问题描述
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）。
一、问题一
法一：（1）浏览一下大致的数据
（2）要选择一个配送中心使得到20个直销中心的配送费用最短，而配送费用只与距离有关，因此很容易想到要求配送中心到各个直销中心的路径最短
（3）要想求路径，首先要将数据进行预处理，把各个位置的实际地理位置图画出来
（4）求最短路可以使用Floyd算法（我这里使用的matlab里面的一个distances()函数，以及自带的画图函数graph()，不了解可以查看一下matlab的解释）
clc;clear all;close all;
%导入数据
cite1 = xlsread("cite.xls", "城市及销售中心数据",'A2:D93' );
cite2 = xlsread("cite.xls", "全省公路路线",'A2:B141' );
%提取城市坐标
location = [cite1(:,2),cite1(:,3)];
%计算公路的起点城市与公路的终点城市的距离
for i=1:length(cite2)
sx=location(cite2(i,1),1);%起始城市的横坐标
ex=location(cite2(i,2),1);%终止城市的横坐标
sy=location(cite2(i,1),2);%起始城市的纵坐标
ey=location(cite2(i,2),2);%终止城市的纵坐标
dist(i)=sqrt(abs(sx-ex)^2+abs(sy-ey)^2);%勾股定理求距离
end
% 求最短路问题
s = cite2(:,1)';
t = cite2(:,2)';
w = dist;
G = graph(s,t,w);%无向图
% G = digraph(s,t,w);%有向图
figure,plot(G, 'EdgeLabel', G.Edges.Weight, 'linewidth', 2)
set( gca, 'XTick', [], 'YTick', [] );
%这个D值在第二三问中要用到
D = distances(G);%D为两两节点之间的最短距离
temp = 0;
for i=1:92
for j=1:20
temp = temp+D(i,j);
end
acc_dist(i) = temp;
temp = 0;
end
format long g
index=find(acc_dist==min(acc_dist))
min(acc_dist)
myplot = plot(G, 'EdgeLabel', G.Edges.Weight, 'linewidth', 2); %首先将图赋给一个变量
for i=1:20
[P,d] = shortestpath(G,35,i);
% P(i)=P;
writematrix(P,'M.xls','WriteMode','append')
% 在图中高亮我们的最短路径
highlight(myplot, P, 'EdgeColor', 'r') %对这个变量即我们刚刚绘制的图形进行高亮处理（给边加上r红色）
hold on
end
运行上面的代码可以得到这个图（这个图是函数自动生成的，并不是实际的位置点）红色标出的为最短路径，两点之间的距离也显示出来了
此外可以计算出配送中心的城市标号为35
接下来就是绘制实际的地理位置图，并把直销中心，配送中心，最短路标记出来
clc;clear all;close all;
%导入数据
cite1 = xlsread("cite.xls", "城市及销售中心数据",'A2:D93' );
cite2 = xlsread("cite.xls", "全省公路路线",'A2:B141' );
%提取城市坐标
location = [cite1(:,2),cite1(:,3)];
%绘制城市坐标散点图
for i=1:length(location)
%将前20号的直销中心单独标出
if i<=20
plot(location(i,1),location(i,2),'r*','MarkerSize',8) %坐标点用红色*表示
text(location(i,1),location(i,2),num2str(cite1(i,1)),'FontSize',8);%标记城市标号
hold on
%其余点绘制
else
plot(location(i,1),location(i,2),'b.','MarkerSize',15)%坐标点用蓝色点表示
text(location(i,1),location(i,2),num2str(cite1(i,1)),'FontSize',8);%标记城市标号
hold on;
end
end
%连接各城市间的公路
for i=1:length(cite2)
start_x=[location(cite2(i,1),1),location(cite2(i,2),1)];%起始城市的横坐标与结束城市的横坐标
end_y=[location(cite2(i,1),2),location(cite2(i,2),2)];%起始城市的纵坐标与结束城市的纵坐标
plot(start_x,end_y,'b-')%画线
hold on;
end
% 画35到前20最短路径
P=xlsread('M.xls');
for i=1:20
for j=1:length(find(isnan(P(i,:))==0))-1
start_x=[location(P(i,j),1),location(P(i,j+1),1)];%起始城市的横坐标与结束城市的横坐标
end_y=[location(P(i,j),2),location(P(i,j+1),2)];%起始城市的纵坐标与结束城市的纵坐标
plot(start_x,end_y,'r-')%画线
hold on;
end
end
%将配送中心单独标记出来，方便区分
%计算出配送中心的标号为城市35
plot(location(35,1),location(35,2),'gp','MarkerSize',8) %坐标点用绿色*表示
法二：lingo
这里面的data中的d变量为两两之间的最短距离，我用的第一问distances()函数求出的，当然可以使用Floyd求出由于这里的数据量太大不好放，下面几问就不再放数据了！
sets:
dmc/1..92/:u;!直销中心i;
dc/1..92/:y;!配送中心j;
tlink(dmc,dc):x,d;
endsets
min=@sum(dmc(i)|i#LE#20:@sum(dc(j):d(i,j)*x(i,j)*u(i)))*2;
@for(dmc(i)|i#LE#20:@sum(dc(j):x(i,j))=1);
@sum(dc(j):y(j))=1;
@for(dc(j):@for(dmc(i)|i#LE#20:x(i,j)<=y(j));
@for(dc(j):x(j,j)=y(j));
@for(tlink:@bin(x));
@for(dc:@bin(y)));
data:
d=
