用LINDO求解线性规划（LP）问题一般步骤及例子
<P >步骤：</P><P ><FONT face="Times New Roman"> 1</FONT>）<FONT face="Times New Roman"> </FONT>首先是输入一个<FONT face="Times New Roman">LP</FONT>问题。为了检查有无错误，可用<FONT face="Times New Roman">LOOK</FONT>命令来显示问题式中的一行，几行或全部。</P>
<P ><FONT face="Times New Roman"> </FONT>例如：<FONT face="Times New Roman"> LOOK 3 ---</FONT>》<FONT face="Times New Roman"> </FONT>屏幕显示第<FONT face="Times New Roman">3</FONT>行</P>
<P ><FONT face="Times New Roman">LOOK 1-3 ---</FONT>》<FONT face="Times New Roman"> </FONT>显示第<FONT face="Times New Roman">1-3</FONT>行</P>
<P ><FONT face="Times New Roman">LOOK ALL ---</FONT>》<FONT face="Times New Roman"> </FONT>显示整个模型</P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><FONT face="Times New Roman">2</FONT>）修正模型。</P>
<P >如果需要对问题中某变量系数进行修正，可用<FONT face="Times New Roman">ALTER</FONT>命令。此时，在<FONT face="Times New Roman">LINDO</FONT>的提示下需输入相应的变量所在的行号，变量名，及新的系数值。</P>
<P >此外下面两种情况也可用<FONT face="Times New Roman">ALTER</FONT>命令：</P>
<P >改动约束条件的右端顶，可以将<FONT face="Times New Roman">RHS</FONT>（即<FONT face="Times New Roman">right-hand side</FONT>）做为变量名。</P>
<P >改变约束条件中的不等号方向（如<FONT face="Times New Roman">< </FONT>或<FONT face="Times New Roman"> >)</FONT>，可以将<FONT face="Times New Roman">DIR</FONT>做为变量名。</P>
<P >修改问题还可用<FONT face="Times New Roman">EXT</FONT>命令<FONT face="Times New Roman">(</FONT>增加新的约束行<FONT face="Times New Roman">), DEL</FONT>命令<FONT face="Times New Roman">(</FONT>去掉一行<FONT face="Times New Roman">), </FONT>和<FONT face="Times New Roman">APPC</FONT>命令<FONT face="Times New Roman">(</FONT>增加一个新的变量<FONT face="Times New Roman">)</FONT>，<FONT face="Times New Roman"> </FONT>也可用<FONT face="Times New Roman">EDIT</FONT>编辑器。</P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><FONT face="Times New Roman">3</FONT>）存储模型</P>
<P >如果输入的问题模型已经不再需要改动，可用<FONT face="Times New Roman">SAVE</FONT>命令将它存入文件中。（此时<FONT face="Times New Roman">LINDO</FONT>会提示你输入一个文件名。）日后如需用到该问题可用<FONT face="Times New Roman">RETR</FONT>命令提取。</P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><FONT face="Times New Roman"> 4</FONT>）键入<FONT face="Times New Roman">GO</FONT>命令可得到<FONT face="Times New Roman">LP</FONT>问题的最优解。如果想将计算结果直接输出到某文件中，可在<FONT face="Times New Roman">GO</FONT>命令前先使用<FONT face="Times New Roman">DIVERT</FONT>命令，<FONT face="Times New Roman">LINDO</FONT>会提示你键入该输出文件的文件名，此后键入<FONT face="Times New Roman">GO</FONT>命令，屏幕上只会显示最优的目标函数值，其它结果都将存入输出文件。<FONT face="Times New Roman">GO</FONT>命令执行后，<FONT face="Times New Roman">LINDO</FONT>会问你是否做敏感性分析，可看需要键入“<FONT face="Times New Roman">Y</FONT>”（<FONT face="Times New Roman">YES</FONT>）或“<FONT face="Times New Roman">N</FONT>”<FONT face="Times New Roman"> </FONT>（<FONT face="Times New Roman">NO</FONT>）<FONT face="Times New Roman">. </FONT>如果没什么错误，求解就结束了。可键入<FONT face="Times New Roman">QUIT</FONT>退出。</P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><FONT face="Times New Roman"> LINDO </FONT>中有下面三种命令可帮助使用者对<FONT face="Times New Roman">LINDO</FONT>的命令有更多的了解<FONT face="Times New Roman">:</FONT></P>
<P ><FONT face="Times New Roman"> HELP: </FONT>若<FONT face="Times New Roman">HELP</FONT>后面跟有具体命令<FONT face="Times New Roman">, </FONT>则解释该命令<FONT face="Times New Roman">. </FONT>若单只一个<FONT face="Times New Roman">HELP, </FONT>将会给出一般性的信息<FONT face="Times New Roman">.</FONT></P>
<P ><FONT face="Times New Roman"> CATEGORIES (</FONT>可简写为<FONT face="Times New Roman">CAT): </FONT>只列出所有命令的类型目录<FONT face="Times New Roman">, </FONT>随后可允许使用者有选择地列出某个具体类型中的所有命令<FONT face="Times New Roman">.</FONT></P>
<P ><FONT face="Times New Roman"> COMMANDS ( </FONT>简写为<FONT face="Times New Roman">COM) COM: </FONT>按类型列出所有有效的命令<FONT face="Times New Roman">, </FONT>例如输入<FONT face="Times New Roman">(INPUT)</FONT>型命令<FONT face="Times New Roman">, </FONT>输出<FONT face="Times New Roman">(OUTPUT)</FONT>型命令<FONT face="Times New Roman">, </FONT>等等<FONT face="Times New Roman">.</FONT></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P >下面即是一个具体应用的例子<FONT face="Times New Roman">: </FONT>（可参照上述使用步骤）</P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P >首先输入问题<FONT face="Times New Roman">: (</FONT>或用命令<FONT face="Times New Roman">RETR</FONT>读取<FONT face="Times New Roman">LINDO</FONT>目录下的例子文件<FONT face="Times New Roman">DAKOTA)</FONT></P>
