全国大学生数学建模竞赛B题获奖论文答卷 - 图文

is one of the practical form of values. The so-called values refers to the objective things are of no value and the value of fundamental perspective. Different values, people's behaviour, attitudes, ways are different. People-oriented focus on human value and reality, we need the broadest masses as values. Adhere to people-oriented values, is to make the economy more development, improve democracy, cultural prosperity, and live a happier; is deeply concerned that human development and human values, development of social and human development of rational unified, insisted in the material civilization, political civilization and spiritual civilization in the overall advancement of Socialist civilization to a higher level. Also want to see that person's value is not only meet your needs, also is to meet the needs of others and the community. Adhere to people-oriented, to strongly advocate every community member, serve others, beneficial to the community of people. The so-called Outlookattitude is on the record, including who, how to create a record of achievements, how to evaluate performance, and so on. What values, what kind of Outlook. Adhere to people-oriented Outlook, is on the premise of respecting the interests and power of people, creating a popular, warm hearts, steady heart performance, creating \one officer, the benefit of\s, and overall construction of well-off society and promoting the all-round development of people's performance. Achievement evaluation in both economic accomplishments, take another look at the effectiveness of social progress; changes in both urban and rural change; both hard environment to strengthen and take another look at the soft environment improvement momentum of development at present, depending on the potential for sustainable development. Leave people to talk about \ople to talk about \ook\not what the performance. 4. people responded to the starting point of the question, and replied to questions point. Man is the sum of social relationships. We cannot leave the chichuanyongdu, housing, tourism and entertainment, entertaining, and even certain political, economic, cultural and social environment, and so on. Due to human needs, all walks of life will come into being. People create for their survival, and continue enjoying the results of the construction. Colorful in the transformation of the people of the world, community vitality in the creation of man. Therefore, any work we do, the starting point is human, what are people. Us speed up development, the core of which is to meet the needs of people, including survival needs, emotional needs and self-actualization needs. It should be noted that people are not machines, not the slave of an object, not to be controlled. People have their own personality, has its own personality, has its own dignity. Person in need of care, you need to understand, need to meet. It is said that in the \society, people plant\society, man is an animal\y, return 2011高教社杯全国大学生数学建模竞赛

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我们仔细阅读了中国大学生数学建模竞赛的竞赛规则.

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我们郑重承诺，严格遵守竞赛规则，以保证竞赛的公正、公平性。如有违反竞赛规则的行为，我们将受到严肃处理。

