数学建模讲义_分类_其他_其他下载-pudn.com

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/6288553d16e0ca7141f741c4/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6288553d16e0ca7141f741c4/bg1.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">数学建模</div><div class="t m0 x2 h4 y3 ff1 fs1 fc0 sc0 ls0 ws0">下　册</div><div class="t m0 x3 h5 y4 ff1 fs2 fc0 sc0 ls0 ws0">主讲：梁满发</div><div class="t m0 x4 h6 y5 ff2 fs3 fc0 sc1 ls0 ws0">Email<span class="ff1 sc0">：</span>mmfliang@scut.edu.cn</div><div class="t m0 x5 h6 y6 ff1 fs3 fc0 sc0 ls0 ws0">华南理工大学理学院应用数学系</div><div class="t m0 x6 h6 y7 ff1 fs3 fc0 sc0 ls0 ws0">２００３．７</div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6288553d16e0ca7141f741c4/bg2.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x7 h7 y8 ff1 fs4 fc0 sc0 ls0 ws0">目录</div><div class="t m0 x8 h8 y9 ff1 fs5 fc0 sc1 ls0 ws0">目　　录</div><div class="t m0 x9 h9 ya ff1 fs6 fc0 sc0 ls0 ws0">第六讲 运筹学模型<span class="ff2 sc1">..............................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>1</span></div><div class="t m0 xa h9 yb ff1 fs6 fc0 sc1 ls0 ws0">问题一：运输问题<span class="ff3">...........................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>1</span></div><div class="t m0 xa h9 yc ff1 fs6 fc0 sc1 ls0 ws0">问题二：投资效益<span class="ff3">...........................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>7</span></div><div class="t m0 xa h9 yd ff1 fs6 fc0 sc1 ls0 ws0">问题三：统筹方法<span class="ff3">.........................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>12</span></div><div class="t m0 xa h9 ye ff1 fs6 fc0 sc1 ls0 ws0">问题四：最佳路线问题<span class="ff3">.................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>15</span></div><div class="t m0 xa h9 yf ff1 fs6 fc0 sc1 ls0 ws0">习题六<span class="ff3">.............................................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>16</span></div><div class="t m0 xa h9 y10 ff1 fs6 fc0 sc1 ls0 ws0">讨论题<span class="ff3">.............................................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>18</span></div><div class="t m0 x9 h9 y11 ff1 fs6 fc0 sc0 ls0 ws0">第七讲　随机模型<span class="ff2 sc1">..................................................................................................................................<span class="_ _0"></span>25</span></div><div class="t m0 xa h9 y12 ff1 fs6 fc0 sc1 ls0 ws0">问题一：生物数量随机模型<span class="ff3">.........................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>25</span></div><div class="t m0 xa h9 y13 ff1 fs6 fc0 sc1 ls0 ws0">问题二：销售商品广告中的问题<span class="ff3">.................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>28</span></div><div class="t m0 xa h9 y14 ff1 fs6 fc0 sc1 ls0 ws0">问题三：性别危机<span class="ff3">.........................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>32</span></div><div class="t m0 xa h9 y15 ff1 fs6 fc0 sc1 ls0 ws0">问题四：报童问题<span class="ff3">.........................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>35</span></div><div class="t m0 xa h9 y16 ff1 fs6 fc0 sc1 ls0 ws0">问题五：火车站售票服务<span class="ff3">.............................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>38</span></div><div class="t m0 xa h9 y17 ff1 fs6 fc0 sc1 ls0 ws0">问题六：机器检修安排问题<span class="ff3">.........................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>43</span></div><div class="t m0 xa h9 y18 ff1 fs6 fc0 sc1 ls0 ws0">习题七<span class="ff3">.............................................