沿大河漂流问题的分析

Ⅱ.IntroductionRafting is an extreme sports with thrills, its purpose is to make every travelers to have a memorable experience. In the past few years, this movement is also popular in the world. British long river rafting. Next it is the situation of the British long river rafting.Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. River trips all start at First Launch and exit the river at Final Exit, 225 miles downstream. Passengers take either oar- powered rubber rafts, which travel on average 4 mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of camping on the river, start to finish. Currently, X trips travel down the Big Long River each year during a six month period (the rest of the year it is too cold for river trips). There are Y camp sites on the Big Long River, distributed fairly uniformly throughout the river corridor. You must remember that no two sets of campers can occupy the same site at the same time. We should decide a reasonable number of camping area during the drift, as well as the development of suitable drifting to ensure that each traveler can feel the shortage vast field experience, as well as to determine the maximum carryingcapacity of the river vessels.Ⅲ.Problem AnalysisThe issues raised in this article is how to arrange the number of arrangements camping area, and to develop an appropriate drift way to ensure that each traveler can feel the shortage vast field experience, as well as to determine the maximum carrying capacity of the river vessels.Contrary to question one, considering the factors has been limited such as rafting period, rafting the ships not in the same time and place meet during the drifting. It can be abstracted to a simple encounter problems to solve it. Thus we can take advantage of the integer programming model to obtain the optimal number of the camping areas.Contrary to question two, according to the analysis of the question one, in accordance with the distance between camping areas and the number of camping areas, and the speed of the boat. We can divide into travel plans for one stop a day, two stops a day, and a day in three stations. According to the factors of the tourism ,such as weather conditions, fares, travel time, service management and so on. We can take full advantage of the AHP to establish the mathematical model to obtain the travel plans of the heavy weights of decision makers, and to seekappropriate travel plans used to calculate the maximum carryingcapacity.Contrary to question three, according to the problem of two,we can obtained the maximum carrying capacity of the river.And we use the known of knowledge again. We can reasonablyarrange to the different drifting way to meet the requirements ofthe castaways.Ⅳ.Symbol Descriptionis the distance between of the camping areas.tY is the number of the camping areas nearby the Big Longriver.w is the ratio between the first boat from a day to the i days isailing distance and lT is the deadline for the camp.Ⅴ. ModelsBasic Model5.1 Model 1Model one is solving the issue of the maximum number ofcamping trips, we use integer programming methods through thelimited conditions , we can list the constraint equations of themaximum number of the camping trips through the LINGOsoftware, you can get that when t = 6,7,9,11,13 days, and w =30,50,80,110,150 ,we can calculate the maximum ofk1. Through the analysis ,we can list the equation of the maximum number of boat trips.According to the ratio between the distance of the last sailing boat from the first day to the last day and t ∆. And it is nott w .but it can get the end place .we can list the followingequation.1i i w w +> (i=2,3,4……t-1)Due to the departure of the ship in the next day can ’t exceed the departure of the ship on the first day. we can list the following equation:1111(1,2,......1)ji j i i t w W j t =-=+>=-∑∑The last departure ship on the fist day must fall behind from the first departure ship in the next day , we can list the following equation:11i ti W Y ==+∑0i w =According to the above equation, we can use the MATLAB software. We can get the following results. When t = 6,7,9,11,13, w = k1 30,50,80,110,150 ,we can get the maximum of k1. It is in the following table:Table 15.2 Model 2:The best scheduling mode :The daily travel arrangements remain unchanged.According to the analysis of the problem ,we can take it as a cycle of the process,so it is easy to solve the problem. Thus we can come to the six months of the largest number of boat drifting period.