运筹基础课程 1

BriefIntroductionto

OperationsResearch***湖南大学

工商管理学院

管理科学与商业智能系LectureOutlineCourseAdministrationOriginsanddevelopmentofORDefinitions&featuresofORMajortopicsofORApplicationsofORApproachofORHowtostudy?ORSoftwareOperationsResearch21.CourseAdministrationInstructorInstructor:Mobile:Office:Email:QQ: OperationsResearch31.CourseAdministrationTime&LocationWednesday,[1-16]week14:30–16:00pm,研B204,16:10–17:40pm,综406Friday,[1-16]evenweek14:30–16:00pm,研B204,16:10–17:40pm,研B204ClassQQGroup:AnnouncementsAssignmentsDiscussionsCoordinationOperationsResearch4CourseObjectivesDevelopessentialquantitativeabilitiesandskillstounderstand,formulate,andsolvediversifiedrealworldoperationsresearchproblems.UsecomputersoftwaretosolveoperationsresearchproblemsMicrosoftExcelAdd-inSolver(Spreadsheet)ORforWindowsOperationsResearch5PrerequisiteCalculusLinearAlgebraMathematicalStatisticsBasicsofComputerProgrammingAchallengingcoursenomanystoriesbutmodelsandalgorithmsnotthattheoreticalforundergraduatesOperationsResearch6TextbookandTeachingMaterialsTextbook（运筹学，机械工业出版社，2025.9）ReferenceFrederickS.Hillier,GeraldJ.Lieberman.IntroductiontoOperationsResearch(10thedition)McGrawHillHigherEducation,2014OperationsResearch7中文参考书龙子泉，陆菊编著，《管理运筹学》，武汉大学出版社，2006年《运筹学》教材编写组，《运筹学》第4版（本科版），清华大学出版社，2017年周华任主编，《运筹学解题指导》，清华大学出版社，2016年OperationsResearch8Website中国运筹学会/国际运筹学联盟（IFORS）的站点/研学论坛/OperationsResearch9GradingPolicy10%,AttendanceandinvolvementBonuspointsforfrequentcontributorsinclassandinQQgroup.20%,homeworkassignments8homeworkassignments70%,Exams

Midterm(20%)Final(50%)OperationsResearch10AcademicIntegrity学生应该事先了解并遵守**大学本科学生学则等系列规则中有关迟到、旷课、考试等各项纪律的定义和处理细则。迟交作业：每次作业需在截止日期(duedate)前提交。除非另有指示，请提交打印稿给任课教师。不接受迟交的作业，除非提前至少24小时和教师沟通并提供合理解释。迟交的作业可能会被处以5%-100%的扣分。

作业抄袭:所提交的内容必须是自己完成的，如有雷同或疑似雷同，该次作业作零分处理。

事先OperationsResearch11FeedbackandsuggestionsYourfeedbackandsuggestionsaremostwelcome!tobetteradaptthecoursetoyourneeds.Shareyourquestionsandconcernswiththeclassverylikelyothersmayhavethesame.NopainnogainThemoreyouputin,themoreyougetYourgradesareproportionaltoyourefforts.OperationsResearch12OperationsResearch13李世石OperationsResearch14OperationsResearch15MatchmakingOperationsResearch16Routing&PlanningOperationsResearch17Logistics,warehouseOperationsResearch18DisasterreliefOperationsResearch19LectureOutlineCourseAdministrationOriginsanddevelopmentofORDefinitions&featuresofORMajortopicsofORApplicationsofORApproachofORHowtostudy?ORSoftwareOperationsResearch202.OriginsofOperationsResearch(OR)古代朴素运筹学思想《史记·高祖本纪》“夫运筹于帷幄之中，决胜于千里之外”。(张良)田忌赛马(孙膑)运筹大师(诸葛亮)肇建紫禁城(永乐年间－陈珪)国外运筹学的先驱(阿基米德)OperationsResearch212.OriginsofOperationsResearch(OR)TherootsofORcanbetracedbackmanydecadesandevencenturies(Newton,Euler,Bernoulli,Bayes,Lagrange,etc).BeginningoftheactivitycalledOperationsResearch---attributedtothemilitaryservicesearlyintheWorldWarII(1937).Needtoallocatescarceresourcestothevariousmilitaryoperationsinaneffectivemanner.TheBritishfirstandthentheU.SmilitarymanagementcalleduponalargenumberofscientiststoapplyascientificapproachtodealingwithseveralmilitaryproblemsOperationsResearch22Britain,WWII(1938).Multi-disciplinaryteamofscientistsexplorehowtouseradarinformationtodeployandusefighterplanes.UnitedStates.Mathematicalmodels(SearchTheory)usedtodevelopoptimalairsearchpatternsforanti-submarinetactics.BombingJapan,Hokadate,Japan,fromtheDefenseVisualInformationCenterdownloadedfromOperationsResearch23Endofwar–scientistsunderstoodthatORcouldbeappliedoutsidethemilitaryaswell.Theindustrialboomfollowingthewarledtoanincreasingcomplexityandspecializationoforganizations

