建模美赛排版.docx

1、建模美赛排版Team Control NumberFor office use only8631For office use onlyT1 _F1 _T2 _F2 _T3 _F3 _T4 _Problem ChosenF4 _145BSummaryIn order to determine the mix of trips, from the point of view of the managers and the passengers, depend on using the dynamic programming, Monte Carlo methods and genetic algo

2、rithm optimization to set up two models, we determine the optimal mix of trips. For Model 1: from the point of view of the managers, , due to the large number of camps along the River is unknown, and in order to ensure the utilization rate of camp at 100% We determine the 26 kinds of trips as 26 tri

3、p packages to be used by analyzing varying duration and propulsion in a certain condition.For Model 2: from the point of view of the managers, to begin with, by considering how to choose two vessels in A trip. Therefore, the average speeds of the vessels, as well as whether campsites are occupied, t

4、he drifting time between the two campsites are determined. Then, we take the any two vessels encounter problem into account. We divide the whole problem into several phases, and simulate the whole trip by using Monte Carlo methods. After the trip simulation, And then using dynamic programming and ge

5、netic algorithms to solve the problem. We conclude that carrying capacity of the river is 1854 vessels and allow for eleven vessels to be launched each day of the season.Contents1. Introduction. 1 1.1 Problem Background . 1 1.2 Our Work. 12. Symbol Definitions. . .33. Model Assumptions.34. Problem A

6、nalysis.55. Model 1 .5 4.1 The Foundation of Model.54.2 Solution and Result.5 4.3 Analysis of the Result.56. Model 2. .55. 1 The Foundation of Model.5 5. 2 Solution and Result.6 5. 3 Analysis of the Result.77. Discussion and Conclusion. .77.1 Strength and Weakness.77.2 Conclusions.8 8. References.23

7、9. Appendix.23 1 Introduction1.1 Problem Background The Big Long River (225 miles downstream) , there are two kinds of vessels could be taken by the passengers: oar- powered rubber rafts, which travel on average 4 mph, or motorized boats, which travel on average 8 mph. The park managers want to dete

8、rmine how they might schedule an optimal mix of trips, and how much more boat trips could be added to the Big Long Rivers rafting season.We are now faced with the following: How to optimize the mix of trips and the schedule? By considering the carrying capacity of the river, how to determine the tim

9、es boat trips could be added to the Big Long Rivers rafting season ?1.2 Our work As we know, Xtrips travel down the Big Long River each year during a six month period. There areYcamp sites on the Big Long River, distributed fairly uniformly throughout the river corridor. The trips range from 6 to 18

10、 nights of camping on the river, start to finish. Thus we will consider as following: Based on the Ycamp sites certain conditions, determine varying duration (measured in nights on the river) and propulsion (motor or oar) to utilize the campsites in the best way possible, with minimal contact with o

11、ther groups of boats on the river. After mathematically analyzing the Camping schedule, our modeling group would like to describe our key findings to the managers of the river.2. Symbol DefinitionsVariable DefinitionThe speed of the i-th driftingi-th drifting push mode ( motor or oar) Variable ( 0 o

12、r 1)Camp site occupied variable ( 0 or 1)SThe length of the riverdThe average distance between the two campsitesYThe number of campsitesXThe number of packagesThe time of starting at i-th drifting to the camp site j-thRandom residence time in the campsitex-th days in the six-month open period（）yy-th

13、 motorized boat in a dayxx-th oar- powered rubber rafts in a dayThe first motorized boat departure time everydayThe oar- powered rubber rafts departure time everydayMotorized boat drifting space（）oar- powered rubber rafts drifting space（）Ma total of vessels in a dayThe number of motorized boat every

14、 daybThe drifting time of motorized boat every day .BThe drifting time of oar- powered rubber rafts every day .Drift days of yth Motorized boat in x-th dayDrift days of yth oar- powered rubber rafts in x-th dayjj-th Camp siteyth motorized boat in x-th day to the j-th camp site at k-th dayyth oar- po

15、wered rubber rafts in x-th day to the j-th camp site at k-th dayProbability of yth oar- powered rubber rafts in x-th day to the j-th camp site at k-th dayProbability of yth motorized boat in x-th day to the j-th camp site at k-th day3. Model AssumptionsWe assume that : For camping 6 to 12 nights tou

16、rists, we only provide oar - powered rubber rafts, called package 1-7; For camping 13 to 18 nights tourists, we only provide oar powered motorized boats, called package 8-13; For the same kind of travel package, every day in the big river rafting distance is the same, start to finish; The oar- power

17、ed rubber rafts which travel on constant average 4 mph. The motorized boats which travel on constant average 8 mph. Changing vessels in a trip can be neglected; The traveling distance of each vessel in a day must be positive. The impact of natural factors of the trip can be temporarily ignored.4. Pr

18、oblem AnalysisTo the question 1: The question 1 belongs to a kind of optimization problem in mathematics, which is, namely, with the different time and the different promotion methods (motor or plasma), arrange an optimal mixed travel plan, make maximum use of camp, and to make ships as little acces

19、s to other ships on the river. In this paper we use the computer simulation, the Monte Carlo method, integer programming, genetic algorithm and other related theory to establish and solution model.To the question 2: We must calculate how many times of trips can be scheduled per day on the basis of t

20、he question 1. Only in this way can we make the maximum use of camp, thus further find out how many times of trips can be scheduled in the six months. Then, the carrying capacity of the river is concluded. To realize the bearing capacity of the river to maximize, we must both consider every hair shi

21、p time, and to consider the maximization of unreasonable ship time minimization. Then, we analyze the bearing capacity of the river and state our own opinions.After solving and analyzing the problem, we set up two models.5. Model 1Model 1: From the view of tourism managerBecause the number of camps

22、along the coast is unknown, and for the convenience of tourism managers to manage, the tourism strategy we have formulated is based on the number of camps. Under the premise of the camp utilization rate of 100%, we make sure the days of trips we can provide for visitors.Taking both travel time and t

23、ravel tool into consideration, we divide travel mode into 13 * 2 = 26 kinds of travel package .But because the number of camps along the river is unknown, and we have to make assumptions: the distance of traveling every day in each package is same and drift constant progress. So according to the num

24、ber of unknown camps, we need to provide the combination of traveling days so as to make the sum of all combinations of the traveling days equal the sum of the number of the camps. And then put all the camp on distribution, make all kinds of camping days drift has a definite camp with the correspond

25、ing, i.e., Before the tourists set off, the given camp visitors should stay in has been made sure. So the utilization rate of camp can reach 100%. And then, the tourists choose from by oar - powered drift, or by rubber rafts drift by themselves. Finally which kinds of the package types should be pro

26、vided for passengers is determined.During 6 months of the tourist season, in addition to the last 17 days, the remaining 163 days of every day are the same, so for the first 163 days, we only need to determine the tour arrangement of the first day, and then the travel arrangements of the rest of the 163 days are the sa