(180)1h t k =-⋅And because the t is more bigger , the k1 is more smaller, to make the six months of drifting boat number within themaximum, it should be necessary to reduce the time of tourism.A day for the hair of the first ship speaking, the ship on the first day finally stay in position can through the formula and the:225l⋅=⨯=303044.7151So the first ship will stay in the camp which distance is 44.7 miles one day later, and most of the time on the river is ten hours, if drifters choose rubber raft will not be able to reach the specified camp, so in this situation ,except the last day the first ship should be adopt combination drift mode.Put on the first day of the ship after distance for x l⋅Tox<. Due to the ship's 40xl⋅<, work out the equation,26.8departure time interval can be very short, for ten hours negligible. So in a day of the fifth on the first day of the ship can use rubber raft to drift, and then start ships need particular case is particular analysis. To deal with the first day and the last day of the other time, but also need to adopt the dynamic way drift. If the daily travel arrangement is not the same.And to reduce travel days, if the ship line according to the original arrangement way, there will be a meeting, so need to do some changes can be achieved.Thus we are easy to find, every journey remain unchanged, the bearing capacity of the river be related to time, travel days,and the number of camping on the river, but the biggest capacity for camping, according to the number of every day on the first ship can achieve the longest camp to obtain the number of send ships in one day, and the next day journey all remain unchanged. Therefore, every day the same time the ship on the location of the camp exactly the same, when the first day of the last ship arrived at the last camping ground, at the t-1 day ,the final ship reach the final camping site, so the maximum carrying capacity of river is (1)w k t Y =-= .When t = 6,7,9,11,13 day, Y = 30,50,110,150 separately obtain the maximum carrying capacity of river, the table below ：Table 25.3 Model 3:According to the meaning of problems ,we can analysis thatfrom start to finish the entire trip need 6-8 nights. During the trip ,the camping areas must set up more than eighteen. Because the average speed of the two drifting tools are 4 mph and 8mph. The total length of the big river is 225mp.We know that the total time of drifting are 56.25h and 28.125h.Thus We can infer that the tourists pass travel drifting place every day are 1 station , 2 station and 3 station.During the process of drifting , we will take into account weather conditions, fare, travel time, service quality impact on the number of the drifting places.We can get the association graph next:5.3.1 The solving of program layer and criteria layer solvingIn this travel,We can think that it is not suitable for thecontemporary consumer groups , the regardless of too many or too few people. Taking into account today's concept of time are higher than the service concept, Three stops in a day are slightly more popular than one stop in a day. We will design different fares, travel time, quality of service during the implementation of the program. First of all, We will analyze the influence between the program scale layer and fare. We can get the result of the comparison:Table 3According to analysis of the matrix ,We can get the largest eight value of the matrix is three with the help of matlab. We can know that the matrix is consistent matrix. We can treat the column vector ()1,5,2Tas its characteristic vector. Again usingmatlab normalization process to obtain the weight vector ()0.125,0.625,0.251T β=.Secondly, we will study the mutual influence of the programlayer to their travel time. Through the meaning of this problem,we know that different trip tools have different speed. It has a decisive impact on the number of the camping sites. So we can get the travel time t:()225118481i i t c p p ≤⋅⋅⋅+⋅- c is the number of stations on a day; when t=1,the travel tool is the rubber boat; when 0i p =,the travel tool is motor boat. Considering the boat depend on the people, the process of trip time should not be too long or people will be feel tired. But the camping trip will not very short. Thus, we will get the program matrix layer guidelines layer diurnal time. According to compare with each other, we can get the table:Table 4According to analysis of the matrix , We can get the largest eight value of the matrix is 3.0505 with the help of matlab. For the look-up table shows that three matrix RI = 0.58,we know thatmax 0.025,0.0440.11n CI CI CR RI n λ-== ==<-Table 5The positive and negative matrix analysis, can be obtained by matlab the matrix biggest characteristic root for 3, then know this matrix