<P ><FONT face="Times New Roman"> MAX 60 DESKS + 30 TABLES + 20 CHAIRS</FONT></P>
<P ><FONT face="Times New Roman"> SUBJECT TO</FONT></P>
<P ><FONT face="Times New Roman"> 2) 8 DESKS + 6 TABLES + CHAIRS <= 48</FONT></P>
<P ><FONT face="Times New Roman"> 3) 4 DESKS + 2 TABLES + 1.5 CHAIRS <= 20</FONT></P>
<P ><FONT face="Times New Roman"> 4) 2 DESKS + 1.5 TABLES + 0.5 CHAIRS <= 8</FONT></P>
<P ><FONT face="Times New Roman"> 5) TABLES <= 5</FONT></P>
<P ><FONT face="Times New Roman"> END</FONT></P>
<P ><FONT face="Times New Roman"> </FONT></P>
<P ><FONT face="Times New Roman"> </FONT>问题求解</P>
<P ><FONT face="Times New Roman">:GO</FONT></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><FONT face="Times New Roman"> LP OPTIMUM FOUND AT STEP 2</FONT></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><FONT face="Times New Roman"> OBJECTIVE FUNCTION VALUE</FONT></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><FONT face="Times New Roman"> 1) 280.00000 </FONT></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><FONT face="Times New Roman"> VARIABLE VALUE REDUCED COST</FONT></P>
<P ><FONT face="Times New Roman"> DESKS 2.000000 .000000</FONT></P>
<P ><FONT face="Times New Roman"> TABLES .000000 5.000000</FONT></P>
<P ><FONT face="Times New Roman"> CHAIRS 8.000000 .000000</FONT></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><FONT face="Times New Roman"> ROW SLACK OR SURPLUS DUAL PRICES</FONT></P>
<P ><FONT face="Times New Roman"> 2) 24.000000 .000000</FONT></P>
<P ><FONT face="Times New Roman"> 3) .000000 10.000000</FONT></P>
<P ><FONT face="Times New Roman"> 4) .000000 10.000000</FONT></P>
<P ><FONT face="Times New Roman"> 5) 5.000000 .000000</FONT></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><FONT face="Times New Roman"> NO. ITERATIONS= 2</FONT></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><FONT face="Times New Roman">DO RANGE(SENSITIVITY) ANALYSIS?</FONT></P>
<P ><FONT face="Times New Roman">? </FONT></P>
<P >随后键入<FONT face="Times New Roman">"Y" </FONT>表示同意做敏感性分析<FONT face="Times New Roman">: </FONT></P>
<P ><FONT face="Times New Roman"> RANGES IN WHICH THE BASIS IS UNCHANGED:</FONT></P>
<P ><FONT face="Times New Roman"> </FONT></P>
<P ><FONT face="Times New Roman"> <st1:place w:st="on"><st1:PlaceName w:st="on">OBJ</st1:PlaceName> <st1:PlaceName w:st="on">COEFFICIENT</st1:PlaceName> <st1:PlaceType w:st="on">RANGES</st1:PlaceType></st1:place></FONT></P>
<P ><FONT face="Times New Roman"> VARIABLE CURRENT ALLOWABLE ALLOWABLE</FONT></P>
<P ><FONT face="Times New Roman"> COEF INCREASE DECREASE</FONT></P>
<P ><FONT face="Times New Roman"> DESKS 60.000000 20.000000 4.000000</FONT></P>
<P ><FONT face="Times New Roman"> TABLES 30.000000 5.000000 INFINITY </FONT></P>
<P ><FONT face="Times New Roman"> CHAIRS 20.000000 2.500000 5.000000</FONT></P>
<P ><FONT face="Times New Roman"> </FONT></P>
<P ><FONT face="Times New Roman"> <st1:place w:st="on"><st1:PlaceName w:st="on">RIGHT</st1:PlaceName> <st1:PlaceName w:st="on">HAND</st1:PlaceName> <st1:PlaceName w:st="on">SIDE</st1:PlaceName> <st1:PlaceType w:st="on">RANGES</st1:PlaceType></st1:place></FONT></P>
<P ><FONT face="Times New Roman"> ROW CURRENT ALLOWABLE ALLOWABLE</FONT></P>
<P ><FONT face="Times New Roman"> RHS INCREASE DECREASE</FONT></P>
<P ><FONT face="Times New Roman"> 2 48.000000 INFINITY 24.000000</FONT></P>
<P ><FONT face="Times New Roman"> 3 20.000000 4.000000 4.000000</FONT></P>
<P ><FONT face="Times New Roman"> 4 8.000000 2.000000 1.333333</FONT></P>
<P ><FONT face="Times New Roman"> 5 5.000000 INFINITY 5.000000</FONT></P>
<P> </P> 好 <P>hao,这样的帖子越多越好哦，呵呵</P> 谢谢了 谢谢了 :D:)你的帖子非常好，十分感谢！
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