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>45</span></div><div class="t m0 xa h9 y19 ff1 fs6 fc0 sc1 ls0 ws0">讨论题<span class="ff3">.............................................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>46</span></div><div class="t m0 x9 h9 y1a ff1 fs6 fc0 sc0 ls0 ws0">第八讲：经济管理模型<span class="ff2 sc1">..........................................................................................................................<span class="_ _0"></span>55</span></div><div class="t m0 xa h9 y1b ff1 fs6 fc0 sc1 ls0 ws0">问题一：消费者的选择<span class="ff3">.................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>55</span></div><div class="t m0 xa h9 y1c ff1 fs6 fc0 sc1 ls0 ws0">问题二：经济增长模型<span class="ff3">.................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>57</span></div><div class="t m0 xa h9 y1d ff1 fs6 fc0 sc1 ls0 ws0">问题三：投入产出模型<span class="ff3">.................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>62</span></div><div class="t m0 xa h9 y1e ff1 fs6 fc0 sc1 ls0 ws0">问题四：对策问题<span class="ff3">.........................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>70</span></div><div class="t m0 xa h9 y1f ff1 fs6 fc0 sc1 ls0 ws0">问题五：风险决策问题<span class="ff3">.................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>77</span></div><div class="t m0 xa h9 y20 ff1 fs6 fc0 sc1 ls0 ws0">习题八<span class="ff3">.............................................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>79</span></div><div class="t m0 xa h9 y21 ff1 fs6 fc0 sc1 ls0 ws0">讨论题<span class="ff3">.............................................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>80</span></div><div class="t m0 x9 h9 y22 ff1 fs6 fc0 sc0 ls0 ws0">第九讲　数模竞赛优秀论文选讲<span class="ff2 sc1">..........................................................................................................<span class="_ _0"></span>82</span></div><div class="t m0 xa h9 y23 ff3 fs6 fc0 sc1 ls0 ws0">2000<span class="_ _1"> </span><span class="ff1">年美国大学生数学建模竞赛Ａ题</span>.............................................................................................<span class="_ _0"></span>82</div><div class="t m1 xb ha y24 ff1 fs7 fc0 sc1 ls0 ws0">论文一：空中交通管制</div><div class="t m0 xc hb y24 ff4 fs6 fc0 sc1 ls0 ws0">.................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>.<span class="_ _0"></span>83</div><div class="t m1 xb ha y25 ff1 fs7 fc0 sc1 ls0 ws0">论文二：飞机间的安全距离和空间扇区的复杂性问题</div><div class="t m0 xd hb y25 ff4 fs6 fc0 sc1 ls0 ws0">.............................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>.<span class="_ _0"></span>94</div><div class="t m0 xa h9 y26 ff3 fs6 fc0 sc1 ls0 ws0">2000<span class="_ _1"> </span><span class="ff1">年美国大学生数学建模竞赛Ｂ题</span>...........................................................................................<span class="_ _0"></span>101</div><div class="t m1 xb ha y27 ff1 fs7 fc0 sc1 ls0 ws0">论文一：频道分配模型……空间跨度</div><div class="t m0 xe hb y27 ff4 fs6 fc0 sc1 ls0 ws0">.......................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>.<span class="_ _0"></span>102</div><div class="t m1 xb ha y28 ff1 fs7 fc0 sc1 ls0 ws0">论文二：无线电频道分配</div><div class="t m0 xf hb y28 ff4 fs6 fc0 sc1 ls0 ws0">............................................................................................................1<span class="_ _2"></span>12</div><div class="t m0 xa h9 y29 ff3 fs6 fc0 sc1 ls0 ws0">2000<span class="_ _1"> </span><span class="ff1">年美国大学生交叉学科建模竞赛题</span>...................