Now, we are in a new historical stage of all-round construction of a well-off society. In perform duties, and carried out work of process in the, we to put people as a guide principles, and a test standard, efforts from masses most hope do of things do up, from masses most care of hot problem grabbed, from masses most not satisfaction of place modified up, not make nominal of formalism, not do grandstanding of cosmetic, to seeking of style, help masses share, is people benefit. (C) the investee people is not only an idea, it is a job requirement. Philosophy through to the people-oriented thought in the work of the Office, must be clear work objectives. Party Office in the city this year remains: Advanced civil strife, local brand. The County (City) Party Committee offices and units directly under the Office to hold high the banner of first to excellence, people-oriented requirements, strengthen the construction and management of the Office towards the work \her level\political participation based on conspiracy to adhere to people-oriented, will be around to promote coordinationDevelopment events, great searchings. The 16 session of the party's scientific Outlook on development, is the new Central collective leadership to the development of connotation, development essentials, further deepen the essence of development and innovation, is our party's ruling idea a leap. At present, establishing and implementing the scientific concept of development has become the party's important work. As the Office of party Committee, working party should service center, initiative to claim leadership of the decision, the current focus is to focus on promoting comprehensive, coordinated and sustainable development with more suggestions, do more research, summarized the typical. One is drafted to raise the level of your presentation. our presentation is the main Office of \he basic carrier staff service, is important to measure service levels. The quality of your presentation, mainly depends on how much we drafted a document recognized by the leadership, how many are listening to the people in favour of the report, how many paid dividends in the practical work. Improve presentation drafting level, requirements we accurate grasp led intent, General led care of work are to as understand, General led consider of problem are to in-depth thinking; requirements we highlight place features, put superior approach policy and local actual combined up, put presentation of theme thrust and masses of by thought by wants to combined up; requirements we seeks to streamlined clear, with simple of language expression deep of thought, with short of length hosted rich of connotation. Second, the survey results more. Investigation of the base, the road to success is something, is our for the Party Committee's policy decision a good idea, an important part of a good staff. This year, to focus around industrial XING city, and farmers increase, and and manpower development, and seeking, major problem and foster advantage industry, and adjustment agricultural structure, and carriedis one of the practical form of values. The so-called values refers to the objective things are of no value and the value of fundamental perspective. Different values, people's behaviour, attitudes, ways are different. People-oriented focus on human value and reality, we need the broadest masses as values. Adhere to people-oriented values, is to make the economy more development, improve democracy, cultural prosperity, and live a happier; is deeply concerned that human development and human values, development of social and human development of rational unified, insisted in the material civilization, political civilization and spiritual civilization in the overall advancement of Socialist civilization to a higher level. Also want to see that person's value is not only meet your needs, also is to meet the needs of others and the community. Adhere to people-oriented, to strongly advocate every community member, serve others, beneficial to the community of people. The so-called Outlookattitude is on the record, including who, how to create a record of achievements, how to evaluate performance, and so on. What values, what kind of Outlook. Adhere to people-oriented Outlook, is on the premise of respecting the interests and power of people, creating a popular, warm hearts, steady heart performance, creating \one officer, the benefit of\s, and overall construction of well-off society and promoting the all-round development of people's performance. Achievement evaluation in both economic accomplishments, take another look at the effectiveness of social progress; changes in both urban and rural change; both hard environment to strengthen and take another look at the soft environment improvement momentum of development at present, depending on the potential for sustainable development. Leave people to talk about \ople to talk about \ook\not what the performance. 4. people responded to the starting point of the question, and replied to questions point. Man is the sum of social relationships. We cannot leave the chichuanyongdu, housing, tourism and entertainment, entertaining, and even certain political, conomic, cultural and social environment, and so on. Due to human needs, all walks of life will come into being. People create for their survival, and continue enjoying the results of the construction. Colorful in the transformation of the people of the world, community vitality in the creation of man. Therefore, any work we do, the starting point is human, what are people. Us speed up development, the core of which is to meet the needs of people, including survival needs, emotional needs and se-actualization needs. It should be noted that people are not machines, not the slave of an object, not to be controlled. People have their own personality, has its own personality, has its own dignity. Person in need of care, you need to understand, need to meet. It is said that in the \society, people plant\society, man is an animal\y, return 2011高教社杯全国大学生数学建模竞赛

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评 阅 人 评 分 备 注 赛区评阅编号（由赛区组委会评阅前进行编号）：

赛区评阅记录（可供赛区评阅时使用）：

全国统一编号（由赛区组委会送交全国前编号）：

全国评阅编号（由全国组委会评阅前进行编号）：

Now, we are in a new historical stage of all-round construction of a well-off society. In perform duties, and carried out work of process in the, we to put people as a guide principles, and a test standard, efforts from masses most hope do of things do up, from masses most care of hot problem grabbed, from masses most not satisfaction of place modified up, not make nominal of formalism, not do grandstanding of cosmetic, to seeking of style, help masses share, is people benefit. (C) the investee people is not only an idea, it is a job requirement. Philosophy through to the people-oriented thought in the work of the Office, must be clear work objectives. Party Office in the city this year remains: Advanced civil strife, local brand. The County (City) Party Committee offices and units directly under the Office to hold high the banner of first to excellence, people-oriented requirements, strengthen the construction and management of the Office towards the work \her level\political participation based on conspiracy to adhere to people-oriented, will be around to promote coordinationDevelopment events, great searchings. The 16 session of the party's scientific Outlook on development, is the new Central collective leadership to the development of connotation, development essentials, further deepen the essence of development and innovation, is our party's ruling idea a leap. At present, establishing and implementing the scientific concept of development has become the party's important work. As the Office of party Committee, working party should service center, initiative to claim leadership of the decision, the current focus is to focus on promoting comprehensive, coordinated and sustainable development with more suggestions, do more research, summarized the typical. One is drafted to raise the level of your presentation. our presentation is the main Office of \he basic carrier staff service, is important to measure service levels. The quality of your presentation, mainly depends on how much we drafted a document recognized by the leadership, how many are listening to the people in favour of the report, how many paid dividends in the practical work. Improve presentation drafting level, requirements we accurate grasp led intent, General led care of work are to as understand, General led consider of problem are to in-depth thinking; requirements we highlight place features, put superior approach policy and local actual combined up, put presentation of theme thrust and masses of by thought by wants to combined up; requirements we seeks to streamlined clear, with simple of language expression deep of thought, with short of length hosted rich of connotation. Second, the survey results more. Investigation of the base, the road to success is something, is our for the Party Committee's policy decision a good idea, an important part of a good staff. This year, to focus around industrial XING city, and farmers increase, and and manpower development, and seeking, major problem and foster advantage industry, and adjustment agricultural structure, and carried

