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mathorcup数学建模挑战赛获奖论文-第四届C题_20009E.doc
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The judges scoring, note
Team number:
20009
The judges scoring, note
The judges scoring, note
Problem:
C
The judges scoring, note
Title:Family Summer Travel Packages Design.
Abstract
With the development of society and economy, and the improvement of people's
living standards, tourism has become one of the important living styles for family. .It
is an important activity to improve the quality of people's life. As a new trend, family
tourism will have a great effect on the further development of the tourism industry.
Different family has different needs for tours. In order to solve the problem, this
paper creates a table which takes all determining varieties into consideration. It bases
its study on the 2011 Yearbook of Tourism Statistics and the expenses cost of different
family, and it adopts principal component analysis and performs the procedures in
SAS. The conclusion is as follows that: the most influential determining factor is time
and the second determining factor is cost.
In order to provide the best tour plan for different family, this paper selects eight
tourist attractions in Xi’an and establishes objective programming model for different
family needs. The model takes route, cost and time into consideration and through
Matlab, it can be concluded as following:
When travel costs are not limited, follow the route " Beilin ,Yang tomb ,
Qianling ,mausoleum , Zhouzhi ,Famen Temple ,Museum, Big Wild Goose
Pagoda ,Cuihuashan " the least time; When the travel time unlimited, in accordance
with the line, "Beilin, Yang tomb ,Qianling, mausoleum, Famen Temple ,Museum,
Cuihuashan, Louguantai Big Wild Goose Pagoda, "the least cost; when travel time is
limited (eg 3 days) when, in accordance with the line," Yang tomb, mausoleum,Beilin,
Museum, Big Wild Goose Pagoda, Cuihuashan ,Famen temple "number of attractions
to visit for up to 5 months; When travel expenses limited (eg 1000) when, according to
the line, "Beilin, Museum, Big Wild Goose Pagoda, mausoleum ,Cuihuashan ,Famen
Temple" number of attractions to visit up to five.
Besides, based on the classification on travel defined by World Tourism
Organization (WTO), the paper analyzes the advantages of Group Travel: travelers can
choose their own way to travel according to their motives and purposes. When their
motive is fully implemented, the expectation of tour from the travelers can be satisfied.
Then, a multivariate linear regression model is put forth to test traveling plans to
determine the best one.
Finally, this paper discusses advantages and possible approaches to improve the
model.
1
Key words : principal component analysis, goal planning, SAS, multiple linear
regression equation, utility maximization
Family Summer Travel Packages Design
1 issue restated
Summer approaching, many parents would choose at this time to take the kids to
travel, but every family is different, you need to consider different factors such as the
number of families, travel time, and the economic situation of families, to establish
tourism tourism purposes the manner, place, route and so on. Some people want to
save time, some people want to save money, as well as to reduce the distance, choose
a suitable way is very important, that facilitate their choice but also take into account
their own circumstances.
Thus this paper there are three problems to be solved, first screened to determine
the most important factor for the following principal components analysis to reduce
the error, and the other is to have different needs to design a family tour packages and
determine the best travel route, This paper considers the traveling by car and tour.
Finally, the best of course, how to test the best of the packages.
2 Analysis
For the problem: First, different families have different needs ( size, cost
constraints , time constraints , etc. ) , they want to know what factors influence the
choice of the greatest ways we need statistics, but too many factors that will analyze
advantageous way to travel trouble , so it is necessary to identify the most important
factor in order to further solve the problem. Referring to past data table to filter out
data to their advantage to create the table. Using principal component analysis method
to get a comprehensive index, and then run the main draw of the first component and
the second principal component in SAS by data.
For question two: selected tourist city in Shanxi eight spots, whether or swim team
Walks tours are an important part of the connection with the tourist destination.
Designed tours conducive to select the destination of the tourists have to arrange their
travel activities, to avoid "roaming" , and it helps to play the function of various
tourist spots and tourist rational use of time , there are plans to also help tourists
disposable travel expenses and so on. First, the way driving line objective function for
the different needs of people considered separately , at least when the objective
function of time
)(
61
~ xxX �
When the cost of a minimum objective function
XaxaxaZ
�
����
6611
�
Then use graph theory to tourist attractions as vertices in the graph, traffic routes can
be seen as the various attractions on the map edge, the edge weights on behalf of other
attractions from a distance to attractions, and finally the use of the shortest path
problem solving selected design issues after tourist attractions tourist routes, using
2
Matlab solve time and cost required for each package.
For question three: The above model established four tour packages, tourists can
choose according to their own situation to fit their circumstances package, but this
package is for the best, how to build a package described in this article is the best
package. Multiple linear regression model in this paper carried out a score draw
packages created package is the best package.
3 Assuming the model
1 weather for tourism
2 scenic open 8:00-18:00
3 Fees and other costs 100RMB per meal;
4 way to travel is by car, the speed of 70 kilometers per hour;
5 car per kilometer oil costs 0.6 RMB per crossing fee is 5RMB;
6 daily driving and travel time is 10 hours, the other for dates, accommodation an
average of 100 per day;
4 Symbols Explain
Symbols
Explain
M
The total cost of travel
T
The total time of travel
N
The number N tour attractions
�
Fractional value travel packages
i
Z
I-attractions Accommodation
i
t
Time spent in the i-th attractions
ij
d
From the i-th to the j-th attractions attractions
i
b
Tourist attractions in the i-th ticket costs spent
ij
t
Tourist attractions from i to j-th attractions time spent driving
0
ij
�r
Said tourists do not reach the first j attractions from the i-th attractions
1
ij
�r
Represents the j-th attractions tourists arrived from the i-th Attractions
ij
c
Transportation costs from the i-th visitor attractions to spend the j attractions
5. The first Modeling and Solution
5.1 model preparation
Different families have different circumstances and some people some time to
3
consider the factors that people should consider the situation to spend, some people
are shopping and some sightseeing tours, some will consider the child's preferences.
Create a table by each of these reasons statistical factors affecting the choice of
approach.
Table 1 The way to travel is not the same variable values
Time
(days)
X1
cost
(RMB)
X2
trip (km)
X3
family
income
X4
Shopping
(%) X5
Tour (%)
X6
car1
3
7000
400
10000
60
30
Group2
5
5000
1000
6000
20
40
Visit3
4
3000
600
4000
10
30
Other 4
2
1000
100
3000
10
10
5.2 model established
There are car, groups, exercise, four other way to travel, time, cost, travel, family
income, shopping, sightseeing six indicators, denoted, design principal component
relationships:
XaxaxaZ
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����
6611
�
(1)
Find the
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1�
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aaa
, the maximum the
� �
ZVar
, i.e.
� � � � � �
�
�
�
�
�
�
� aaaXVaraXaVarZVar
is the maximum, correlation matrix:
�
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2
21
2
2
2221
112
2
1
pppp
p
p
x
���
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Find the characteristic roots and the corresponding unit eigenvectors and
cumulative contribution rate.
In SAS run the program receive:
Index
Index
Value
Variable
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