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《运筹学》练习题 一、填空题 1.由线性规划的图解法知,如果一个线性规划有最优解,则一般最优解会取在可行域的( )处。 2.设某线性规划问题的可行域有界,那么一般来说,该线性规划的基可行解和其可行域中

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 运筹学练习题8sE★济宁成人高考报名0537-2229526

一、填空题8sE★济宁成人高考报名0537-2229526

1.由线性规划的图解法知,如果一个线性规划有最优解,则一般最优解会取在可行域的( )处。8sE★济宁成人高考报名0537-2229526

2.设某线性规划问题的可行域有界,那么一般来说,该线性规划的基可行解和其可行域中的( )是一一对应的。8sE★济宁成人高考报名0537-2229526

3.将现行规划MAXZ=CX,AX≤b,X≥0的目标函数系数C,直接填入原始单纯形表检验数行,则当所有决策变量的检验数都( )时,可以断定此时得到最优解。8sE★济宁成人高考报名0537-2229526

4.某运输问题,各产地产量和为50,各销地销量和为60,用表上作业法求解应添加一个虚拟的( )地。8sE★济宁成人高考报名0537-2229526

5.已知某产销平衡的运输问题有M个产地,N个销地,根据产销平衡条件一共有M+N个等式约束条件,则其中最多有( )个等式约束条件线性无关。8sE★济宁成人高考报名0537-2229526

6.在动态规划中,如果我们知道初始状态S1,一般用( )推法求解比较方便。8sE★济宁成人高考报名0537-2229526

7.连通多重图G有欧拉圈,当且仅当G中无( )点。8sE★济宁成人高考报名0537-2229526

8.在网络计划中,完成各个工序需要时间最长的路线叫( )路线。8sE★济宁成人高考报名0537-2229526

9.对于指标函数为各阶段指标之和的动态规划问题,边界条件一般取值为( )8sE★济宁成人高考报名0537-2229526

10.一个网络的最大流量,取决于其中各个截集中截量最( )的一个。8sE★济宁成人高考报名0537-2229526

11.在任意一个图中,奇点的个数总是( )数。8sE★济宁成人高考报名0537-2229526

12.一个无( )的连通图称为树。8sE★济宁成人高考报名0537-2229526

13.某运输问题要求,产地2不能向销地4供应,则产地2到销地4的单位运价C24应设为( )8sE★济宁成人高考报名0537-2229526

14.在MAX型线性规划中增加约束条件,最优目标函数值Z*将变( )8sE★济宁成人高考报名0537-2229526

15.某目标规划第1级别目标要求是成本X1+X2不得高于30,即X1+X2≤30。引入正负偏差变量之后则成为X1+X2+d--d+=30,相对应的其目标函数应表达为minz=P1( )。8sE★济宁成人高考报名0537-2229526

16.在线性规划中,基可行解既是可行解,又是( )解。8sE★济宁成人高考报名0537-2229526

17.一个网络的最大流量,取决于其中各个截集中截量最( )的一个。8sE★济宁成人高考报名0537-2229526

18.在某线性规划问题的最优单纯形表中,得到一个非退化的解,其中某一个非基变量的检验数为零,可以断定该线性规划问题有( )最优解。8sE★济宁成人高考报名0537-2229526

19.求解整数规划常用的方法有分支定界法和割平面法,其中的( )不仅可以用来求解纯整数规划,还可以用来求解混合整数规划。8sE★济宁成人高考报名0537-2229526