0 18.9874900741771 38.8388424388990 45.3521671649493 93.7428887802830 95.3751780750068 115.003493341272 90.2262468980646 92.2543782736907 146.495675153162 190.879287179071 222.361527292051 220.017534167589 160.284737217503 142.493184810572 92.8681220547703 35.9120534630931 25.6457218732303 17.5834641249318 52.6319903264411 192.934392652132 210.962149029452 225.017534167589 228.932027950891 210.904271573571 181.879287179071 189.312321552730 190.011602292639 195.158061940366 120.834445236117 112.811540651260 103.601739090281 98.5027195766880 97.2793160842512 88.0117375865715 90.8236321229407 95.9226516365334 58.8093493229175 55.8093493229175 38.1316797932538 44.4120534630931 26.0631956612970 18.0009379129984 28.4743230546823 81.3035336540721 80.9257092791955 108.303108558844 118.501147586030 88.7428887802830 86.0673210334800 82.2594344805481 80.6557679474780 82.0346848477836 59.2311763458008 51.4978313400711 76.4131272603587 64.0337088572188 71.5337088572188 79.3439585331254 62.7446111543991 97.4577210698187 48.8521671649493 35.0444031009052 25.9890179627678 23.5990917847708 20.4368141246024 16.1941734374831 12.0710678118655 5 10.3851648071345 11.4031242374328 16.4031242374329 10.2961109172201 6.26498204307083 9.30053761886914 12.8360715248019 16.4031242374329 6.40312423743285 13.1113281699322 17.5834641249318 32.3539258057297 36.4392135935608 31.0308866803649 40.8797444821610 48.1598543714415 56.2375416019050 51.9420022304595 47.9108733563102 43.8797444821610 45.1713381918473 49.9147546820999 69.9397390766007
18.9874900741771 0 21.1165363301181 56.8506754850531 78.3371132868933 98.4207712225369 97.2811872324914 72.5039407892838 74.5320721649099 128.773369044382 173.156981070290 204.639221183271 201.030044093412 141.297247143326 124.770878701791 73.8806319805931 25.9111155500947 43.8475984199131 36.5709541991089 70.8338668731238 173.946902577955 191.974658955275 206.030044093412 211.209721842111 193.181965464791 164.156981070290 171.590015443949 172.289296183858 177.435755831585 103.112139127337 95.0892345424794 85.8794329815000 80.7804134679072 79.5570099754704 70.2894314777906 71.8361420487635 76.9351615623563 39.8218592487403 36.8218592487403 19.1441897190766 34.4111155500947 16.0622577482986 8 9.48683298050514 63.5812275452913 63.2034031704146 92.8973330654544 103.095372092640 73.3371132868933 83.2819622861648 79.4740757332328 75.1729130997115 66.6289093543940 43.8254008524112 33.7755252312903 79.4155537868308 75.5322171773225 83.0322171773225 82.3895516806555 74.2431194745029 108.956229389922 60.3506754850531 46.5429114210089 37.4875262828715 31.6565743880262 28.4942967278578 24.2516560407385 21.0585578860426 13.9874900741771 8.60232526704263 20.3906143116100 16.0622577482986 24.1245154965971 25.2524721172480 25.5862504551113 29.1217843610441 33.5939203160436 25.3906143116100 32.0988182441094 36.5709541991089 50.5558023524125 54.6410901402436 49.2327632270476 59.0816210288437 66.3617309181242 74.4394181485878 70.1438787771423 66.1127499029930 62.0816210288437 63.3732147385301 68.1166312287827 80.7279591385777