交巡警服务平台的设置与调度

摘要

本文针对交巡警服务平台的设置和调度的问题，综合运用0-1规划模型、层次分析法、多元线性回归模型、最小二乘法、最悲观时间法和观察法，依次解决了五个问题：（1）对A区服务平台分配管辖范围，（2）确定A区20个服务平台对13个节点警力合理的调度方案，（3）确定A区需要增加的平台个数和位置，（4）分析全市服务平台设置的合理性和解决方案，(5)面对重大事件全市服务平台警力资源的最佳围堵方案。

对于问题(1)，以某个节点是否被某个平台管理为决策变量，选取各平台到达所管节点的总距离最小为目标函数，把每个平台的办案数不超过平均办案数的2倍和以距离为3千米的1.2倍为距离上限作为约束条件，建立0-1规划模型。用LINGO进行求解可得到管理方案，图表列出分配方案。 对于问题（2），把各节点是否被某个平台管理为决策变量，以20个平台达到所管节点的总距离最小为目标函数，约束条件是13条要道的节点处必须有从20个平台分配的警力资源和一个平台的警力最多封锁一个路口，建立0-1规划模型。用LINGO进行求解确定出调度方案，表列出分配方案。

对于问题（3），为了使各平台的工作量均匀，在原有平台基础上逐次增加平台个数，利用0-1规划模型确定每次的办案数，并计算出办案数的方差，利用最小二乘的思想确定增加平台的个数和位置。

针对问题（4），将与每个区域平台设置合理性有关的四个指标进行标准化，运用层次分析法确定各项指标的权值，利用多元线性回归的思想建立判断合理性标准的模型。根据已知数据和建立的评价标准判断各个区域平台设置的合理性，确定需要改进的区域。把达到合理的最小值作为上限根据该合理性模型确定出需要增加的平台数。把各区域各项指标的大小与每个区域的平均值进行比较，确定出影响这些区域不合理的主要因素，根据这些因素，利用MATLAB做出的交通网络与平台设置示意图确定要增加的位置。

对于问题（5），通过封锁城市出入口、围堵罪犯、搜捕罪犯三个步骤抓捕罪犯。利用计算机软件绘制出该城区的地图，并分别注明了各节点的标号，绘制出罪犯在几个不同时刻逃窜的范围。根据图形观察分配离城市出入口最近的平台警力进行封锁。对于围堵方案，采用最悲观时间的思想，对罪犯可能经过的每个节点进行围堵，最后包围罪犯。观察图形，对圆环域之间的节点与附近平台进行分析，最后确定具体的调度方案。