20.在网络计划中,完成各个工序需要时间最长的路线叫( )路线。8sE★济宁成人高考报名0537-2229526

21.在大M法和两阶段法中,我们一般引入( )变量,来解决含有等式约束条件的线性规划。8sE★济宁成人高考报名0537-2229526

22.一个图若有( )圈,则被称为欧拉图。8sE★济宁成人高考报名0537-2229526

23.在网络计划图中始点和终点的个数都必须是( )个。8sE★济宁成人高考报名0537-2229526

24.对于指标函数为各阶段指标之和的动态规划问题,边界条件一般取值为( )。8sE★济宁成人高考报名0537-2229526

25.在运输问题中,当各产地产量和销地销量均为整数时,最优调运方案也一定是( )数解。8sE★济宁成人高考报名0537-2229526

26.二维平面的图解法只能用于求解含有( )个决策变量的线性规划问题。8sE★济宁成人高考报名0537-2229526

27.运输问题中,闭回路上的变量所对应的系数列向量是线性( )关的。8sE★济宁成人高考报名0537-2229526

28.在排队论中,我们实际应用的系统状态概率都是( )态概率。8sE★济宁成人高考报名0537-2229526

29M/M/1排队系统,默认的服务规则是先到( )服务。8sE★济宁成人高考报名0537-2229526

30.动态规划中,状态变量的定义必须满足无( )性。8sE★济宁成人高考报名0537-2229526

二、判断题8sE★济宁成人高考报名0537-2229526

1.图解法理论上可以用来求解任意多个决策变量的线性规划问题。8sE★济宁成人高考报名0537-2229526

2.在运用两阶段法求解线性规划时,如果第一阶段的最优解是0,则该问题有无穷多最优解。8sE★济宁成人高考报名0537-2229526

3.当用单纯形法求解线性规划问题时,如果最优表某决策变量的检验数为0,则可以判断,该问题有无穷多最优解。8sE★济宁成人高考报名0537-2229526

4.单纯形法中,换基迭代的过程,其实质是行变换。8sE★济宁成人高考报名0537-2229526

5.运输问题表上作业法中,用位势法求非基变量检验数时,我们可令任一位势为任意值来开始各位势的求解。8sE★济宁成人高考报名0537-2229526

6.产销不平衡的运输问题,不能不经处理,直接用表上作业法求解。8sE★济宁成人高考报名0537-2229526

7.图G是树的充要条件是,任意两点间有且只有一条链。8sE★济宁成人高考报名0537-2229526

8.在动态规划中,状态变量的选取要满足“无后效”性。8sE★济宁成人高考报名0537-2229526

9.在动态规划中,用顺推法和逆推法得到的最优解通常不一样。8sE★济宁成人高考报名0537-2229526

10.一个网络不会同时存在多个最大流量方案。8sE★济宁成人高考报名0537-2229526

11.一个线性规划问题的基可行解的数目是有限的,通常不会超过决策变量的个数。8sE★济宁成人高考报名0537-2229526

12.每一个运输问题都可以表述为一个线性规划问题,表上作业法中每个单元格也对应线性规划问题中的一个决策变量和一个相应的系数列向量。而一个完整闭回路中的各决策变量,所对应的线性系数列向量,线性无关。8sE★济宁成人高考报名0537-2229526

13.在动态规划模型中,问题的阶段数等于问题中的限制条件数。8sE★济宁成人高考报名0537-2229526

14.对于指标函数为各阶段指标之乘积的动态规划问题,边界条件一般取0。8sE★济宁成人高考报名0537-2229526

15.动态规划计算中的“维数障碍”主要是由于问题阶段数的急剧增加引起的。8sE★济宁成人高考报名0537-2229526

16.在运输问题中,当各产地产量和销地销量均为整数时,运输问题的最优解也是整数值。8sE★济宁成人高考报名0537-2229526

17.在网络计划中的网络图,只能有一个始点和一个终点。8sE★济宁成人高考报名0537-2229526

18.对偶单纯形法通常不单独使用,而是作为原始单纯形法的补充,常应用在灵敏度分析中。8sE★济宁成人高考报名0537-2229526

19.在单纯形法计算中,如不按最小比值原则选取换出变量,则在下一次迭代中至少有一个基变量的值为负。8sE★济宁成人高考报名0537-2229526

20.网络图中任一中间结点都表示上一工序的结束,和下一工序的开始。8sE★济宁成人高考报名0537-2229526

三、计算题8sE★济宁成人高考报名0537-2229526

1.试求解以下产销平衡的运输问题。要求用差额元素法求初始解,直接将各基变量取值填在表1内。用位势法求检验数,填在表2中(表2各单元格只允许填非基变量检验数和位势,求位势时令U1=0,如表所示)。8sE★济宁成人高考报名0537-2229526

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2.用单纯形法求解下列问题要求:(1)标准化该模型(2)完成1步迭代8sE★济宁成人高考报名0537-2229526