38.8388424388990 21.1165363301181 0 40.4338517511550 57.2205769567752 77.3042348924187 76.1646509023732 51.3874044591656 53.4155358347918 107.656832714263 152.040444740172 183.522684853152 187.405069790790 127.672272840703 103.654342371673 60.2556576779707 47.0276518802128 58.9490961866828 41.9425665283851 85.9353646398936 160.321928275332 178.349684652652 192.405069790790 190.093185511992 172.065429134672 143.040444740172 150.473479113831 151.172759853740 156.319219501467 81.9956027972185 73.9726982123613 64.7628966513818 59.6638771377891 58.4404736453522 49.1728951476725 54.1728951476725 59.2719146612653 60.9383955788585 57.9383955788585 40.2607260491948 55.5276518802128 37.1787940784167 29.1165363301181 11.6297033496130 42.4646912151731 42.0868668402965 71.7807967353362 81.9788357625218 52.2205769567752 62.1654259560466 58.3575394031147 54.0563767695933 45.5123730242758 22.7088645222931 12.6589889011722 58.2990174567126 59.1153934434244 66.6153934434244 61.2730153505373 57.8262957406048 92.5394056560244 43.9338517511550 30.1260876871109 21.0707025489735 15.2397506541282 18.4020283142966 22.6446690014158 26.7677746270335 33.8388424388990 29.7188615971608 40.2419666763318 37.1787940784167 45.2410518267153 45.1038244819698 31.1571066775222 27.6215727715894 32.0937087265890 42.0937087265890 46.4147024833847 50.8868384383843 65.6573001191822 69.7425879070133 64.3342609938173 74.1831187956134 81.4632286848940 89.5409159153575 85.2453765439120 81.2142476697627 77.1831187956134 78.4747125052998 83.2181289955524 101.844495468696
45.3521671649494 56.8506754850531 40.4338517511550 0 49.2004352427692 50.0230109100575 76.5669034961960 83.2728284880542 89.8666812150673 144.107978094539 188.491590120447 219.973830233428 209.817942572597 150.085145622510 114.750669680270 82.6685304597777 74.7052463448907 63.8436190552409 46.8370893969432 67.9888003074942 182.734801057139 200.762557434459 214.817942572597 226.544330892268 208.516574514948 179.491590120447 186.924624494107 162.269087162336 155.353378564630 81.0297618603813 99.6733576579070 87.9686577471873 91.5493011666776 94.8916190256278 85.6240405279480 80.6240405279480 85.7230600415408 48.6097577279248 45.6097577279248 63.2874272575885 83.2052463448907 64.8563885430946 56.7941307947961 47.3638425045479 79.9722908691850 73.9722908691850 63.7606550213303 73.9586940485158 50.5558084603455 40.7151538685307 36.9072673155987 35.3036007825286 43.8476045278462 34.4945373089398 44.5444129300607 31.0609600954094 18.6815416922694 26.1815416922694 33.9917913681761 17.3924439894498 52.1055539048694 3.50000000000000 10.3077640640442 19.3631492021816 25.1941010970269 28.3563787571953 32.5990194443145 36.7221250699322 43.7931928817977 49.1783576889322 50.1963171192305 55.1963171192305 55.6482780821695 51.6171492080202 36.0516295460802 32.5160956401475 36.9882315951471 46.9882315951471 51.3092253519427 55.7813613069423 70.5518229877402 74.6371107755713 69.2287838623754 70.7967742417752 63.5166643524946 71.5943515829582 81.8590319900737 77.8279031159244 73.7967742417752 77.3323081477079 80.8692843810735 100.894268775574