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>.117</div><div class="t m1 xb ha y2a ff1 fs7 fc0 sc1 ls0 ws0">论文一：大象数目问题： 一个线性的模型</div><div class="t m0 x10 hb y2a ff4 fs6 fc0 sc1 ls0 ws0">...........................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>.<span class="_ _0"></span>1<span class="_ _2"></span>18</div><div class="t m0 xa h9 y2b ff1 fs6 fc0 sc1 ls0 ws0">讨论题<span class="ff3">...........................................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>124</span></div><div class="t m0 x9 h9 y2c ff1 fs6 fc0 sc0 ls0 ws0">第十讲 <span class="ff2 sc1">MA<span class="_ _2"></span>TLAB<span class="_ _1"> </span><span class="ff1 sc0">软件简介</span>..............................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>133</span></div><div class="t m0 xa h9 y2d ff1 fs6 fc0 sc1 ls0 ws0">一、<span class="ff3">MA<span class="_ _3"></span>TLAB<span class="_ _1"> </span><span class="ff1">简介</span>............................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>133</span></div><div class="t m0 xa h9 y2e ff1 fs6 fc0 sc1 ls0 ws0">二、数组、矩阵计算<span class="ff3">...................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>133</span></div><div class="t m0 xa h9 y2f ff1 fs6 fc0 sc1 ls0 ws0">三、关系和逻辑运算<span class="ff3">...................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>136</span></div><div class="t m0 xa h9 y30 ff1 fs6 fc0 sc1 ls0 ws0">四、多项式<span class="ff3">...................................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>138</span></div><div class="t m0 x11 hc y31 ff1 fs8 fc0 sc1 ls0 ws0">作者：<span class="ff3">liangmanfa- 1 -</span></div></div><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>

<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6288553d16e0ca7141f741c4/bg3.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x7 h7 y8 ff1 fs4 fc0 sc0 ls0 ws0">目录</div><div class="t m0 xa h9 y32 ff1 fs6 fc0 sc1 ls0 ws0">五、曲线拟合与插值<span class="ff3">...................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>141</span></div><div class="t m0 xa h9 y33 ff1 fs6 fc0 sc1 ls0 ws0">六、数值分析<span class="ff3">...............................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>147</span></div><div class="t m0 xa h9 y34 ff1 fs6 fc0 sc1 ls0 ws0">七、<span class="ff3">MA<span class="_ _3"></span>TLAB<span class="_ _1"> </span><span class="ff1">语言</span>............................................................................................................<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>...<span class="_ _0"></span>..<span class="_ _0"></span>148</span></div><div class="t m0 x11 hc y31 ff1 fs8 fc0 sc1 ls0 ws0">作者：<span class="ff3">liangmanfa- 2 -</span></div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>

<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6288553d16e0ca7141f741c4/bg4.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x12 h7 y8 ff1 fs4 fc0 sc0 ls0 ws0">运筹学模型</div><div class="t m0 x13 hd y35 ff1 fs9 fc0 sc0 ls0 ws0">第六讲 运筹学模型</div><div class="t m0 x14 he yf ff1 fsa fc0 sc0 ls0 ws0">问题一：运输问题</div><div class="t m0 x15 h8 y36 ff1 fs5 fc0 sc0 ls0 ws0">问题<span class="ff3 sc1"> <span class="ff1">要把<span class="_ _1"> </span><span class="ff5">m<span class="_ _4"> </span></span>个发点的货物运到<span class="_ _4"> </span><span class="ff5">n<span class="_ _1"> </span></span>个收点去，已知<span class="_ _5"> </span>发点有货物<span class="_ _6"> </span>吨，<span class="_ _6"> </span>收点需要</span></span></div><div class="t m0 x9 h8 y37 ff1 fs5 fc0 sc1 ls0 ws0">货物<span class="_ _7"> </span>吨，单位货物<span class="_ _0"></span>从<span class="_ _5"> </span>发点运到<span class="_ _6"> </span>收点的运<span class="_ _0"></span>费为<span class="_ _8"> </span>元，应采用<span class="_ _0"></span>哪一种运输方<span class="_ _0"></span>案才能</div><div class="t m0 x9 h8 y38 ff1 fs5 fc0 sc1 ls0 ws0">使总运费最省<span class="ff5">? </span>这问题称为运输问题。