1.1926999e+002 1.3740774e+002 1.4760578e+002 1.2420290e+002 1.1436224e+002 1.1055435e+002 1.0895069e+002 1.1749469e+002 9.5956651e+001 8.9842108e+001 1.0470805e+002 9.2328629e+001 9.9828629e+001 1.0763888e+002 8.4189218e+001 1.1890233e+002 7.0296774e+001 7.1769878e+001 6.2714492e+001 6.1943368e+001 5.8781090e+001 6.0073918e+001 5.5950812e+001 4.8879744e+001 5.4264909e+001 4.8091512e+001 4.6019363e+001 3.7957106e+001 4.1988234e+001 5.3097080e+001 4.9561546e+001 4.5089410e+001 3.7476620e+001 3.0768416e+001 2.6296280e+001 1.7292596e+001 1.2267659e+001 1.2848858e+001 3.0000000e+000 1.0280110e+001 1.3092384e+001 8.0622577e+000 4.0311289e+000 0.0000000e+000 3.5355339e+000 7.0725101e+000 2.7097495e+0014.5171338e+001 6.3373215e+001 7.8474713e+001 7.7332308e+001 1.2638306e+002 1.2720563e+002 1.5374952e+002 1.2986212e+002 1.3189025e+002 1.8613155e+002 2.3051516e+002 2.6199740e+002 2.6274665e+002 2.0301385e+002 1.8212905e+002 1.3559724e+002 5.3981433e+001 1.9525616e+001 3.6532146e+001 1.3022367e+001 2.3566351e+002 2.5369126e+002 2.6774665e+002 2.6856790e+002 2.5054014e+002 2.2151516e+002 2.2894819e+002 2.2964747e+002 2.3253600e+002 1.5821238e+002 1.5244741e+002 1.4323761e+002 1.3813859e+002 1.3691519e+002 1.2764761e+002 1.3264761e+002 1.3774663e+002 1.0153846e+002 9.8538463e+001 8.0860793e+001 6.2481433e+001 6.3435472e+001 5.5373215e+001 7.2860048e+001 1.2093940e+002 1.2056158e+002 1.4094328e+002 1.5114131e+002 1.2675996e+002 1.1789777e+002 1.1408989e+002 1.1248622e+002 1.2005175e+002 9.7248245e+001 9.1133701e+001 1.0824358e+002 9.5864162e+001 1.0336416e+002 1.1117441e+002 8.7724752e+001 1.2243786e+002 7.3832308e+001 7.3061471e+001 6.4006086e+001 6.3234962e+001 6.0072684e+001 6.1365512e+001 5.7242406e+001 5.0171338e+001 5.5556503e+001 4.9383106e+001 4.7310957e+001 3.9248699e+001 4.3279828e+001 5.4388674e+001 5.0853140e+001 4.6381004e+001 3.8768214e+001 3.2060010e+001 2.7587874e+001 1.3757062e+001 8.7321246e+000 1.4140452e+001 6.5355339e+000 1.3815644e+001 1.6627918e+001 1.1597792e+001 7.5666628e+000 3.5355339e+000 0.0000000e+000 4.7434165e+000 2.4768401e+0014.9914755e+001 6.8116631e+001 8.3218129e+001 8.0869284e+001 1.2992003e+002 1.3074261e+002 1.5728650e+002 1.3460553e+002 1.3663366e+002 1.9087496e+002 2.3525857e+002 2.6674081e+002 2.6749006e+002 2.0775727e+002 1.8687247e+002 1.4034065e+002 5.8724850e+001 2.4269033e+001 4.1275562e+001 1.5987703e+001 2.4040692e+002 2.5843468e+002 2.7249006e+002 2.7331131e+002 2.5528356e+002 2.2625857e+002 2.3369161e+002 2.3439089e+002 2.3607298e+002 1.6174936e+002 1.5719083e+002 1.4798103e+002 1.4288201e+002 1.4165860e+002 1.3239102e+002 1.3739102e+002 