93.7428887802830 78.3371132868933 57.2205769567752 49.2004352427692 0 29.4262885258795 27.3664682534267 35.3568541216465 46.9542676263897 100.416058844392 144.799670870300 176.281910983281 186.550621456981 129.696286006540 65.5502344375003 62.2796708438072 104.248228836988 112.234340670575 95.2278110122768 117.039548145494 162.345941441169 177.495236318844 191.550621456981 182.852411642121 164.824655264801 135.799670870300 143.232705243959 113.068651919567 106.152943321860 31.8293266176121 50.4729224151377 38.7682225044181 43.6333268002699 51.1996997754807 51.1969083135089 56.1969083135089 57.7802809049178 94.2111911135321 91.2111911135321 97.4813030059700 112.748228836988 94.3993710351919 86.3371132868933 68.8502803063882 50.6573917405156 44.6573917405156 14.5602197785610 24.7582588057466 5 8.48528137423857 12.2931679271705 16.5943305606918 11.7082039324994 34.5117124344821 44.5615880556030 20.8369712478111 30.5188935504998 23.0188935504998 15.2086438745932 38.6583038485497 53.7582588057466 52.5507478379995 58.6984856793778 67.7538708175152 72.4603276109034 75.6226052710717 79.8652459581910 83.9883515838087 91.0594193956742 86.9394385539360 97.4625436331070 94.3993710351919 102.461628783490 100.007870823354 84.4423511614138 80.9068172554811 85.3789532104807 95.3789532104807 99.6999469672764 104.172082922276 118.942544603074 123.027832390905 117.619505477709 119.847522079775 112.567412190494 120.645099420958 130.909779828073 126.878650953924 122.847522079775 126.383055985707 129.920032219073 149.945016613574
95.3751780750068 98.4207712225368 77.3042348924187 50.0230109100575 29.4262885258795 0 27.6723172221842 35.6627030904039 47.2601165951471 100.721907813149 145.105519839058 176.587759952038 186.856470425739 130.002134975297 65.8560834062578 62.5855198125646 124.331886772632 113.866629965298 96.8601003070006 117.862123812782 162.651790409926 177.801085287601 191.856470425739 183.158260610878 165.130504233558 136.105519839058 143.538554212717 113.374500888325 106.458792290618 32.1351755863696 50.7787713838952 39.0740714731756 43.9391757690274 51.5055487442381 51.5027572822664 56.5027572822664 58.0861298736753 94.5170400822896 91.5170400822896 109.194709611953 132.831886772632 114.483028970835 106.420771222537 88.9339382420317 50.9632407092731 44.9632407092731 14.8660687473185 25.0641077745041 33.1948885511466 22.7545820422360 18.9466954893040 23.2478581228254 31.7918618681429 54.5953703701257 64.6452459912466 27.4904988099446 31.3414692177881 23.8414692177881 16.0312195418814 39.4808795158379 54.0641077745041 53.3733235052877 60.3307749741016 69.3861601122390 75.2171120070843 78.3793896672527 82.6220303543720 86.7451359799897 93.8162037918551 99.2013685989896 100.219328029288 105.219328029288 105.671288992227 101.640160118078 86.0746404561377 82.5391065502049 87.0112425052045 97.0112425052045 101.332236262000 105.804372217000 120.574833897798 124.660121685629 119.251794772433 120.670097747063 113.389987857782 121.467675088246 131.732355495361 127.701226621212 123.670097747063 127.205631652996 130.742607886361 150.767592280862
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47.9108733563102 66.1127499029930 81.2142476697627 77.8279031159244 126.878650953924 127.701226621212 154.245119207351 132.601652128928 134.629783504554 188.871080384026 233.254692409934 264.736932522915 267.142793996405 207.409997046319 184.868590041436 139.993381883586 61.5480959111665 22.2651514830799 39.2716811413776 12.9463221215987 240.059652480948 258.087408858268 272.142793996405 271.307433181755 253.279676804435 224.254692409934 231.687726783594 232.387007523503 233.031594275784 158.707977571536 