The Time Window Model and Shortest Path Model Design for Travel All 5A Scenic Spot in China

Travel has became one of the most popular ways of modern lifestyle. This paper mainly discusses the route planning of travel all 5A scenic spots in the China. Firstly, We establish a mathematical model and transform the limited conditions include the scenic tour time, driving time, accommodation and other aspects to the mathematical formulas. Then, we introduce the relevant variables from the basic formula and draw the flow chart of the algorithm. In some places that densely-scenic spot, we use the "postman problem" to give the solution and specific analysis some places according to the specific conditions. Specifically, according to the seven regions of the country, we find the best path. In the same area, according to the specific circumstances such as the time and route of the integration, while considering the requirements of the subject like visit time and proportion of driving time, we plan to visit scenic spots one provine by province In order to improve the utilization rate of the time, we arrange the tour attractions in different regions in one year, let the vistor feel the difference between different areas of the landscape, fully enjoy the great rivers and mountains of the motherland, enhance the overall quality of tour.


Background of Problem
With the improvement of people's living standards, tourism has become one of the activities that people love, and it is becoming one of the important driving force for the development of the global economy. More and more people like to travel the scenic spots and historical sites or famous mountains and great rivers to relax their body and mind, improve their self-cultivation on a holiday.
A self driving travel enthusiasts plan to travel the all 201 5A level scenic spots to be released by the National Tourism Administration. The travel time of this enthusiasts every year not more than 30 days, the number of trips per year is not more than 4 times, each time not more than 15 days. At the same time, according to the degree of interest, determine the minimum tour time in each 5A scenic spots. The travel enthusiasts based on safety considerations, travel time is also set to 7:00 to 19:00 per day, every day is not more than 8 hours of driving time. In order to ensure the quality of the tour and physical problems, in the daily schedule, if visit in all day, the driving time need under 3 hours; if visit a half day driving time control within 5 hours. The average speed of driving on the highway is 90 km / h, and the average speed is 40 km / h on the average road. The plan of the tourist lovers in every capital city to stay for at least 24 hours, to arrange a time to visit the city characteristic construction and experience local customs (not arrange scenic view). The opening time of the scenic spot is unified to 8:00 to 18:00.

Analysis of the Problem
The topic background can be considered as a path problem with time windows. The topic has the earliest opening time and the closeing time of the scenic spot. Under these restrictions, in addition to the spatial aspects of the path to consider, also have to add time scheduling considerations. At the same time, due to the time window of the driving car, also led to the limitation of the length of the path problem, so we not only need contains the cost of the way, but also have to consider the time cost. Therefore, the discussion of time and space is very important.
In the course of analysis the problem, firstly we consider the limiting conditions are given in the subject, according to the time window of travel to establish a model. In the route planning, we take the regional approach, travel the spots that distance close, or add some scattered spots to try to make the total travel time is close to 30 days. And then according to the number of days each tourist trip, arrangement and combination, to achieve the minimum number of total travel days. The different regions of the attractions travel in a year help to enhance the experience of tour.

Model Assumptions
1. All of the links between the provinces and cities can be passed smoothly, there will be no traffic jams, etc.; 2. We do not take into account changes in the weather, tourists sick and other unexpected situation; 3. The speed of the car to maintain constant speed unchanged; 4. Some scenic spots need to visit in one day and can accommodation in the scenic spots area can be divided into two half day tour, such as Chengde Mountain Resort scenic spots, Mountain Resort and the surrounding temples can be separated from the tour. 5. This design don't reflect the time about traveller dining and going to the toilet, the default in driving, traveling or accommodation time to solve those problem.  M : The time required for visit some scenic area, the value of 4 or 8; ' 1 d G + : The highway has not been completed in d day, it needs to go on in d+1 day. ' 1 d P + : The non highway has not been completed in d day, it needs to go on in d+1 day.

Constraint Condition of the Model
According to the problem, the constraints are listed as follows, When 19

Analysis Model Method
Situation one: can reach the destination within one day.
Then visitor go to the next destination.
To judge the distance between the starting and destination circulatly and get the maximum value of each trip. The result obtained by this method is the feasible solution under certain conditions, and it is not the optimal solution.

Model Solving and Route Planning
According to the established model and the information provided in the attach, through access to information collection involved between provinces mileage to divide the area into modules, uphold the principle of concentrated spots together travel, scatter spots combination travel, introduce the "a pen to draw" and "Chinese postman problem"to design a reasonable route, see in the table below: The self driving tour to finished the national 5A level scenic spots spend on 12 years and 9 days. In the planning process, the the spots in same areas visit toghter, but taking into account each year only 30 days time to visit, so in a year we will arrange the tour attractions in different regions to improve the utilization rate of the time, on the other hand can also reflect differences in different areas of the landscape, fully enjoy the great rivers and mountains of the motherland and enhance the overall quality of tour, such as in the fifth year of visit Shandong and Hainan, the ten year visit Xinjiang and Sichuan, the eleventh year of visit Tibet, Qinghai, Gansu, Ningxia and other northwest regions and Chongqing.

Conclusion
We divided the country into seven regions, according to the defined conditions and requirements eatablish a linear programming model. Then we plan out every time travel route under the background of "Chinese postman problem", according to the specific conditions, uphold the principle of concentrated spots together travel and scatter spots combination travel to improve the tour quality, reduce travel time and travel times.
The design integrates the constraints of the linear programming, Chinese postman problem, variable neighborhood search algorithm etc. eatablish a mathematical model, get the reasonable results under many conditions. Due to our limited level, and collected information on the existence of errors, this result is not the best solution, but it has been possible to make full use of condition, balance the time and cost, to ensure the quality of travel.