杭州电子科技大学07年数模美国赛特等奖文章!The Kidney Exchange Problem

Contents1.Introduction--------------------------------------------------------------------------------12.Assumptions-------------------------------------------------------------------------------33.SymbolsandDefinitions----------------------------------------------------------------34.Solutions-----------------------------------------------------------------------------------44.1Task1--------------------------------------------------------------------------------44.1.1ProblemAnalysis------------------------------------------------------------44.1.2Modeldesign-----------------------------------------------------------------74.1.3PotentialBottlenecksAnalysis--------------------------------------------104.1.4FurtherDiscussion----------------------------------------------------------104.1.5Exampleanalysis------------------------------------------------------------114.1.6Modelimprovement---------------------------------------------------------124.2Task2--------------------------------------------------------------------------------134.2.1EvaluatingtheOPTNpolicy-----------------------------------------------134.2.2One-pageReport-------------------------------------------------------------174.3Task3--------------------------------------------------------------------------------184.3.1ProblemAnalysis------------------------------------------------------------184.3.2ModelDesign----------------------------------------------------------------194.3.3Simulationsexample--------------------------------------------------------234.3.4Conclusion--------------------------------------------------------------------254.4Task4---------------------------------------------------------------------------------264.4.1ProblemAnalysis-----------------------------------------------------------264.4.2ModelDesign-----------------------------------------------------------------264.4.3Solutionandresult-----------------------------------------------------------304.5Task5---------------------------------------------------------------------------------324.5.1AnalysisonEthicalandPoliticalissues-----------------------------------324.5.2ChangingandRankingorderthecriteria---------------------------------------354.5.3ModifyingtheModelsinTask3andTask4-----------------------------394.5.4Organcanbesoldornot?-----------------------------------------------------404.5.5One-pageReport-------------------------------------------------------------434.6Task6---------------------------------------------------------------------------------444.6.1RisksAnalysis-----------------------------------------------------------------444.6.2Modeldesign-------------------------------------------------------------------454.6.3ModifyModels-------------------------------------------------------------------------474.6.4Appealtomoredonors----------------------------------------------------------485.StrengthsandWeaknesses------------------------------------------------------------------496.References-----------------------------------------------------------------------------------507.Appendix------------------------------------------------------------------------------------517.1AppendixⅠ---------------------------------------------------------------------------517.2AppendixⅡ---------------------------------------------------------------------------57Team#1477Page1of69OrganTransplant:TheKidneyExchangeProblemOrganTransplant:Thekidneytransplantationproblem石佳乐（自动化）邬仲臻（信息与计算科学）李焕森（软件）美国特等奖ExecutiveSummaryAlongwiththecontinuingandrapidadvancesinmedicineandhealthtechnology,theproblemofOrganTransplantisbecomingahotspotnow.However,manybottleneckproblemsinOrganTransplanthavenotbeenhandleduptothepresent.ThisthesisdiscussessomekeyissuesaboutOrganTransplant.AccordingtotheanalysisofOPTNpolicy,webuildanetworkmodel,wherethenetworkcontainsthreeparts.AmongthemthekeypartistheOrganBank(OB),aninformationprocessingsitetodefinethebestorganmatchingprocess.WeintroducetheobjectionfunctionandsomeconstrainsfortheOBsystemtodefinetheprioritymatchingproblem.MonteCarloSimulation,baseduponthePointSystem(anallocationstrategyusedinUNOS),isadoptedtoanalyzethisissue.Fromtheresultsweobtainthatmoreresourceswillbringanimprovedorganmatchingwhereassmallnetworkwillhavesomeimpactontheorganmatchingdespiteofareduceofthematchingcost.Weexploresomebottlenecksoftheorgantransplantproblem,accordingtoourmodelandthestatisticsdata.Then,withcomprehensiveanalysisofpoliciesinU.K,SpainandtheKoreaonorgantransplantation,weevaluatetheOPTNbycomparisonandmakesomeimprovements.Whenitcomestothekidneyexchangeproblem,weestablishamodeltomaximizethenumberandqualityofthekidneyexchanges,weintroduceaTopTradingCyclesandChains(TTCC)mechanisminourmodeltofindabetterexchangeprogram.Takethemedicalandpsychologicaldynamicsofthesituationintoaccount,webuiltapreferenceconstructionmechanism(R-C)inordertoimprovetheexchangequality.Then,fromtheperspectiveofthepatient,wediscussthestrategyhewillchooseinourdecisionmodelunderStochasticDynamicprogramming.Accordingtothepa