155.186945882124 145.977144321145 140.878124807552 139.654721315115 130.387142817435 135.387142817435 140.486162331028 105.934609151733 102.934609151733 85.2569396220697 69.3832092481329 66.1750076512916 58.1127499029930 75.5995828834981 123.678938884936 123.301114510059 141.438870732485 151.636909759671 128.234024171500 118.393369579685 114.585483026753 112.981816493683 121.525820239001 99.9877797191722 93.8732365709349 108.739175806564 96.3597574034241 103.859757403424 111.670007079331 88.2203471053742 122.933457020794 74.3279031159244 75.8010064742766 66.7456213361392 65.9744970156345 62.8122193554662 64.1050467937934 59.9819411681757 52.9108733563102 58.2960381634447 52.1226410884120 50.0504921546945 41.9882344063959 46.0193632805452 57.1282088041060 53.5926748981733 49.1205389431737 41.5077491188774 34.7995451863780 30.3274092313784 21.3237251889289 16.2987873783685 16.8799866759454 7.03112887414928 14.3112387634298 9.34077084613470 4.03112887414928 0 4.03112887414928 7.56666278008201 3.04138126514911 23.0663656596499
43.8797444821610 62.0816210288437 77.1831187956134 73.7967742417752 122.847522079775 123.670097747063 150.213990333201 128.570523254779 130.598654630405 184.839951509877 229.223563535785 260.705803648766 263.111665122256 203.378868172170 180.837461167286 135.962253009437 57.5169670370172 18.2340226089306 35.2405522672283 9.48683298050514 236.028523606799 254.056279984119 268.111665122256 267.276304307606 249.248547930286 220.223563535785 227.656597909444 228.355878649353 229.000465401635 154.676848697387 151.155817007975 141.946015446995 136.846995933402 135.623592440966 126.356013943286 131.356013943286 136.455033456879 101.903480277584 98.9034802775841 81.2258107479204 66.0169670370172 62.1438787771423 54.0816210288437 71.5684540093489 119.647810010787 119.269985635910 137.407741858336 147.605780885521 124.202895297351 114.362240705536 110.554354152604 108.950687619534 117.494691364852 95.9566508450230 89.8421076967856 104.708046932415 92.3286285292748 99.8286285292748 107.638878205181 84.1892182312250 118.902328146645 70.2967742417752 71.7698776001273 62.7144924619899 61.9433681414853 58.7810904813169 60.0739179196441 55.9508122940264 48.8797444821610 54.2649092892955 48.0915122142628 46.0193632805452 37.9571055322466 41.9882344063959 53.0970799299567 49.5615460240240 45.0894100690244 37.4766202447281 30.7684163122287 26.2962803572292 17.2925963147797 12.2676585042192 12.8488578017961 3 10.2801098892805 13.0923842559691 8.06225774829855 4.03112887414928 0 3.53553390593274 7.07251013929838 27.0974945337992
45.1713381918473 63.3732147385301 78.4747125052998 77.3323081477079 126.383055985707 127.205631652996 153.749524239134 129.862116964465 131.890248340092 186.131545219563 230.515157245472 261.997397358452 262.746647616851 203.013850666765 182.129054876973 135.597235504032 53.9814331310845 19.5256163186170 36.5321459769147 13.0223668864379 235.663506101394 253.691262478714 267.746647616851 268.567898017292 250.540141639972 221.515157245472 228.948191619131 229.647472359040 232.535999307568 158.212382603319 152.447410717661 143.237609156682 138.138589643089 136.915186150652 127.647607652972 132.647607652972 137.746627166565 101.538462772179 