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mathorcup数学建模挑战赛获奖论文-第四届C题_10486e.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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Score,signature and note
of Judge one
Team number:
10486
Score,signature and note of
Judge three
Score,signature and note
of Judge two
Choose:
C
Score,signature and note of
Judge four
Topic:
Choose and Optimization of Reasonable Travel Route
Abstract
This article will be the best tourist attractions in Luoyang attractions selection,
determined the travel route based on the selected attractions, evaluated and optimized
the travel route by established a mathematical model.
According problem requires, answers will be divided into three steps. Firstly,
determined the best tourist attractions, secondly according to the determined tourist
attractions to identify and evaluate routes, finally optimized the reasonable travel
route.
For step one, selected the value of the attractions, ticket prices, and regional conditions of
attractions for the first layer index and based on this to deepen stratification, determined
the weight of index in each layer. Finally got the consolidated evaluation model by
linear weighting, evaluated tourist attractions in Luoyang then determined travel routes
from those attractions.
For step two, depending on the selected attractions, determine the tourist routes under
different attractions by using "loop" type capture method, established fuzzy evaluation
model. Structured evaluation matrix R and obtained fuzzy evaluation weight matrix C.
Got the ultimate function of satisfaction, brought each tourist routes corresponding
fuzzy evaluation weight matrix C into Satisfaction function to score, finally evaluated
and analysis the determined ten travel routes.
For step three, according to pairs evaluation and analysis of tourist routes satisfaction
of step two, considering the impact of economic conditions, travel time, and the family
structure of the travel route,optimized the selected tourist route, determined about
travel time, the number of attractions and tourist spending three constraints, by
collecting and collating the distance between attractions, attractions and other data on
length of stay, and assumptions about family structure, such as travel costs and travel
time by using 0-1 variables, reasonably analysis by using Lingo software, gave sound
advice for families of different structure, and broaden the specific model.
Keyword: Fuzzy Comprehensive Evaluation; Fuzzy evaluation weight matrix;
0-1Variables; Satisfaction
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1
1. Problem Restatement
Summer holiday is coming, many parents may choose to bring their children to go
travel, but different families have different needs, so choosing a tourist city,
comprehensively considered important factor such as itinerary, time and cost to design
a tour package for families having different needs.
With people’s material life got better, travel is increasingly becoming one of the
important events in people's lives, Luoyang, the ancient capital of nine dynasties,is the
must go place for many tourists, there is a family that want to travel to Luoyang on
summer holiday, considering transportation costs, accommodation costs and meal
costs,etc. Selected the best tourist attractions and draw the appropriate travel route and
evaluated the travel route.
In summary, according to the meaning of the questions we need to address the
following three questions:
(1) Draw the best tourist attractions in Luoyang by building models;
(2) Gather information and determine the best travel route,evaluate and analysis the
travel route without considering the time and money constraints;
(3) Based on (2), get the best travel route with considering the time and money
constraints.
2. Problem Analysis
2.1 Analysis of the problem A
According to the analysis of the best travel route in problem restatement, for the
problem one, firstly analyzed the impact index of sightseeing, then stratified
indicators and calculated weights of different index. Establish a comprehensive
evaluation model
[1]
.
Value of the attractions, ticket prices, regional conditions of attractions is the first
layer index, value of the attractions include the size and quality of attractions, regional
conditions of attractions include infrastructure, tourism facilities and relationships
with other attractions and traffic conditions, quality of attractions include water,
climate, geology and topography, flora and fauna, cultural monuments, customs, size
of attractions include capacity and concentration of attractions.
According to the classification of these selected indicators, structured judgment
matrix,analysis of weight calculation and consistency check, eventually structured
evaluation model through linear weighted, chose different attractions,collected data of
corresponding attractions, finally, deal with data of every attraction by dimensionless
processing, got different attractions weighted score by comprehensive evaluation
model, ranked attractions based the scores on different attractions, then determined
the tourism value of every attraction.
