大连理工大学数学建模优秀论文
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Team Control Number For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________
13219
Problem Chosen
For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________
B
2012 Mathematical Contest in Modeling (MCM) Summary Sheet
Fra Baidu bibliotekSummary
Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. To meet the demands of tourists, we get two kinds of solution by using Dynamic Programming. The article use class cellular automatic model programming to get optimal project. The whole trip is transformed into 256 points, then this 256 points consist of a array. Analyzing the distance that boats travel everyday, and the distance of two kinds of boats range in a certain extent. Y is determined to confirm camp sites. By analyzing the distance between two camp sites, then we can draw the conclusion that we can get more trip scheme in 180 days. The first solution method use a large number of motorized boats , so traveling on the river last about 8 days. This speed, and motorized tours are not practically. As everyone known that more people prefer oar-powered rubber rafts, it will be unpopular. On the other hands, its advantage is that having more passenger flow volume. The second solution can't allow changing boats. Compare with the solution 1,the passenger flow volume of this method is less than solution 1. Especially the number of camp sites range from 13 to 18, volume of solution 2 is half of solution 1. But the proportion of using oar-powered rubber boats has risen,it will enlarge the tourist choosing space, and more meet the demand of river manager.
Team #13219
page 2 of 9
Ⅲ. Models 3.1 Problem analysis 3.1.1 Analysis of ships velocity It is demanded that the trips range from 6 to 18 nights of camping on the river, start to finish. It means that it range from 7 to 19 days of camping. As a result of the fastest speed of motorized boats, it needs 7 days over the whole trip. And because of the average speed of motorized boats is 2 times of the oar-powered rubber rafts, it require 14 days to finish the whole trip least. Consequently we can assume that the trip range from 7-13days by motorized boats and 14-19days by oar-powered rubber rafts. 3.1.2 Analysis of camp sites It is known that the tourists need to rest at night, for the reason that highest speed need 7 days finish the whole trip we should set 6 camp sites at least. On the other hands, considering the capacity on both sides of the river and cost that we analysis 50 camp sites most in the following analysis. 3.2 Total solution 3.2.1 Solution 1 We assume that tourists can change boat when they are on the camp sites. Under the circumstance, to simplify the problem, two kinds of boats can be transformed into a boat that velocity can change from one camp site to another. So we can get the conclusion by analyzing the speed of the boats. 3.2.1.1 Model 1: 1.Transforming the whole journey to 225 parts.(1miles=1parts) 2.Preset a y, part of（n*225）/（y+1) is the n camp sites. 3.Due to one camper occupy one camp site, statistics the occupied point we can get how many camper join the trip. 4.Each boat travel range from 12 miles to 32 miles every day 5.New boats add to the trip and occupied the most sites every day. 6.Get results after 180 days.
Team #13219
page 1 of 9
Solving Big Long River Camping Trip with Dynamic Program
Key words：Dynamic Program
Ⅰ.Introduction
cellular automata
optimization
Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The river is inaccessible to hikers, so the only way to enjoy it is to take a river trip that requires several days of camping. .The article using the dynamic programming method to solve the big long river problem. Using class cellular automatic model programming get optimal project. We make full use of camping sites to arrange more trip. The first solution is in that situation of allowing changing boat during the trip. The second solution is assuming that can't change the boat through the kind of cellular automata programming for results Ⅱ.The Description of Problem Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. 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. The government agency responsible for managing this river wants every trip to enjoy a wilderness experience, with minimal contact with other groups of boats on the river. 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. Given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. They want to determine how they might schedule an optimal mix of trips, of varying duration (measured in nights on the river) and propulsion (motor or oar) that will utilize the campsites in the best way possible. In order to indicate the origin of the River Camping problems, the following key point is worth mentioning: 1.The whole journey and every day journey should be quantified. 2.Camping the position of the set point, and number of the lower. 3.Clear top and bottom speed limitation of two kinds of boat.
13219
Problem Chosen
For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________
B
2012 Mathematical Contest in Modeling (MCM) Summary Sheet
Fra Baidu bibliotekSummary
Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. To meet the demands of tourists, we get two kinds of solution by using Dynamic Programming. The article use class cellular automatic model programming to get optimal project. The whole trip is transformed into 256 points, then this 256 points consist of a array. Analyzing the distance that boats travel everyday, and the distance of two kinds of boats range in a certain extent. Y is determined to confirm camp sites. By analyzing the distance between two camp sites, then we can draw the conclusion that we can get more trip scheme in 180 days. The first solution method use a large number of motorized boats , so traveling on the river last about 8 days. This speed, and motorized tours are not practically. As everyone known that more people prefer oar-powered rubber rafts, it will be unpopular. On the other hands, its advantage is that having more passenger flow volume. The second solution can't allow changing boats. Compare with the solution 1,the passenger flow volume of this method is less than solution 1. Especially the number of camp sites range from 13 to 18, volume of solution 2 is half of solution 1. But the proportion of using oar-powered rubber boats has risen,it will enlarge the tourist choosing space, and more meet the demand of river manager.
Team #13219
page 2 of 9
Ⅲ. Models 3.1 Problem analysis 3.1.1 Analysis of ships velocity It is demanded that the trips range from 6 to 18 nights of camping on the river, start to finish. It means that it range from 7 to 19 days of camping. As a result of the fastest speed of motorized boats, it needs 7 days over the whole trip. And because of the average speed of motorized boats is 2 times of the oar-powered rubber rafts, it require 14 days to finish the whole trip least. Consequently we can assume that the trip range from 7-13days by motorized boats and 14-19days by oar-powered rubber rafts. 3.1.2 Analysis of camp sites It is known that the tourists need to rest at night, for the reason that highest speed need 7 days finish the whole trip we should set 6 camp sites at least. On the other hands, considering the capacity on both sides of the river and cost that we analysis 50 camp sites most in the following analysis. 3.2 Total solution 3.2.1 Solution 1 We assume that tourists can change boat when they are on the camp sites. Under the circumstance, to simplify the problem, two kinds of boats can be transformed into a boat that velocity can change from one camp site to another. So we can get the conclusion by analyzing the speed of the boats. 3.2.1.1 Model 1: 1.Transforming the whole journey to 225 parts.(1miles=1parts) 2.Preset a y, part of（n*225）/（y+1) is the n camp sites. 3.Due to one camper occupy one camp site, statistics the occupied point we can get how many camper join the trip. 4.Each boat travel range from 12 miles to 32 miles every day 5.New boats add to the trip and occupied the most sites every day. 6.Get results after 180 days.
Team #13219
page 1 of 9
Solving Big Long River Camping Trip with Dynamic Program
Key words：Dynamic Program
Ⅰ.Introduction
cellular automata
optimization
Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The river is inaccessible to hikers, so the only way to enjoy it is to take a river trip that requires several days of camping. .The article using the dynamic programming method to solve the big long river problem. Using class cellular automatic model programming get optimal project. We make full use of camping sites to arrange more trip. The first solution is in that situation of allowing changing boat during the trip. The second solution is assuming that can't change the boat through the kind of cellular automata programming for results Ⅱ.The Description of Problem Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. 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. The government agency responsible for managing this river wants every trip to enjoy a wilderness experience, with minimal contact with other groups of boats on the river. 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. Given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. They want to determine how they might schedule an optimal mix of trips, of varying duration (measured in nights on the river) and propulsion (motor or oar) that will utilize the campsites in the best way possible. In order to indicate the origin of the River Camping problems, the following key point is worth mentioning: 1.The whole journey and every day journey should be quantified. 2.Camping the position of the set point, and number of the lower. 3.Clear top and bottom speed limitation of two kinds of boat.