1.4249004e+002 1.0628188e+002 1.0328188e+002 8.5604210e+001 6.6341828e+001 6.8178889e+001 6.0116631e+001 7.7603464e+001 1.2568282e+002 1.2530500e+002 1.4448025e+002 1.5467829e+002 1.3127541e+002 1.2143475e+002 1.1762686e+002 1.1602320e+002 1.2456720e+002 1.0199166e+002 9.5877118e+001 1.1178056e+002 9.9401139e+001 1.0690114e+002 1.1471139e+002 9.1261728e+001 1.2597484e+002 7.7369284e+001 7.7804888e+001 6.8749503e+001 6.7978378e+001 6.4816101e+001 6.6108928e+001 6.1985822e+001 5.4914755e+001 6.0299919e+001 5.4126522e+001 5.2054373e+001 4.3992116e+001 4.8023245e+001 5.9132090e+001 5.5596556e+001 5.1124420e+001 4.3511630e+001 3.6803427e+001 3.2331291e+001 1.8500479e+001 1.3475541e+001 1.8883868e+001 1.0072510e+001 1.7352620e+001 1.2382152e+001 7.0725101e+000 3.0413813e+000 7.0725101e+000 4.7434165e+000 0.0000000e+000 2.0024984e+0016.9939739e+001 8.0727959e+001 1.0184450e+002 1.0089427e+002 1.4994502e+002 1.5076759e+002 1.5992201e+002 1.4524923e+002 1.3365182e+002 1.8789311e+002 2.3227672e+002 2.6375896e+002 2.4760308e+002 1.8787028e+002 1.8389062e+002 1.2045367e+002 5.4816844e+001 4.4294017e+001 6.1300547e+001 3.6012688e+001 2.2051994e+002 2.3854769e+002 2.5260308e+002 2.7032947e+002 2.5230171e+002 2.2327672e+002 2.3070976e+002 2.3140904e+002 2.4007658e+002 1.6575296e+002 1.5420898e+002 1.5134215e+002 1.4624313e+002 1.3867675e+002 1.2940918e+002 1.2440918e+002 1.2950819e+002 8.6394892e+001 8.9394892e+001 8.1696204e+001 4.6316844e+001 6.4665701e+001 7.2727959e+001 9.0214792e+001 1.3611738e+002 1.4211738e+002 1.6450524e+002 1.7282403e+002 1.5130039e+002 1.4145974e+002 1.3765185e+002 1.3604818e+002 1.4459219e+002 1.2201665e+002 1.1450348e+002 1.3180554e+002 1.1942612e+002 1.2692612e+002 1.3473637e+002 1.1128671e+002 1.4599982e+002 9.7394269e+001 9.7829872e+001 8.8774487e+001 8.8003363e+001 8.4841085e+001 8.6133913e+001 8.2010807e+001 7.4939739e+001 8.0324904e+001 7.4151507e+001 7.2079358e+001 6.4017100e+001 6.8048229e+001 7.9157075e+001 7.5621541e+001 7.1149405e+001 6.3536615e+001 5.6828411e+001 5.2356275e+001 3.8525463e+001 3.3500525e+001 3.8908852e+001 3.0097495e+001 3.7377604e+001 3.2407137e+001 2.1377558e+001 2.3066366e+001 2.7097495e+001 2.4768401e+001 2.0024984e+001 0.0000000e+000;
xu=17 21 22 17 21 25 24 24 21 16 26 24 22 25 21 26 25 19 18 19 14 14 24 11 16 12 8 13 14 21 16 15 14 17 14 11 19 12 14 17 14 18 17 11 20 12 16 14 12 11 20 16 14 19 20 5 8 11 9 7 6 12 20 18 17 21 18 19 11 19 11 18 12 21 8 11 8 8 16 18 14 11 19 10 12 24 11 19 14 25 19 18;
enddata
最后根据程序可以得出：
（2）
在问题二中：
将是否选中的城市考虑为0-1变量，在考虑到成本最小的情况下，建立方程式：
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