(1)标准化该模型8sE★济宁成人高考报名0537-2229526

MAXZ=2X1+3X2+2X38sE★济宁成人高考报名0537-2229526

X1+2X2+X3≤38sE★济宁成人高考报名0537-2229526

2X1-X2+2X3≤48sE★济宁成人高考报名0537-2229526

X1,X2,X3≥08sE★济宁成人高考报名0537-2229526

(2)完成1步迭代8sE★济宁成人高考报名0537-2229526

XB8sE★济宁成人高考报名0537-2229526

b8sE★济宁成人高考报名0537-2229526

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检验数行8sE★济宁成人高考报名0537-2229526

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 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

检验数行8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

3.用最小元素法求下列运输问题的初始解(10分),然后用闭回路法求解非基变量检验数(10分)。8sE★济宁成人高考报名0537-2229526

用最小元素法求初解                   用闭回路法求检验数8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

B18sE★济宁成人高考报名0537-2229526

B28sE★济宁成人高考报名0537-2229526

B38sE★济宁成人高考报名0537-2229526

B48sE★济宁成人高考报名0537-2229526

8sE★济宁成人高考报名0537-2229526

A18sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

68sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

38sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

28sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

58sE★济宁成人高考报名0537-2229526

58sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

A28sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

28sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

108sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

38sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

108sE★济宁成人高考报名0537-2229526

28sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

A38sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

88sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

58sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

118sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

68sE★济宁成人高考报名0537-2229526

38sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

8sE★济宁成人高考报名0537-2229526

28sE★济宁成人高考报名0537-2229526

38sE★济宁成人高考报名0537-2229526

18sE★济宁成人高考报名0537-2229526

48sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

非基变量8sE★济宁成人高考报名0537-2229526

闭回路8sE★济宁成人高考报名0537-2229526

检验数8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

  8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

4.求下面网络图中的网络最大流。请以VS-Vi-VT的形式给出增广链(Vi表示中间节点)。网络图中弧旁的数字为该弧的容量。8sE★济宁成人高考报名0537-2229526

增广链8sE★济宁成人高考报名0537-2229526

调整量8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

5.试求解以下产销平衡的运输问题,要求用最小元素法求初始解,并将结果填在表1内。用位势法求检验数,并填在表2中,其中表2各单元格只允许填检验数位势,求位势时令U1=0,如表所示,并说明该解有何特点。(10分)。8sE★济宁成人高考报名0537-2229526

1                                             28sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

B18sE★济宁成人高考报名0537-2229526

B28sE★济宁成人高考报名0537-2229526

B38sE★济宁成人高考报名0537-2229526

B48sE★济宁成人高考报名0537-2229526

8sE★济宁成人高考报名0537-2229526

A18sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

48sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

128sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

48sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

118sE★济宁成人高考报名0537-2229526

168sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

A28sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

28sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

108sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

38sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

108sE★济宁成人高考报名0537-2229526

108sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

A38sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

88sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

58sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

118sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

68sE★济宁成人高考报名0537-2229526

228sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

8sE★济宁成人高考报名0537-2229526

88sE★济宁成人高考报名0537-2229526

148sE★济宁成人高考报名0537-2229526

128sE★济宁成人高考报名0537-2229526

148sE★济宁成人高考报名0537-2229526

488sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

B18sE★济宁成人高考报名0537-2229526

B28sE★济宁成人高考报名0537-2229526

B38sE★济宁成人高考报名0537-2229526

B48sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

A18sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

48sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

128sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

48sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

118sE★济宁成人高考报名0537-2229526

U1=08sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

A28sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

28sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

108sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

38sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

108sE★济宁成人高考报名0537-2229526

U2=8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

A38sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

88sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

58sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

118sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

68sE★济宁成人高考报名0537-2229526

U3=8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

V1=8sE★济宁成人高考报名0537-2229526

V2=8sE★济宁成人高考报名0537-2229526

V3=8sE★济宁成人高考报名0537-2229526

V4=8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

6.求出下图中网络的最大流,弧上数(Cij,fij)分别为该弧的容量和实际流量。增广链按调整顺序填入“增广链表”中,并给出最小截集(10分)8sE★济宁成人高考报名0537-2229526

增广链8sE★济宁成人高考报名0537-2229526

调整量8sE★济宁成人高考报名0537-2229526

VS-             -VT8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

VS-             -VT8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

VS-             -VT8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

VS-             -VT8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

VS-             -VT8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

VS-             -VT8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

7.改正下面的工序图,并用破圈法求出关键路线。8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

 8sE★济宁成人高考报名0537-2229526

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