运筹学实验报告作业余兴发.doc

重 庆 交 通 大 学学 生 实 验 报 告实验课程名称 运筹学上机实验报告 开课实验室 学 院 交通运输学院 年级 13级 专业班 汽服三班 学 生 姓 名 余兴发 学 号 631305080327 开 课 时 间 2015 至 2016 学年第 一 学期总 成 绩教师签名运筹学算法软件简介LINDO和LINGO是美国LINDO SYSTEMS公司近年才推出的两个专门用于分析与求解运筹学及其它最优化问题的十分方便和非常有效的软件。前者主要用于线性规划、整数规划及0-1型整数规划。后者主要用于非线性规划及其它范围广泛的最优化问题。1997年的6.01版LINDO，完全基于WINDOWS系统，只需输入数学模型，即可用菜单栏的SOLVE命令或工具栏上的求解按钮即可方便地获得最优解并可进行灵敏度分析、还可得到单纯形表、图形及其它详细信息，既易学也好用。1998年的4.0版LINGO系统的功能更加强大、应用范围更广。它可以将目标函数、约束条件及有关数据分开。既可直接输入模型求解，也可用LINGO的与数学的语言非常一致的语言编程序。它不仅能求解线性规划和非线性规划问题，而且还可求解包括目标规划、网络规划、动态规划、存储论、排队论、回归分析、预测分析等许多方面的问题。它还收集了各个领域的五十多个最优化问题模型并有相应的程序，用户类似问题的求解只需作简单的修改即可，使用也非常简单方便。LINDO 和LINGO 有多个版本:VersionConstraintsVariablesDemo/Web50100Solver Suite100200Super5001,000Hyper2,0004,000Industrial8,00016,000Extended32,000100,000可满足不同用户的需要,最小的100个变量、50个约束条件，最大的可到100000个变量、32000个约束。一、线性规划和灵敏度分析1max3x1+2x2+0x3+0x4+0x5st2x1+2x2+x3=10x1+3x4=204x2+x5=18EndOPTIMUM FOUND AT STEP 1 OBJECTIVE FUNCTION VALUE 1) 15.00000 VARIABLE VALUE REDUCED COST X1 5.000000 0.000000 X2 0.000000 1.000000 X3 0.000000 1.500000 X4 5.000000 0.000000 X5 18.000000 0.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 1.500000 3) 0.000000 0.000000 4) 0.000000 0.000000 NO. ITERATIONS= 1 RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X1 3.000000 INFINITY 1.000000 X2 2.000000 1.000000 INFINITY X3 0.000000 1.500000 INFINITY X4 0.000000 3.000000 INFINITY X5 0.000000 INFINITY 0.250000 RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 2 10.000000 30.000000 10.000000 3 20.000000 INFINITY 15.000000 4 18.000000 INFINITY 18.000000二、线性规划和灵敏度分析2ax 2x1+x2+0x3+0x4st3x1+3x2+x3=186x1+1x2+x4=28EndLP OPTIMUM FOUND AT STEP 0 OBJECTIVE FUNCTION VALUE 1) 10.40000 VARIABLE VALUE REDUCED COST X1 4.400000 0.000000 X2 1.600000 0.000000 X3 0.000000 0.266667 X4 0.000000 0.200000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 0.266667 3) 0.000000 0.200000 NO. ITERATIONS= 0 RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X1 2.000000 4.000000 1.000000 X2 1.000000 1.000000 0.666667 X3 0.000000 0.266667 INFINITY X4 0.000000 0.200000 INFINITY RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 2 18.000000 66.000000 4.000000 3 28.000000 8.000000 22.000000 LP OPTIMUM FOUND AT STEP 0 OBJECTIVE FUNCTION VALUE 1) 10.40000 VARIABLE VALUE REDUCED COST X1 4.400000 0.000000 X2 1.600000 0.000000 X3 0.000000 0.266667 X4 0.000000 0.200000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 0.266667 3) 0.000000 0.200000 NO. ITERATIONS= 0 RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X1 2.000000 4.000000 1.000000 X2 1.000000 1.000000 0.666667 X3 0.000000 0.266667 INFINITY X4 0.000000 0.200000 INFINITY三、整数规划max 50x1+100x2st10x1+7x2768x1+20x2100endgin x1gin x2LP OPTIMUM FOUND AT STEP 0 OBJECTIVE VALUE = 556.944458 NEW INTEGER SOLUTION OF 550.000000 AT BRANCH 0 PIVOT 1 BOUND ON OPTIMUM: 550.0000 ENUMERATION COMPLETE. BRANCHES= 0 PIVOTS= 1 LAST INTEGER SOLUTION IS THE BEST FOUND RE-INSTALLING BEST SOLUTION. OBJECTIVE FUNCTION VALUE 1) 550.0000 VARIABLE VALUE REDUCED COST X1 5.000000 -50.000000 X2 3.000000 -100.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 5.000000 0.000000 3) 0.000000 0.000000 NO. ITERATIONS= 1 BRANCHES= 0 DETERM.= 1.000E 0四、目标规划min d12+d21+d22+d31st 3x1+x2+xs=112x1-x2+d11-d12=04x1+x2+d21-d22=106x1+8x2+d31-d32=56endVARIABLE VALUE REDUCED COST D12 0.000000 1.000000 D21 0.000000 1.000000 D22 0.000000 1.000000 D31 0.000000 1.000000 X1 0.923077 0.000000 X2 6.307693 0.000000 XS 1.923077 0.000000 D11 4.461538 0.000000 D32 0.000000 0.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 0.000000 3) 0.000000 0.000000 4) 0.000000 0.000000 5) 0.000000 0.000000 NO. ITERATIONS= 2 RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE D12 1.000000 INFINITY 1.000000 D21 1.000000 INFINITY 1.000000 D22 1.000000 INFINITY 1.000000 D31 1.000000 INFINITY 1.000000 X1 0.000000 0.000000 3.250000 X2 0.000000 4.333333 0.000000 XS 0.000000 0.000000 1.444444 D11 0.000000 1.181818 0.000000 D32 0.000000 INFINITY 0.000000 RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 2 11.000000 INFINITY 1.923077 3 0.000000 INFINITY 4.461538 4 10.000000 2.777778 3.000000 5 56.000000 24.000000 19.333332五、0-1规划max 4x1+3x2+2x3st2x1-5x2+x3=3x1+x3=1endint x1int x2int x3LP OPTIMUM FOUND AT STEP 3 OBJECTIVE VALUE = 9.00000000 NEW INTEGER SOLUTION OF 9.00000000 AT BRANCH 0 PIVOT 3 RE-INSTALLING BEST SOLUTION. OBJECTIVE FUNCTION VALUE 1) 9.000000 VARIABLE VALUE REDUCED COST X1 1.000000 -4.000000 X2 1.000000 -3.000000 X3 1.000000 -2.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 4.000000 0.000000 3) 5.000000 0.000000 4) 1.000000 0.000000 NO. ITERATIONS= 5 BRANCHES= 0