2016數(shù)學建模美賽f題論文

1、For office use onlyT1 ________________T2 ________________T3 ________________T4 ________________Team Control Number 49365 49365Problem ChosenFFor office use onlyF1 ________________F2 ________________F3 ________________F4

2、________________2016 2016 MCM/ICM MCM/ICMSummary Summary Sheet Sheet(Your team's summary should be included as the first page of your electronic submission.) Type a summary of your results on this page. Do not includ

3、ethe name of your school, advisor, or team members on this page.SummaryOur analysis and targets: In essence, this problem is kind of a case of maximum flow and minimum consumption with multiple sources and targets. “Mult

4、iple sources” refers to different original countries of refugees involved in the case, while “multiple targets” refers to different target countries where refugees arrive. It’s our aim to rationalize the flows of refugee

5、s and to optimize the target country for each refugee, i.e. to optimize the choice of transmitting routes and the allocation of available resources with various condition factors.The general idea and method: Set an indic

6、ator which consists of different parts of different factors. The indicator is designed to reflect the severity of both transportation and resources consumption. Every sub-factor should inflect the gap between theoretical

7、 value and actual conditions. For the actual conditions, we can get enough data to describe or estimate it. As for the theoretical value, we introduce the advanced Dijkstra algorithm inspired by Edmond-Karp algorithm. Be

8、sides, we proposed the conceptions: weighting factor matrix, resources factor matrix, a series sub factor matrices which is designed to describe the effect caused by different factors. The problem is quite similar to the

9、 model of water supply system. So we use the similar defining method to tackle the problems. Main results and conclusions:The model works well under dynamic conditions and the results fit the real situation well, while t

10、he factor of politics and the factor of adjustments can be changed thus it is able to assess the cascading effects. It is helpful when the population of refugees grows rapidly and is able to make prediction of the maximu

11、m capacity of European mainland to consume the flow of refugees.Key points:Maximum flow and minimum expense /Water supply network model Dijkstra algorithmTeam#49365

12、 Page 2of 25problem.It’s our aim to rationalize the flows of refugees and to optimize the target country for each refugee, i.e. to optimize the choice of transmitting routes and the allocation of available r

13、esources.1.3.2Our work1) We build a basic refugee flow model based on the water supply pipe network model and Maximum flow and minimum expense model.2) The basic algorithms are Dijkstra(optimal route for flow from a sing

14、le origin) algorithm and Edmond-Karp(maximum flow with multiple origins) algorithm. We modified this two algorithms to adapt this multiple source and multiple targets problems. 3) The concepts of weighting factor matrix

15、and available resource matrix are introduced into our model. Both matrices are composed of various factor matrices which represent different situation parameters.4) We proposed a series of formulas to calculate different

16、 factors.5) We extended and modified the model under different new conditions, and introduced corresponding factor matrix to measure the situation. For example, feedback factor matrix, cascading effect factor matrix.6) S

17、ensitivity of the model has been analyzed under different situations.7) An optimal policy has been proposed according to the result of our model.8) Scalability is discussed in different situations.2 Assumption and Justif

18、ication2.1 Basic Assumptions1) Terrain factor is out of other consideration.Reason: The terrain of the most regions referenced in the problem is flat. So it can be taken as a plane problem.2) Every refugee is regard as e

19、quivalent individuals except for their position and religion attributes.Reason: Human nature is nearly all the same. The desire to high income and rest social environment and better welfare policy is similar to each othe

20、r.3) Not every country will be included in this model. Only typical and crucial countries are selected in our model.Reason: There is nearly no refugees on certain routes out of position or other factors and the adjustmen

21、t of policy won’t change this situation which means it means nothing for our model.2.2 Special Assumptions for different situations1) At the beginning of modeling, apart from the six routes mentioned in the question, we

22、 do not consider other routes that refugees may choose and assume all the refugee we will concerning choose one of the six routes.2) Second, at the beginning of modeling, we do not consider all the countries that have ac

23、cepted the refugee, main countries producing refugees and main countries accepting refugees, such as Germany,France,Spain,Sweden,Afghan,Iran,Iraq,Syria,Turkey,Greece,Albania,Macedonia,Bulgaria,Rumania,Serbia,Montenegro,B