</div><div class="t m0 x9 hf y39 ff3 fs5 fc0 sc1 ls0 ws0"> </div><div class="t m0 xb h8 y3a ff1 fs5 fc0 sc0 ls0 ws0">数学模型<span class="ff3 sc1"> <span class="ff1">设<span class="_ _9"> </span>为由<span class="_ _5"> </span>发点运送到<span class="_ _a"> </span>收点的货物量。上述问题可以描述为：</span></span></div><div class="t m0 x9 hf y3b ff3 fs5 fc0 sc1 ls0 ws0">(1)</div><div class="t m0 x9 h8 y3c ff1 fs5 fc0 sc1 ls0 ws0">这里我们设货物总收量等于总发量，即</div><div class="t m0 x9 hf y3d ff3 fs5 fc0 sc1 ls0 ws0"> </div><div class="t m0 x9 h8 y3e ff1 fs5 fc0 sc1 ls0 ws0">否则可设一个虚的发点或收点。</div><div class="t m0 x9 h8 y3f ff3 fs5 fc0 sc1 ls0 ws0"> <span class="_ _0"></span> <span class="_ _0"></span><span class="ff1">运<span class="_ _0"></span>输问题<span class="_ _0"></span>的解法<span class="_ _0"></span>很多，<span class="_ _0"></span>这里我<span class="_ _0"></span>们介绍<span class="_ _0"></span>一种方<span class="_ _0"></span>法，<span class="_ _0"></span>一般情<span class="_ _0"></span>况下可<span class="_ _0"></span>以减少<span class="_ _0"></span>大量的<span class="_ _0"></span>计算。<span class="_ _0"></span>这种</span></div><div class="t m0 x9 h8 y40 ff1 fs5 fc0 sc1 ls0 ws0">方法实质是对偶单纯形法，不过我们的讨论不依赖于单纯形法的一般理论。</div><div class="t m0 xb h8 y41 ff1 fs5 fc0 sc0 ls0 ws0">引理<span class="ff3 sc1"> <span class="ff1">设在<span class="_ _0"></span>问题</span>(1)<span class="ff1">中，<span class="_ _0"></span>每一行</span>(<span class="_ _0"></span><span class="ff1">或列</span>)<span class="ff1">的运价<span class="_ _0"></span>同时加上一个<span class="_ _0"></span>常数，则所得<span class="_ _0"></span>新问题的最优<span class="_ _0"></span>解</span></span></div><div class="t m0 x9 h8 y42 ff1 fs5 fc0 sc1 ls0 ws0">与原问题相同。</div><div class="t m0 x9 h10 y43 ff3 fs5 fc0 sc1 ls0 ws0"> <span class="_ _0"></span> <span class="ff1">证<span class="_ _0"></span></span> <span class="_ _0"></span><span class="ff1">假设第<span class="_ _4"> </span></span>i<span class="_ _4"> </span><span class="ff1">行的运价<span class="_ _0"></span>同时加<span class="_ _0"></span>上<span class="_ _9"> </span>，所得<span class="_ _0"></span>问题的<span class="_ _0"></span>目标<span class="_ _0"></span><span class="ff6">函</span>数<span class="ff6">记<span class="_ _0"></span></span>为<span class="_ _b"> </span>，则对<span class="_ _0"></span><span class="ff6">变</span>量的<span class="_ _0"></span>同一组<span class="_ _0"></span>值</span></div><div class="t m0 x16 h8 y44 ff1 fs5 fc0 sc1 ls0 ws0">，有</div><div class="t m0 x11 hc y31 ff1 fs8 fc0 sc1 ls0 ws0">作者：<span class="ff3">liangmanfa- 1 -</span></div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>

<div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6288553d16e0ca7141f741c4/bg5.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x12 h7 y8 ff1 fs4 fc0 sc0 ls0 ws0">运筹学模型</div><div class="t m0 x9 h10 y45 ff6 fs5 fc0 sc1 ls0 ws0">因<span class="ff1">为<span class="_ _c"> </span>是常量，所以</span>当<span class="_ _1"> </span><span class="ff3">f<span class="_ _1"> </span></span>取<span class="ff1">最</span>小<span class="ff1">值时，<span class="_ _b"> </span></span>也取<span class="ff1">最</span>小<span class="ff1">值。</span>反之亦然<span class="ff1">。