98.5384627721794 80.8607932425157 62.4814331310845 63.4354724868286 55.3732147385301 72.8600477190352 120.939403720473 120.561579345596 140.943275764268 151.141314791454 126.759956989191 117.897774611469 114.089888058537 112.486221525467 120.051753056692 97.2482445547093 91.1337014064720 108.243580838348 95.8641624352076 103.364162435208 111.174412111114 87.7247521371577 122.437862052577 73.8323081477079 73.0614713098137 64.0060861716763 63.2349618511716 60.0726841910033 61.3655116293305 57.2424060037128 50.1713381918473 55.5565029989818 49.3831059239491 47.3109569902315 39.2486992419330 43.2798281160823 54.3886736396431 50.8531397337104 46.3810037787108 38.7682139544145 32.0600100219151 27.5878740669155 13.7570624088469 8.73212459828649 14.1404515114825 6.53553390593274 13.8156437952133 16.6279181619019 11.5977916542313 7.56666278008201 3.53553390593274 0 4.74341649025257 24.7684008847534
49.9147546820999 68.1166312287827 83.2181289955524 80.8692843810735 129.920032219073 130.742607886361 157.286500472500 134.605533454718 136.633664830344 190.874961709816 235.258573735724 266.740813848705 267.490064107104 207.757267157017 186.872471367225 140.340651994285 58.7248496213370 24.2690328088695 41.2755624671673 15.9877033867478 240.406922591646 258.434678968966 272.490064107104 273.311314507545 255.283558130225 226.258573735724 233.691608109383 234.390888849292 236.072975540933 161.749358836685 157.190827207914 147.981025646934 142.882006133341 141.658602640905 132.391024143225 137.391024143225 142.490043656818 106.281879262432 103.281879262432 85.6042097327683 66.3418279829838 68.1788889770812 60.1166312287827 77.6034642092878 125.682820210725 125.304995835849 144.480251997634 154.678291024820 131.275405436649 121.434750844834 117.626864291903 116.023197758832 124.567201504150 101.991661044962 95.8771178967245 111.780557071713 99.4011386685732 106.901138668573 114.711388344480 91.2617283705233 125.974838285943 77.3692843810735 77.8048878000663 68.7495026619288 67.9783783414242 64.8161006812558 66.1089281195830 61.9858224939654 54.9147546820999 60.2999194892344 54.1265224142017 52.0543734804841 43.9921157321856 48.0232446063348 59.1320901298957 55.5965562239629 51.1244202689634 43.5116304446671 36.8034265121677 32.3312905571681 18.5004788990995 13.4755410885391 18.8838680017350 10.0725101392984 17.3526200285789 12.3821521112838 7.07251013929838 3.04138126514911 7.07251013929838 4.74341649025257 0 20.0249843945008
69.9397390766007 80.7279591385777 101.844495468696 100.894268775574 149.945016613574 150.767592280862 159.922007408294 145.249229435072 133.651815930329 187.893112809801 232.276724835709 263.758964948690 247.603077287858 187.870280337772 183.890622467210 120.453665175039 54.8168435884830 44.2940172033703 61.3005468616681 36.0126877812486 220.519935772401 238.547692149721 252.603077287858 270.329465607530 252.301709230210 223.276724835709 230.709759209368 231.409039949277 240.076576007387 165.752959303139 154.208978307899 151.342146229693 146.243126716100 138.676753740889 129.409175243210 124.409175243210 129.508194756802 86.3948924431865 89.3948924431865 81.6962036999142 46.3168435884830 64.6657013902791 72.7279591385777 90.2147921190828 