for consistent matrix, take its column vector ()2,1,6TAs its feature vector.Again, the matlab isnormalized the weight vector is obtained()30.22,0.11,0.67T β=5.3.2 The influence of guidelines layer and the target layer Due to the weather changed, we inquire that weather conditions are generally stable in the Mississippi. We only consider that the impact of criteria layer fare, travel time, quality of service to the target layer. Because of its proportion can’t decided, we will be based on each collection of information to compare. We will get the matrix as follows table:Table 6According to analysis of the matrix , We can get the largest eight value of the matrix is 3 with the help of matlab. We can accept inconsistencies of the matrix. We can treat the column vector ()1,7,2Tas its characteristic vector. Again using matlabnormalization process to obtain the weight vector()0.22,0.11,0.67TW =.5.3.3 Seeking the influence of program layer and the target layerFirst, we will get CI and CR. So we get the next formula:()1230.00275CI CI CI CI W =⋅=，，0.00470.1CI CR RI==<Examination shows that the target layer the combination matrix layer of the programs can be used as the basis for decision making. We will get the result:()()131223,,,,TC C C W βββ=⋅1230.1250.750.220.220.310.650.120.110.110.520.170.250.130.670.67C C C ⎛⎫⎛⎫⎛⎫ ⎪ ⎪ ⎪⎪⎪⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎛⎫ ⎪⋅= ⎪ ⎪⎝⎭=So we get the program layer in the share of the impact of the proportion of the target layer of decision-making()()()1:2:30.31:0.52:0.17n n n α==On the basis of this ratio, the proportion of traveling different camping places on a daily is ()()()1,2,3n n n .5.3.4 based on the actual situation analysis solutionAbove is the basic theoretical scheme, in the actual operation than the design more complicated, so in order to make the ships of less as far as possible to meet, but also to prevent the river congestion problems and the same camp stay days of problem arises, the model should consider when day line more camping site ships could not travel on the same day, and because the date line camping site many ships will catch up with the date line camping site less number of ships, this kind of situation will lead to two ship in the same place meet, if the day line stationnumber less in day line station number on the back of the camping site will lead to idle, in order to match the economy and demand synchronization, we need to arrange your time and make the entire river is full day line camp station number of the same ships, only by this way can we avoid meeting and conflicting problem, also makes the camping site no idle phenomenon to appear.Ⅵ.The strengths and weaknesses of the mode:6.1 The advantage of the model(1)In this model, we treat the complex reality into the ideal ofthe pursuit problem, we take advantage of chase ideal obtained optimization program.(2)In this model, we make use of the analytic hierarchy process,we analyze the proportion of each factor, we get the best allocation ratio.(3)In this model, we use the integer programming to solve theallocation problem. It is very easy to understand. We analyzed each problem with the actual solution.(4)In this model, not only we analyze the optimal solution of theidealized. We analyze the problem with actual situation.Finally, we arranged for the travel time list reasonable.6.2The disadvantage of the modelAlthough we combined the ideal model with the actual model each other. But the actual phenomenon is very complex, The results obtained must exit in the assuming range. If it exceeds this rang, we will make other decision.Promotion and optimization of the model:Due to the error caused by the ideal and the reality, During the solution of the model, the error is very difficult to avoid. Especially, when the weather is not very sunny and t he boats’ travel speed are unreasonable. Its will affect the implementation of the program. We can use the computer to simulate and fit the ideal and the reality repeatedly. Making sure the results more flexibility. Finally, we are able to obtain the results for each case.Ⅶ.ReferencesDaganzo, C.F., et al. 1997. Causes and effects of phase transitions in highwaytrafpc. ITS Research Report UCB-ITS-RR-97-8 (December 1997).Halliday, David, Robert Resnick, and Jearl Walker. 1993. Fundamentals ofPhysics. 4th ed. New York: Wiley.Yates, Daniel, David Moore, and George McCabe. 1999. ThePractice of Statistics.New York: W.H. Freeman.. 2000. Voluntary and Involuntary (“Bumped”) Denied Boarding(Jan-Sep2000)./library/stats/blrpt8.htm . Airlines overbooking project. DATE???./~brycw/classes/ date???361/overbook.htm .。