scientificmanagementtechniquesbecamemoreandmorecrucial.Bytheearly1950s,ORtechniqueswerebeingappliedtoavarietyoforganizationsinbusiness,industry,andgovernment.OperationsResearch24EvolutionofORORmovesintoindustrialdomain(1950’s),parallelscomputers’growthasbusinessplanning/managementtool.Focusondevelopmentofmathematicalmodelingtechniquestoimproveoroptimizereal-worldsystems.1951computercorememoryOperationsResearch25ImpactofOperationsResearch26KeyFactorsforRapidGrowthofORSubstantialprogresswasmadeearlyinimprovingthetechniquesinORSimplex,DynamicProgramming,IntegerProgramming,InventoryTheory,QueuingTheory,etc.Computerrevolution-1980sthePCfurtherboostedthistrend.OperationsResearch27OperationsResearchOvertheYears1950's Lotsofexcitement,mathematicaldevelopments,queuingtheory,mathematicalprogramming.

cf.A.I.inthe1960's1960's Moreexcitement,moredevelopmentandgrandplans. cf.A.I.inthe1980's.1947 ProjectScoop(ScientificComputationofOptimumPrograms)withGeorgeDantzigandothers.Developedthesimplex

methodforlinearprograms.OperationsResearch28OperationsResearchOvertheYears1970's Disappointment,andasettlingdown.NP-completeness.Morerealisticexpectations.1980's Widespreadavailabilityofpersonalcomputers.Increasinglyeasyaccesstodata.Widespreadwillingnessofmanagerstousemodels.1990's ImproveduseofO.R.systems.

FurtherinroadsofO.R.technology,e.g.,optimizationandsimulationadd-instospreadsheets,modelinglanguages,largescaleoptimization.MoreintermixingofA.I.andO.R.OperationsResearch29OperationsResearchinthe00’sLOTSofopportunitiesforORasafieldData,data,dataE-businessdata(clickstream,purchases,othertransactionaldata,E-mailandmore)ThehumangenomeprojectanditsoutgrowthNeedformoreautomateddecisionmakingNeedforincreasedcoordinationforefficientuseofresources(Supplychainmanagement)OperationsResearch30EarlydevelopmentofOR1917年丹麦工程师爱尔朗(Erlang)—排队论1939年苏联数学家康托洛维奇—线性规划1947年美国学者丹兹格—单纯形法1944年冯·诺伊曼和摩根斯坦—对策论1951年美国学者贝尔曼—动态规划OperationsResearch31运筹学在中国1956年:中国科学院力学研究所1956运用学(钱学森)→1957运筹学(许国志)OperationsResearch32运筹学在中国1959年，中科院数学所，主要研究方向为排队论、非线性规划和图论，还有人专门研究运输理论、动态规划和经济分析(刘源张、管梅谷)OperationsResearch33刘源张(院士)管梅谷教授运筹学在中国华罗庚,1965年起到农村、工厂讲解基本的优化技术和统筹方法,使用于日常的生产和生活中1980年1981年1982年中国运筹学会成为国际运筹学联合会（IFORS）的成员OperationsResearch34中国优选法统筹法与经济数学研究会LectureOutlineCourseAdministrationOriginsanddevelopmentofORDefinitions&featuresofORMajortopicsofORApplicationsofORApproachofORHowtostudy?ORSoftwareOperationsResearch353.WhatisOperationsResearch?WorldWarII:BritishmilitaryleadersaskedscientistsandengineerstoanalyzeseveralmilitaryproblemsDeploymentofradarManagementofconvoy,bombing,antisubmarine,etc.TheresultwascalledMilitaryOperationsResearch,laterOperationsResearchOperationsResearch363.WhatisOperationsResearch?Today:“...isadisciplinethatdealswiththeapplicationofadvancedanalyticalmethodstohelpmakebetterdecisions.”“

