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mathorcup数学建模挑战赛获奖论文-第四届C题_20027E.pdf
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mathorcup数学建模挑战赛获奖论文,历届,单项文件,内容丰富,大学生数学,数学竞赛,参考资料
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The judges scoring, note Team number:
20027
The judges scoring, note
The judges scoring, note Problem
:
C
The judges scoring, note
Title
:
Family summer tour packages designed
Abstract
Many parents bring their children to travel during the summer holiday. However,
different families have different needs. Considering the route, cost, time and other
important factors comprehensively, different tour packages should be designed for
different families. Taking Beijing for example, 18 representative sites are selected
which consider a combination of various factors about culture, learning, fun and
landscape and others. Then the idea of clustering is used to combine the sight spots
into a spot. The sight spots should have short distance from each other. Finally, the 14
spots are got. 14 spots are evaluated and sorted. Then the fit spot is selected and the
route is planned. Linear regress is used for the distance and cost information by the
software of MATLAB. A function about the relationship of distance and cost is got for
calculating the total cost of tour package. About this problem, the following three
conditions are discussed:
Aimed to the factor of time, the tour package can be divided into long-term and
short-term course. Long-term is 5days and short-term is 2days.In the long-term, we
have plenty of time to traverse 14 spots. The problem of calculating total cost is
translated into the problem of getting shortest distance. We can use WinQSB to solved
Hamilton optimal circuits. Then we calculate the cost based on the best circuits. In the
short-term, time is limited to traverse 14 spots. We should make the tour package
contains as more spots as possible in 2days. The fuzzy evaluation method was used to
make the time have a relative large weight. Evaluating the spots based on the cost,
scenic desirability and traffic conditions scenic so as to determine the five scenic
spots. We can use WinQSB to solved Hamilton optimal circuits, and then we calculate
the cost based on the best circuits.
Aimed to the factor of time, the constraint of 0-1 variables is used to make sure
that each scenic spot is reached only once. Then evaluating and ranking the spots
based on the cost. Five scenic spots are given as starting point, the number of scenic
tours for optimal Hamiltonian circuit were 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and
calculating the cost.
There are different needs of tour content for different families. Therefore,
another four lines were developed .They are cultural lines, traveling and learning lines,
landscape lines and interesting lines.
15 packages are given to be chosen for visiting Beijing in summer, as shown in
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table 4.For the summer to visit Beijing, a total of 15 packages are given to choose
from. In addition to choose suitable travelling route, paying attention to the weather
and avoiding the peak of abortion.,
Key words : Clustering, WinQSB, Hamiltonian circuit, LINGO software, fuzzy
evaluation, 0-1 constraints
![](https://csdnimg.cn/release/download_crawler_static/88965845/bg3.jpg)
1
Family summer tour packages designed
1 Problem restatement
With the summer vocation approaching, a family is planning a one-week travel
to a city. The goal of this problem is to design a ‘comfortable’ travel plan for this
family, with considerations of multiple effects on their trips. Select any city you are
interested in as the example.
2 The model assumes
1 , all the sights , attractions are the nodes ;
2 , between each two tourist attractions in the same car as a transport , take the way
without considering other costs other than transport costs and travel expenses from the
same unit (both 0.50Yuan) ;
3 , only consider the connection between the different attractions roads , highways as
paths between nodes ;
4 , continuous auto departure time , travel time is not calculated separately , without
considering the traffic accidents;
5 , travelers will not be stranded in unexpected situations such as travel process ;
6 , each day, food and other consumer 100 Yuan / day ;
3 Symbol Conventions
sign instruction
c
The all travel cost of everyone
i
t
The time they stay at the
i
sight of everyone
i
c
The all cost at the
i
sight of everyone
ij
t
The time we need from the
i
sight to the
j
sight
ij
c
The fare we spend from the
i
sight to the
j
sight
ij
r
0
1
ij
r
others
strightlysightjtosightithefrom
ij
d
The distance between the
i
sight and the
j
sight
v
The average speed of bus
m
The average fare of by bus
![](https://csdnimg.cn/release/download_crawler_static/88965845/bg4.jpg)
2
4 Problem analyses
According to the present problems in the subject, the paper selected China's
political, economic and cultural center -- Beijing, as the summer tourist destination.
First of all, we consider in the absence of any constraint conditions, a choice of 18
well-known tourist resorts by statistical analysis, and the shortest route map that
tourism. Then, we as main constraint condition in time, the optimal line drawn in
different time. Then, the travel costs as the main constraint conditions, a number of
attractions as a supplement, planning of the shortest tour. Finally, in order to meet the
needs of different family, make travel plan, more features theme travel does not bring
the same travel experience for all the family.
5 Establish and solve the model
5.1 Model preparation
We collected in the Beijing 18 spots of data, many of which are very close, so we
will they are clustered according to geographical location, finally got 14 spots. Based
on transportation costs and path length is proportional to the various attractions,
accommodation costs are equal, driving on the highway and railway speed constant
and other assumptions with the shortest distance between 14 sites in two two and set
up the table, preparing for the establishment of model.
When not considering time, cost constraints, Hamilton overall optimal loop
making 14 spots, the maximum to meet the unrestricted visitors, and visitors can
quickly, with a minimum cost tour of the 14 spots. In order to solve the optimal
Hamiltonian circuit, networking model module in WinQSB software was used for the
dynamic programming on line, and get the optimal solution.
When time is limited, the course is divided into short and long term. Long-term
initially set at seven days, short-term initially set at 2 days. Solving the results of the
first case is long, not too much to repeat here. Short-term is fuzzy evaluation method
14 attractions based on a comprehensive evaluation of time and rank, to choose the
five highest-ranked applications WinQSB Software Networking model module based
on the data in Appendix 2 to get the optimal Hamiltonian circuit, and the optimal
route.
When restricted fee, based on the understanding of the subject, we can know the
total cost of travel, including travel expenses, accommodation expenses and costs of
attractions to visit when, and in determining the number of attractions you want to
visit, our goal is to satisfy all constraints in the case, find the minimum cost. In the
design of suitable tourist routes, to make the least amount of money to spend as much
sightseeing attractions within a very short time. Our approach here is to use the 0-1
variable constraint method that satisfies the various attractions in the corresponding
constraints , first determine the number of sightseeing attractions , sights and then
select the appropriate number of fuzzy evaluation method, then calculate in this case
the minimum cost under .
Through the establishment of the model, we make the constraint:
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