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mathorcup数学建模挑战赛获奖论文-第四届C题_10560e.pdf
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Optimization design for the needs of multi-level
Xi'an tourism line
Number:10560
Abstract
This paper focuses on the summer vacation parents lead children to Xi'an tourism, travel
route optimization problems are studied, the Xi'an fifteen spots as a tourist attraction, tourist
routes through the analysis of cost, time, number of tourist attractions, according to the
different demand for tourism, is divided into five types: (1) the cost is not restricted spend the
least time, (2) no time limit, cost the least cost (3) limit cost, actually may be more attractions
(4) limited time, as much as possible attractions (5) limited time and cost, as much as possible
to visit scenic spots.
To solve the problem (1), first of all, carries on the analysis to the total travel time
consumption, which is mainly composed of traffic time, residence time and stay time spots in
3 parts. In view of saving time, choose the more fast taxi as tourists travel transport. The
Hamilton loop is established to minimize travel time as the objective function of the
optimization model based on. Finally, through the Lingo programming to solve the optimal
tour packages, the minimum travel time is 4 days 17 hours 30 minutes.
Problem (2) requires the least cost, primarily by the cost of transportation, tourism
accommodation, attractions tickets cost and meals and other expenses of 4 parts, this paper
choose cheaper bus as tourists travel transport. Because the problem is essentially and demand
(1) problem is consistent, use and demand (1) the same method to obtain the minimum total
travel cost is 2080 yuan / person.
For the problem (3) no time limit, so choose buses as tourists travel in order to save
transportation fee. The problem based on (2) to travel cost as constraint conditions, this paper
established the travel cost constraint, to maximize the number of attractions for the objective
function of the optimization model. The final calculated restricted travel costs 400 yuan, 900
yuan of tourists can visit the 5 and 9 spots, and for the formulation of the itinerary.
The travel time constraints of problem (4) on the basis of (1) , this paper establishes the
travel time constraint, to maximize the number of attractions for the objective function of the
optimization model. The final are restricted travel time is 2 days, 3 days and 4 days, visitors
can tour 8, 12 and 14 spots, and in 3 days as an example, the development of tourism
itinerary.
Aiming at the problem (5),which based on(3) and (4) increased the binding of travel time
and cost constraints. Therefore, the same set to maximize the number of attractions for the
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objective function of the optimization model. Finally solving the different time and cost
constraints travel routes, and gives 4 days 1300 yuan travel itinerary, the only tour of the 12
spots.
At the end of the paper, the advantages and disadvantages of the model are analyzed, the
improvement scheme is proposed, which makes the model more consistent with the actual.
Key words:
tourism route different needs cost time number of attractions
1 Restatement of the problem
Summer vacation is coming, many parents will choose this time to take the
children to the city tourism, but different families have different needs (number, cost
constraints, time constraints), please choose a tourism city (such as your city),
considering the travel route, cost, time and other factors do you think more important,
design a best travel packages for the different needs of the family.
(1)The ancient city of Xi'an as one of the cradles of Chinese civilization,
tourism resources be richly endowed by nature, is a famous historical city in the world.
Therefore, we choose the ancient city of Xi'an is modeled as a tourist city, tourists
visit Xi'an to Xi’an Railway Station as starting point, Mausoleum of the First Qin
Emperor, Huaqing Hot Spring, Terracotta Army has been selected the Ban po, Mount
Li scenic area, Shaanxi History Museum, Tang Paradise, Qu Jiang marine Museum,
Xi'an city wall, the big wild goose pagoda square, Bell Tower and Drum Tower,
Qujiang cold kiln ruins park, Datang sleepless city, Hui street, Qinglong temple and
Cui Huashan fifteen most Xi'an Representative of the tourist attractions as the place to
visit, as shown in figure 1. Considering the cost of time and travel routes, scenic spots
number of these factors, according to the different needs of people travel, make travel
play different packages of Xi'an, concrete is mainly to solve the following five
problems:
(2)The cost is not restricted, spending time at least needs, establish the
corresponding mathematical model, design tourism itinerary and give the
corresponding package.
(3)In no time limit, cost the least cost requirements, establish the
corresponding mathematical model, design tourism itinerary and give the
corresponding package.
(4)Aiming at the limited time, as much as possible attractions needs, establish
the corresponding mathematical model and design tourism itinerary.Visitors of only 3
days of travel time develop the best travel packages.
(5)According to the time limit and the cost, as many scenic spots, establish
the corresponding mathematical model and design tourism itinerary. And defining a
4 days 1300 yuan tourists to develop the best travel packages.