2.2 Analysis of the problem B
According substantial attractions ranking in problem A, captured the front seven
attractions, connected four spots, five spots, six and seven attractions attractions
together via a loop, selected the number of attractions, attractions quality and route
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2
stay time for Satisfaction Index, determined each proposed route evaluation value and
ranking of tourist Route by using fuzzy comprehensive evaluation method
[2]
,
conducted quantitative analysis and qualitative comparison of different systems for
tourist route based on fuzzy comprehensive scores.
2.3 Analysis of the problem C
According to Satisfaction analysis of the tourist route in problems B, considering the
impact of economic conditions, travel time, and the family structure of the travel route,
combined with the result of satisfaction analysis, reasonably optimized the travel
route, set a typical family structure as an example, established the objective function
of cost by using 0-1 variable and determined constraints, collected more data,Solved
and analysis the results by using Lingo software, selected the appropriate travel route
for instance family and Broaden the specific model.
3. Problem Assuming
(1) Evaluation and dimensionless processing can use the abstract indicators such as
high, medium, low, and excellent, good, fair, poor;
(2) The average speed of the taxi is 60km / h, the average cost is 2 ¥/ km;
(3) The family will stay in hotel every night,and they need two rooms;
(4) The family have 10 hours a day for travel,including sightseeing and ride time;
(5) A trip without considering the impact of weather, traffic and other special
situations;
(6) The entire tourist route is a loop;
(7) The journey will not appear the phenomenon of the repeated visit;
![](https://csdnimg.cn/release/download_crawler_static/88965823/bg4.jpg)
3
4. Symbol Description
Symbol Description
A Function expression pf attractions comprehensive evaluation model
B
i
The first layer composite indicators(i=1,2,3)
C
i
The second layer composite indicators(i=1,2,...6)
D
i
The third layer composite indicators(i=1,2,...8)
Bi
w
The weights of B
i
Ci
w
The weights of C
i
Di
w
The weights of D
i
max
Largest eigenvalue of judgment matrix
W
Weight set of every indicator
t
i
Stay time of attraction i
J The total cost of the Family
J
1
The total transportation cost of the family
J
2
The cost of family in attractions
ij
q
The total transportation cost from attraction i to attraction j
ij
p
The 0-1 variable between attraction i and attraction j
i
r
The total cost in Attraction i
ij
t
The time from attraction i to attraction j
T
1
The total transportation time
T
2
Stay time in attraction
T Total time of travel process
7 7
1 1
ij
i j
p
The number of attractions for the Family
n
The number of attractions
ij
d
Distance between attraction i and attraction j
m
The average cost of taxi ride
v The average speed of the taxi
e
i
total consumption in attraction i
U
i
Index in tourist route evaluation(i=1,2...4)
V
i
Comment level(i=1,2...5)
a Judgment matrix
R
ij
The percentage of indicators i in level j
R Evaluation matrix
A Satisfaction of tourist route
C Fuzzy evaluation weight matrix
![](https://csdnimg.cn/release/download_crawler_static/88965823/bg5.jpg)
4
5. Establishment and solution of model
5.1 Establishment and solution of model A
5.1.1 Stratification of each index
By layering and refine indicators, the index system was eventually see Figure 1
Figure1:Indicator system after stratification and refinement
5.1.2 Determination of each index
According to the index system,Listed the following judgment matrix,determined the
weight of each indicator and listed corresponding weights in the following table1
—
7
Table1: Judgment matrix(A-B) and corresponding indicators weights
Systematic
Review
Value of
the
attractions
ticket
prices
regional
conditions of
attractions
W
Value of the
attractions
1 2 4 0.5584
ticket prices 1/2 1 3 0.3196
regional
conditions of
attractions
1/4 1/3 1 0.1220
Consistency checked has solved the largest eigenvalues by Matlab:
max
,
1
n
CI
CI CR
n RI
Corresponding values random consistency index in the following Table 2:
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