最后分析模型的优缺点、模型的改进和模型的推广。

关键字：0-1规划模型 层次分析法 多元线性回归模型 最悲观时间思想

1

is one of the practical form of values. The so-called values refers to the objective things are of no value and the value of fundamental perspective. Different values, people's behaviour, attitudes, ways are different. People-oriented focus on human value and reality, we need the broadest masses as values. Adhere to people-oriented values, is to make the economy more development, improve democracy, cultural prosperity, and live a happier; is deeply concerned that human development and human values, development of social and human development of rational unified, insisted in the material civilization, political civilization and spiritual civilization in the overall advancement of Socialist civilization to a higher level. Also want to see that person's value is not only meet your needs, also is to meet the needs of others and the community. Adhere to people-oriented, to strongly advocate every community member, serve others, beneficial to the community of people. The so-called Outlookattitude is on the record, including who, how to create a record of achievements, how to evaluate performance, and so on. What values, what kind of Outlook. Adhere to people-oriented Outlook, is on the premise of respecting the interests and power of people, creating a popular, warm hearts, steady heart performance, creating \one officer, the benefit of\s, and overall construction of well-off society and promoting the all-round development of people's performance. Achievement evaluation in both economic accomplishments, take another look at the effectiveness of social progress; changes in both urban and rural change; both hard environment to strengthen and take another look at the soft environment improvement momentum of development at present, depending on the potential for sustainable development. Leave people to talk about \ople to talk about \ook\not what the performance. 4. people responded to the starting point of the question, and replied to questions point. Man is the sum of social relationships. We cannot leave the chichuanyongdu, housing, tourism and entertainment, entertaining, and even certain political, conomic, cultural and social environment, and so on. Due to human needs, all walks of life will come into being. People create for their survival, and continue enjoying the results of the construction. Colorful in the transformation of the people of the world, community vitality in the creation of man. Therefore, any work we do, the starting point is human, what are people. Us speed up development, the core of which is to meet the needs of people, including survival needs, emotional needs and se-actualization needs. It should be noted that people are not machines, not the slave of an object, not to be controlled. People have their own personality, has its own personality, has its own dignity. Person in need of care, you need to understand, need to meet. It is said that in the \society, people plant\society, man is an animal\y, return 1、问题重述

已知：A、B、C、D、E、F区分别有92个、73个、154个、152个、103个、108

个节点，并分别有20个、8个、17个、 9个、15个、11个交巡警服务平台（以下用“平台”简称）。已知个节点的坐标、全市交通路线、全市区出入口位置、各区面积和人口数。 求解：（1）a：确定各平台的管辖范围，尽量保证交巡警到达所管节点时间3分

钟之内（速度为60km/h）。

b：对20个平台与A区13个出入口节点进行配对，保证每个平台至

多对应一个节点，且每个节点都有对应的平台。

c:：若要避免平台的工作量不均衡和出警时间过长的情况，在该区增

加2到5个平台，确定其个数和位置。

（2）a：分析该市现有平台设置方案的合理性。若有明显不合理，请给出

解决方案。

b：若该市地点P（第32个节点）处发生了重大刑事案件，在案发3

分钟后接到报警，犯罪嫌疑人已驾车逃跑。为了快速搜捕嫌疑犯，请给出调度全市平台警力资源的最佳围堵方案。

2、模型假设

假设:

1、每辆警车的平均速度都为60km/h；

2、近似地认为两节点的实际路程为两点的直线距离； 3、每个区内人口分布均匀；

4、每个平台的职能和警力配备基本相同且都能正常出警； 5、每条路段都是双向连通且保持通；

6、罪犯犯案后选择背离案发点的路径逃窜，速度为60km/h； 7、平台接到报案后立即出警。

3、符号说明

Ai A区第i个节点

AJi A区第i个平台

dij 第i个节点与第个节点之间的距离 判断第i个平台是否管理第j个节点

jXij

Wi 第i个平台的办案数

Lj 第个节点的案发率 第条进出该区的重要通道

jKjjNow, we are in a new historical stage of all-round construction of a well-off society. In perform duties, and carried out work of process in the, we to put people as a guide principles, and a test standard, efforts from masses most hope do of things do up, from masses most care of hot problem grabbed, from masses most not satisfaction of place modified up, not make nominal of formalism, not do grandstanding of cosmetic, to seeking of style, help masses share, is people benefit. (C) the investee people is not only an idea, it is a job requirement. Philosophy through to the people-oriented thought in the work of the Office, must be clear work objectives. Party Office in the city this year remains: Advanced civil strife, local brand. The County (City) Party Committee offices and units directly under the Office to hold high the banner of first to excellence, people-oriented requirements, strengthen the construction and management of the Office towards the work \her level\political participation based on conspiracy to adhere to people-oriented, will be around to promote coordinationDevelopment events, great searchings. The 16 session of the party's scientific Outlook on development, is the new Central collective leadership to the development of connotation, development essentials, further deepen the essence of development and innovation, is our party's ruling idea a leap. At present, establishing and implementing the scientific concept of development has become the party's important work. As the Office of party Committee, working party should service center, initiative to claim leadership of the decision, the current focus is to focus on promoting comprehensive, coordinated and sustainable development with more suggestions, do more research, summarized the typical. One is drafted to raise the level of your presentation. our presentation is the main Office of \he basic carrier staff service, is important to measure service levels. The quality of your presentation, mainly depends on how much we drafted a document recognized by the leadership, how many are listening to the people in favour of the report, how many paid dividends in the practical work. Improve presentation drafting level, requirements we accurate grasp led intent, General led care of work are to as understand, General led consider of problem are to in-depth thinking; requirements we highlight place features, put superior approach policy and local actual combined up, put presentation of theme thrust and masses of by thought by wants to combined up; requirements we seeks to streamlined clear, with simple of language expression deep of thought, with short of length hosted rich of connotation. Second, the survey results more. Investigation of the base, the road to success is something, is our for the Party Committee's policy decision a good idea, an important part of a good staff. This year, to focus around industrial XING city, and farmers increase, and and manpower development, and seeking, major problem and foster advantage industry, and adjustment agricultural structure, and carried

H 各区域内平台设置的合理度

Z1 各区域内平均每个平台所负责节点数的指标得分

e1 各区域内平均每个平台所负责节点数指标在合理性标准中的权重

Z2 各区域内平均每个平台所负责区面积的指标得分

e2 各区域内平均每个平台所负责区面积指标在合理性标准中的权重

Z3 各区域内平均每个平台所负责人数的指标得分

e3 各区域内平均每个平台所负责人数指标在合理性标准中的权重

Z4 各区域内平均每个平台办案数的指标得分

e4 各区域内平均每个平台办案数指标在合理性标准中的权重

4、问题分析

4．1问题一：

这一问需要依次解决的问题是A区各平台的管理范围，警力合理的调度方案以及需要增加平台的个数和位置的确定。

（1）对于各平台管理范围的问题，即为把节点分配给平台的问题。对于分配问题，可以采用0-1规划模型，以某个平台是否管理某个节点为决策变量。对于重大事件，我们需要巡警到达案发地的时间最短，也就是距离最短，则我们可以以各平台到达所管节点的距离最小为目标函数。由于考虑到每个服务平台的办案数不能过大，则可以以每个平台的办案数不超过平均办案数的某个百分比为约束条件。又由于尽量要在3分钟之内到达，则所走的距离尽量控制在3千米以内，不妨以距离为3千米的某个百分比作为距离上限约束。继而我们可以用LINGO进行求解，获得优化分配方案。

（2）对于A区平台警力合理调度的方案，其实就是一个把20个平台的警力资源合理分配给13条交通要道的问题。对于分配问题，我们依然可以用0-1规划模型。由于要达到快速封锁，且警车的速度一定，则我们可以以各个平台处的警力资源到达各个要道的路口节点的总路程最小为目标函数。再加上把这13条要道的节点处必须有平台分配的警力资源且一个平台的警力最多封锁一个路口作为约束条件，则我们可以用LINGO进行求解。

（3）对于增加平台个数和位置的问题，由题目知,分配平台时,需要注意的两个重要的因素，分别是：1.距离不能太远,否则会导致出警时间过长；2.服务平台的办案数不能太高,否则警员会过于繁忙,导致不能及时办理案件。由于在第（1）问的解答里，我们已经解决了距离的问题，则在此我们只需在其基础上考虑案发率即可。为了达到各平台的办案数均匀，则需在案发率较高的区域增加平台。

为了确定增加平台的个数，我们可以依次增加2到5个，然后相应地分析办

1