136.117379175709 142.117379175709 164.505236392135 172.824027115004 151.300389831150 141.459735239335 137.651848686403 136.048182153333 144.592185898651 122.016645439463 114.503484369868 131.805541466214 119.426123063074 126.926123063074 134.736372738981 111.286712765024 145.999822680444 97.3942687755743 97.8298721945671 88.7744870564296 88.0033627359250 84.8410850757566 86.1339125140838 82.0108068884662 74.9397390766007 80.3249038837352 74.1515068087025 72.0793578749849 64.0171001266864 68.0482290008356 79.1570745243965 75.6215406184637 71.1494046634642 63.5366148391678 56.8284109066685 52.3562749516689 38.5254632936003 33.5005254830398 38.9088523962358 30.0974945337992 37.3776044230797 32.4071365057846 21.3775583264320 23.0663656596499 27.0974945337992 24.7684008847534 20.0249843945008 0;
u=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
运行出结果
二、问题二
简要分析：要求成本最小的5年计划配送计划，成本（配送费，建设费）最小，表中给的路费为月计费，目标函数中的路费要乘以60=5年*12月
sets:
dmc/1..92/:u;!直销中心i;
dc/1..92/:y;!配送中心j;
tlink(dmc,dc):x,d;
endsets
min=@sum(dmc(i)|i#LE#20:@sum(dc(j):d(i,j)*x(i,j)*u(i)))*2*60+300000*@sum(dc(j):y(j));
@for(dmc(i)|i#LE#20:@sum(dc(j):x(i,j))=1);
@for(dc(j):@for(dmc(i)|i#LE#20:x(i,j)<=y(j));
@for(dc(j):x(j,j)=y(j));
@for(tlink:@bin(x));
@for(dc:@bin(y)));
data:
!省略自己补充
enddata
结果：
所以应该设立三个配送中心分别为8、11、69
三、问题三
简要分析： 比起第二问，目标函数要算上收益再减去成本即为最后的利润
sets:
dmc/1..92/:u,z;!直销中心i;
dc/1..92/:y;!配送中心j;
tlink(dmc,dc):x,d;
endsets
max=@sum(dmc(i):z(i)*u(i))*300*5*12-@sum(dmc(i):@sum(dc(j):d(i,j)*x(i,j)*u(i)))*2*60-@sum(dc(j):y(j))*300000;
@for(dmc(i):@sum(dc(j):x(i,j))=z(i));
@sum(dmc(i):z(i))=20;
@for(dc(j):@for(dmc(i):x(i,j)<=y(j));
@for(dc(j):x(j,j)=y(j));
@for(tlink:@bin(x));
@for(dc:@bin(y)));
@for(dmc:@bin(z));
data:
!省略自己补充
enddata
结果：
设立3个配送中心
20个直销中心
文章来源：https://www.toymoban.com/news/detail-455473.html
四、问题四
问题四有多种做法，这里为老师给的一种参考做法
文章来源地址https://www.toymoban.com/news/detail-455473.html
model:
sets:
nodesr/n1..n92/:xu,ddist;!一般城市集合;
nodesc/m1..m92/:y;!配送中心集合;
nodest/t1..t92/:z,xxu;!直销中心集合;!xxu为直销中心的需求量;
links(nodest,nodesc): dist,x;!直销中心和配送中心下标;
links1(nodesr,nodest): dist1,ddist2,h;!一般城市和直销中心集合.h(i,j)为判定城市i是否去直销中心j购物的0-1变量;
endsets
!目标函数;
min=zz;
zz=@sum(nodesc(J): y(J))*300000+@sum(nodest(I):@sum(nodesc(J): dist(I,J)*x(I,J)))*2*60;
!约束条件;
@for(nodest(I):@sum(nodesc(J):x(I,J))=xxu(I) );!配送量=需求量;
@sum(nodest(I):@sum(nodesc(J):x(I,J)))=1491;!总需求平衡;
@sum(nodest(I):z(I))=20;
@for(nodesc(J):@for(nodest(I):x(I,J)<=800*y(J)));!反映x与y的关系;
@for(nodesr(i):@for(nodest(k)|i#NE#k:ddist2(i,k)=dist1(i,k)*(1001-1000*z(k))+1000*z(i)));!z(k)=0,则城市i至k的距离换算为无穷大；z(i)=1,则城市i至k的距离换算为无穷大;
@for(nodesr(i):@for(nodest(k)|i#EQ#k:ddist2(i,k)=1000));!i=k,则城市i至k的距离换算为无穷大;
!目前ddist2矩阵中，只有一般城市i到直销中心k的距离才为真实距离，其它都为无穷大;
@for(nodesr(i):@for(nodest(k):ddist2(i,k)>=ddist(i)));
@for(nodesr(i):@for(nodest(k):ddist2(i,k)-ddist(i)<=1000000*h(i,k)));
@for(nodesr(i):@sum(nodest(k):h(i,k))=92-1);
@for(nodest(J):xxu(J)=xu(J)*z(J)+@sum(nodesr(I) |I#NE#J: xu(I)*(1-h(I,J))));
@for(links1:@bin(t));
@for(links1:@bin(h));
@for(nodesc:@bin(y));
@for(nodesr:@bin(z));
!@FOR( nodest( I): @PRIORITY( z(I), 100));
!@FOR(links: @PRIORITY( x, 20));
calc:
!dist1=dist;
endcalc
data:
!和上面一样，省略
enddata
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