</span></div><div class="t m0 x9 h10 y46 ff3 fs5 fc0 sc1 ls0 ws0"> <span class="_ _0"></span> <span class="_ _0"></span> <span class="_ _0"></span> <span class="_ _0"></span><span class="ff6">此<span class="ff1">方<span class="_ _0"></span>法<span class="_ _0"></span></span>基<span class="_ _0"></span>本<span class="ff1">的<span class="_ _0"></span>原<span class="_ _0"></span>理<span class="_ _0"></span></span>就<span class="ff1">是<span class="_ _0"></span>，<span class="_ _0"></span>通过<span class="_ _0"></span>把<span class="_ _0"></span></span>各<span class="_ _0"></span><span class="ff1">行<span class="_ _0"></span></span></span>(<span class="_ _0"></span><span class="ff1">列<span class="_ _0"></span></span>)<span class="ff1">的<span class="_ _0"></span>运<span class="_ _0"></span>价<span class="_ _0"></span>同加<span class="_ _0"></span>、<span class="_ _0"></span>减一<span class="_ _0"></span>个<span class="_ _0"></span>数，<span class="_ _0"></span>使<span class="_ _0"></span><span class="ff6">各<span class="_ _0"></span></span>行<span class="_ _0"></span>列<span class="_ _0"></span>的<span class="ff6">零<span class="_ _0"></span></span>运<span class="_ _0"></span>价<span class="_ _0"></span><span class="ff6">尽</span></span></div><div class="t m0 x9 h10 y47 ff1 fs5 fc0 sc1 ls0 ws0">量<span class="_ _0"></span>多<span class="ff3">(<span class="_ _d"></span></span>同时<span class="_ _0"></span><span class="ff6">保<span class="_ _0"></span>持<span class="_ _0"></span></span>所<span class="_ _0"></span>有<span class="_ _0"></span>运<span class="_ _0"></span>价<span class="_ _0"></span><span class="ff6">非<span class="_ _0"></span>负<span class="_ _0"></span><span class="ff3">)<span class="_ _0"></span></span></span>，<span class="_ _0"></span>最<span class="_ _0"></span><span class="ff6">后<span class="_ _0"></span>求<span class="_ _0"></span></span>出<span class="_ _0"></span>一<span class="_ _0"></span>个<span class="_ _0"></span>总<span class="_ _0"></span>运输<span class="_ _0"></span>费<span class="_ _0"></span>用<span class="_ _0"></span>为<span class="_ _e"> </span><span class="ff3">0<span class="_ _4"> </span></span>的<span class="_ _0"></span>方案<span class="_ _0"></span>，<span class="_ _0"></span><span class="ff6">当<span class="_ _0"></span>然<span class="_ _0"></span>就<span class="_ _0"></span></span>得<span class="_ _0"></span>到<span class="_ _0"></span>原<span class="_ _0"></span>问<span class="_ _0"></span>题</div><div class="t m0 x9 h8 y48 ff1 fs5 fc0 sc1 ls0 ws0">的最优解。</div><div class="t m0 x9 h10 y49 ff3 fs5 fc0 sc1 ls0 ws0"> <span class="ff1">我们用以下<span class="ff6">例</span>题<span class="ff6">来说明</span>这种方法。</span></div><div class="t m0 x9 h10 y4a ff3 fs5 fc0 sc1 ls0 ws0"> <span class="ff6">例</span> <span class="ff1">设有<span class="ff6">如表<span class="_ _1"> </span></span></span>1<span class="_ _1"> </span><span class="ff1">所<span class="ff6">示</span>的运输问题，<span class="ff6">试求</span>出最优运输方案。</span></div><div class="t m0 x9 h10 y4b ff6 fs5 fc0 sc1 ls0 ws0">表<span class="_ _1"> </span><span class="ff3">1</span></div><div class="t m0 x17 h8 y4c ff3 fs5 fc0 sc1 ls0 ws0">1<span class="_ _f"> </span>2<span class="_ _f"> </span>3<span class="_ _f"> </span>4<span class="_ _10"> </span>5<span class="_ _11"> </span><span class="ff1">发</span> <span class="ff1">量</span></div><div class="t m0 x18 hf y4d ff3 fs5 fc0 sc1 ls0 ws0">1<span class="_ _12"> </span>15<span class="_ _12"> </span>9<span class="_ _12"> </span>22<span class="_ _13"> </span>30<span class="_ _13"> </span>1<span class="_ _0"></span>8<span class="_ _13"> </span>3<span class="_ _0"></span>0</div><div class="t m0 x18 hf y4e ff3 fs5 fc0 sc1 ls0 ws0">2<span class="_ _f"> </span>6<span class="_ _12"> </span>12<span class="_ _12"> </span>7<span class="_ _12"> </span>15<span class="_ _13"> </span>20<span class="_ _14"> </span>16</div><div class="t m0 x18 hf y4f ff3 fs5 fc0 sc1 ls0 ws0">3<span class="_ _12"> </span>13<span class="_ _12"> </span>5<span class="_ _12"> </span>18<span class="_ _13"> </span>19<span class="_ _13"> </span>1<span class="_ _0"></span>6<span class="_ _13"> </span>2<span class="_ _0"></span>3</div><div class="t m0 x18 hf y50 ff3 fs5 fc0 sc1 ls0 ws0">4<span class="_ _12"> </span>10<span class="_ _13"> </span>14<span class="_ _14"> </span>16<span class="_ _13"> </span>21<span class="_ _14"> </span>14<span class="_ _14"> </span>15</div><div class="t m0 x18 hf y51 ff3 fs5 fc0 sc1 ls0 ws0">5<span class="_ _12"> </span>18<span class="_ _13"> </span>19<span class="_ _14"> </span>20<span class="_ _13"> </span>22<span class="_ _14"> </span>25<span class="_ _14"> </span>16</div><div class="t m0 x19 h8 y52 ff1 fs5 fc0 sc1 ls0 ws0">发<span class="ff3"> </span>量</div><div class="t m0 x1a hf y53 ff3 fs5 fc0 sc1 ls0 ws0">20<span class="_ _13"> </span>17<span class="_ _14"> </span>15<span class="_ _13"> </span>25<span class="_ _14"> </span>23<span class="_ _15"> </span>100</div><div class="t m0 x9 h10 y54 ff1 fs5 fc0 sc0 ls0 ws0">解<span class="sc1">：第一<span class="ff6">步</span>，把<span class="ff6">各</span>列运价减去<span class="ff6">该</span>列最<span class="ff6">小</span>运价，<span class="ff6">并</span>对<span class="ff6">零</span>运价<span class="ff6">尽</span>量</span></div><div class="t m0 x9 h10 y55 ff1 fs5 fc0 sc1 ls0 ws0">安排运量，得<span class="ff6">表<span class="_ _1"> </span><span class="ff3">2</span></span>。</div><div class="t m0 x9 h10 y56 ff6 fs5 fc0 sc1 ls0 ws0">表<span class="_ _1"> </span><span class="ff3">2</span></div><div class="t m0 x1b hf y57 ff3 fs5 fc0 sc1 ls0 ws0">-6<span class="_ _16"> </span>-5<span class="_ _16"> </span>-7<span class="_ _17"> </span>-15<span class="_ _18"> </span>-14</div><div class="t m0 x18 hf y58 ff3 fs5 fc0 sc1 ls0 ws0">0<span class="_ _f"> </span>9<span class="_ _f"> </span>4<span class="_ _12"> </span>15<span class="_ _14"> </span>15<span class="_ _12"> </span>4<span class="_ _12"> </span>30</div><div class="t m0 x18 hf y59 ff3 fs5 fc0 sc1 ls0 ws0">0<span class="_ _19"> </span>7<span class="_ _f"> </span>0<span class="_ _f"> </span>0<span class="_ _10"> </span>6<span class="_ _f"> </span>0</div><div class="t m0 x18 hf y5a ff3 fs5 fc0 sc1 ls0 ws0">0<span class="_ _f"> </span>7<span class="_ _1a"> </span>1<span class="_ _2"></span>1<span class="_ _1b"> </span>4<span class="_ _f"> </span>2<span class="_ _f"> </span>6</div><div class="t m0 x18 hf y5b ff3 fs5 fc0 sc1 ls0 ws0">0<span class="_ _f"> </span>4<span class="_ _f"> </span>9<span class="_ _f"> </span>9<span class="_ _10"> </span>6<span class="_ _19"> </span>0</div><div class="t m0 x18 hf y5c ff3 fs5 fc0 sc1 ls0 ws0">0<span class="_ _12"> </span>12<span class="_ _13"> </span>14<span class="_ _14"> </span>13<span class="_ _12"> </span>7<span class="_ _12"> </span>11<span class="_ _13"> </span>16</div><div class="t m0 x17 hf y5d ff3 fs5 fc0 sc1 ls0 ws0">4<span class="_ _f"> </span>0<span class="_ _12"> </span>15<span class="_ _13"> </span>25<span class="_ _12"> </span>8</div><div class="t m0 x11 hc y31 ff1 fs8 fc0 sc1 ls0 ws0">作者：<span class="ff3">liangmanfa- 2 -</span></div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>