thescienceofallocation,planningandschedulinginthefaceofuncertaintiesandthefluctuatingdynamicsofsupplyanddemand”37运筹学的定义运筹学（OperationsResearchorOperationalResearch)直译为“运作研究”。是采用定量化的方法，为管理决策提供依据的一门学科。它把复杂的管理系统归结为模型（多数是数学模型），然后应用数学方法，并用计算机求解与分析得到最优方案，从而实现对人力、物力、财力等资源的统筹安排，达到最有效的管理目的。OperationsResearch38TerminologyTheterm“OperationsResearch”(“OR”)Americansreferto“operationsresearch”Europeansreferto“operationalresearch”Bothareoftenshortenedtojust"OR"OthertermsManagementscience(MS)OR/MS,ORMSIndustrialEngineeringDecisionscienceEtc.OperationsResearch39ORNature“Operations”:operationsresearchis“researchonoperations”“Research”:scientificapproachtodecisionmakingOrganizationalpointofviewittriestomeetthegoalsoftheoverallorganization.immaterial“searchforoptimality”(best,optimalsolution)isanimportantthemeinOR.运筹学的定义与特征运筹学研究对象经济、军事及科学技术等活动中能用数量关系描述的有关运用、筹划与管理等方面的问题运筹学的特征引进数学研究方法系统性着重实际应用跨学科性理论与应用的发展相互促进OperationsResearch41WhatisaModel?Amodelisapurposefulrepresentationofthekeyfactorsofanobjectorsystemandtherelationshipsamongthosefactors.AbstractrepresentationofarealsituationEnoughdetailsothatkeyfactorsandrelationshipsareaccuratelyrepresentedOmitunnecessarydetails“Everythingshouldbemadeassimpleaspossible,butnotsimpler.”(AlbertEinstein)OperationsResearch42TypesofModelsMentalModelsVisualModelsPhysicalModelsMathematicalModels用字母、数字和运算符号将系统或过程的某些特征及相互关系表达出来。它试图精确地和定量地表示系统的各种关系。43CharacteristicsofaMathematicalModelUsuallymotivatedbyadecisionInputsQuantitiesorfactorsthataffectadecisionControllableInputs(DecisionVariables)UncontrollableInputs(Parameters)OutputsPrimarySecondary44FormulateamathematicalmodeltorepresenttheproblemFormulatetheproblemintoawaythatisconvenientforanalysis typicallyusingamathematicalmodel.Mathematicalmodelsidealizedrepresentationsexpressedintermsofmathematicalsymbolsandexpressions.Famousmathematicalmodels F=ma(Newton’ssecondlawofmotion)and E=mc²(Einstein’sfamousequationofconservationof energyintomass).45Exam.ofMathematicalModelABCD甲2125715乙5151371546例1设要从甲地调出物资2000吨，从乙地调出物资1100吨，分别供给A地1700吨、B地1100吨、C地200吨、D地100吨。已知每吨运费如表1.1所示。假定运费与运量成正比，怎样才能找出一个运费最省的调拨计划？销地运费产地表1.1调拨费用47minf=21x11+25x12+7x13+15x14+51x21+51x22+37x23+15x24甲乙ABCDx11x12x13x14x21x22x23x2448minf=21x11+25x12+7x13+15x14+51x21+51x22+37x23+15x24

x11+x12+x13+x14=2000

x21+x22+x23+x24=1100x11+x21=1700x12+x22=1100x13+x23=200x14+x24=100xij

0,i=1,2;j=1,2,3,4.s.t.LectureOutlineCourseAdministrationOriginsanddevelopmentofORDefinitions&featuresofORMajortopicsofORApplicationsofORApproachofORHowtostudy?ORSoftwareOperationsResearch494.MajortopicsofORMathematicalProgrammingLinearprogrammingIntegerprogrammingGoalprogrammingNon-linearprogrammingDynamicprogrammingDecisionAnalysisGameTheoryQueuingTheoryNetworkanalysisInventoryMgmtetc.50LectureOutlineCourseAdministrationOriginsanddevelopmentofORDefinitions&featuresofORMajortopicsofORApplicationsofORApproachofORHowtostudy?ORSoftwareOperationsResearch515.ApplicationsinBusinessmanagementProductionplanning

logistics

Resourceplanning

Inventorymanagement

marketing

accountingReliabilityProjectmanagement52CareerOpportunitiesAccountingActuarialWorkComputerServicesCorporatePlanningEconomicAnalysisFinancialModelingIndustrialEngineeringInvestmentAnalysisLogisticsManufacturingServices53ManagementConsultingManagementTrainingMarketResearchOperationsResearchPolicyPlanningProductionEngineeringQuanti