Figure 1 xi 'an attractions map
2 Model assumptions
During the summer holiday is the golden period of parents to lead children to
travel, Xi'an tourist attractions to attract a large number of tourists sightseeing.
Considering the tourist route still exist some uncertain factors. In order to facilitate
research, we propose the following hypothesis:
(1)Passengers were the first to arrive Xi’an Railway Station, namely from the
train station to start sightseeing, left Xi'an is also from the train station. Return the
original city.
(2)Xi'an Metro is in construction, leading to the attractions of the line is few, so
the city transportation assumptions to bus (including the shuttle bus, minibus) and
taxi.
(3)Members of the same family travel route, the time required and costs are the
same.
(4)Travel expenses including transportation, accommodation, attractions tickets.
20:00 in the evening to the morning between 7:00, if you stay more than 6 hours, in a
place to stay, accommodation costs no more than 150 yuan / person / day. Eating and
other costs 60 yuan / person / day.
(5) the scenic spots have a hotel to hotel.
(6) the hypothesis on the trail no accidents, no blocking, no traffic jam.
(7) suppose waiting for a bus or a taxi time is very short, negligible;
(8) hypothesis spots open time of 8:00 to 20:00; Including da tang city that never
sleeps to 24:00.
(9) the hypothesis in the process of tourism weather conditions are good, does
not affect the schedule.
3 Symbolic description
Symbol instructions
i,j (i,j=0,1,2·······15) Represents the i or j attractions
m Represents the total cost plan during the
trip
ij
c
Transportation costs between the i
scenic spot to j attractions
ij
t
Traffic time required the i sites to the j
sites
i
Z
Article i attractions accommodation costs
T
The total time travel spending.
t
i
The residence time in the i spots
y
i
In the i attractions accommodation time
n The number of tourist attractions
ij
r
=1
Represents directly from i to j attractions
attractions
ij
r
=0
Not go to the attractions directly from i to
j attractions
i
S
=1
Represents in the article i attractions
accommodation
i
S
=0
Not in the i attractions accommodation
4 Analysis of the problem
4.1 Analysis of problem one
Problem one requirement in the no limit cost, visiting fifteen spots, and make
cost least time travel packages. Travel time by traffic time, 3 parts attractions
residence time and stay, while taxi is far faster than the bus, so in this problem, we try
to choose the taxi as a means of transport. This problem belongs to the typical TSP
(traveling salesman problem), so we set up the minimum travel time as the objective
function of the optimization model, through the LINGO programming for the optimal
scheme.
4.2 Analysis of problem two
Problem two requirements in under the condition of limited time, visiting 15
spots, and to develop a cost minimum travel packages. Total travel cost by traffic
expenses, accommodation cost, attractions tickets and eating, and other expenses of 4
parts, the taxi fees generally higher than that of the bus, so in this problem, we choose
to use the bus as a means of transport. The problem in essence is a problem with a
consistent, also belong to the typical TSP problem, only optimization objective
function is a cost minimum, with a similar problem solving methods.
4.3 Analysis of problem three
Question three is based on the limited travel expenses, as much as possible
tourist attractions. From the two analysis, the total travel costs included in the cost of
transportation, but the problem there is no restriction on the travel time, but also meet
the requirements of travel expenses. In view of the bus and taxi cost significantly
cheaper, therefore, in this issue, we as a means of transportation to the bus. The
problem is the problems on the basis of the two, add to the travel cost constraints,
therefore, we establish the constraint conditions in the travel costs, and use Lingo to
solve the largest number of attractions for the objective function of the optimization
model.
4.4 Analysis of problem four
Question four is based on the limited travel time, as much as possible tourist
attractions. From problem analysis, travel time generally includes traffic takes time,
but the problem there is no limit to the cost of travel, and travel time is limited. In
view of the taxi fast is better than a bus. Therefore, in this problem, we take taxi as the
gateway to the attractions between the traffic tools. The problem is essentially based
on the problem of a, join the travel time constraints, therefore, we establish the
constraint conditions in the travel time, to scenic spots number as the objective
function of the optimization model is solved for different travel time, travel packages
are given the corresponding.
4.5 Analysis of problem five
Question four is based on the travel time limit cost, as many scenic spots. The
problem is essentially further restrictions on questions three and four, at the same time
constraints on the travel time and travel cost. Therefore, we establish the constraint
conditions in the travel time and travel costs, to the largest number of attractions for
the objective function of the optimization model, different time and cost constraints of
travel packages.
5 Establishing and solving the model
5.1 The cost is not restricted, spending time at least problem
5.1.1 The establishment of objective function
The passengers were the first to arrive Xi’an Railway Station, from the train
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