2022高中数学人教A版必修2 3.2.1直线的点斜式方程 课件

3.2.1直线的点斜式方程 若直线l经过点P1(x1,y1)，斜率为k,求直线l的方程.设点P(x,y)是直线l上不同于点P1的任意一点，则化简为——直线方程的点斜式3.2.1直线的点斜式 此时直线的方程是x=x1当直线的倾斜角为0°时，当直线的倾斜角为90°时，直线没有斜率此时直线的方程是特殊直线 例3.已知直线l在x轴上的截距比在y轴上的截距大1，且过定点(6,-2)，求直线l的方程.解：由已知可设直线l的方程为：令x=0,则直线l在y轴上的截距为令y=0,则直线l在x轴上的截距为由题意得即即或∴直线l的方程为：或即或 例3.已知直线l在x轴上的截距比在y轴上的截距大1，且过定点(6,-2)，求直线l的方程.解2：由已知可设直线l的方程为：令x=0,则直线l在y轴上的截距为：令y=0,则直线l在x轴上的截距为：由题意得解得∴直线l的方程为：或或 TheNewsvendorModel报童模型 “Toomuch”and“toolittle”costsCo=overagecostThecostoforderingonemoreunitthanwhatyouwouldhaveorderedhadyouknowndemand.Inotherwords,supposeyouhadleftoverinventory(i.e.,youoverordered).Coistheincreaseinprofityouwouldhaveenjoyedhadyouorderedonefewerunit.Cu=underagecostThecostoforderingonefewerunitthanwhatyouwouldhaveorderedhadyouknowndemand.Inotherwords,supposeyouhadlostsales(i.e.,youunderordered).Cuistheincreaseinprofityouwouldhaveenjoyedhadyouorderedonemoreunit. BalancingtheriskandbenefitoforderingaunitOrderingonemoreunitincreasesthechanceofoverage…ExpectedlossontheQthunit=CoxF(Q)F(Q)=Distributionfunctionofdemand=Prob{DemandTheratioCu/(Co+Cu)iscalledthecriticalratio.（临界比或关键比例）Hence,tomaximizeprofit,chooseQsuchthatwedon’thavelostsales(i.e.,demandisQorlower)withaprobabilitythatequalsthecriticalratio TheNewsvendorModel:Performancemeasures绩效指标 NewsvendormodelperformancemeasuresForanyorderquantitywewouldliketoevaluatethefollowingperformancemeasures:Expectedlostsales（期望销售损失）TheaveragenumberofunitsdemandexceedstheorderquantityExpectedsales（期望销售）(comparedtoexpecteddemand)Theaveragenumberofunitssold.Expectedleftoverinventory（期望售后剩余库存）Theaveragenumberofunitsleftoverattheendoftheseason.ExpectedprofitExpectedfillrate（期望订单完成率）ThefractionofdemandthatissatisfiedimmediatelyIn-stockprobability（存货满足概率）ProbabilityalldemandissatisfiedStockoutprobability（缺货概率）Probabilitysomedemandislost formulaExpectedsales=m-Expectedlostsalesm:ExpecteddemandL(z):lossfunction(标准正态)损失函数,随机变量超过一个固定值的期望值之和。ExpectedLeftOverInventory=Q-ExpectedSales formulaIn-stockprobability=F(Q)=Φ(z)Stockoutprobability=1–F(Q)=1–In-stockprobability TheNewsvendorModel:Thetargetin-stockprobabilityandthetargetfill-rateobjectivesforchoosingQin-stockprobability：缺货情况，对杂货店较重要fill-rate：多少顾客满足的情况，对目录零售商较重要 ChooseQsubjecttoaminimumin-stockprobabilitySupposewewishtofindtheorderquantityfortheHammer3/2thatminimizesleftoverinventorywhilegeneratingatleasta99%in-stockprobability.Step1:Findthez-statisticthatyieldsthetargetin-stockprobability.IntheStandardNormalDistributionFunctionTablewefindF(2.32)=0.9898andF(2.33)=0.9901.Choosez=2.33tosatisfyourin-stockprobabilityconstraint.Step2:Convertthez-statisticintoanorderquantityfortheactualdemanddistribution.Q=m+zxs=3192+2.33x1181=5944 ChooseQsubjecttoaminimumfillrateconstraintSupposewewishtofindtheorderquantityfortheHammer3/2thatminimizesleftoverinventorywhilegeneratingatleasta99%fillrate.Step1:Findthelostsaleswithastandardnormaldistributionthatyieldsthetargetfillrate.Step2:Findthez-statisticthatyieldsthelostsalesfoundinstep1.FromtheStandardNormalLossFunctionTable,L(1.53)=0.0274andL(1.54)=0.0267Choosethehigherz-statistic,z=1.54Step3:Convertthez-statisticintoanorderquantityfortheactualdemanddistribution.Q=m+zxs=3192+1.54x1181=5011 讨论不足成本大时（毛利高），订购量大于期望需求（关键比例大于0.5）；反之相反。剩余成本可能是可见成本，而销售损失是机会成本，在报表中看不到。剩余成本可能是积压的库存，如未及时清理，造成虚假利润除了利润最大化目标外，很多情况下会选服务水平目标，因为要考虑长期效应。 Assemble-to-order,make-to-orderandQuickResponsewithreactivecapacity按订单装配、按订单生产和以反应性能力快速响应 Thedemand-supplymismatchcostDefinition–thedemandsupplymismatchcostincludesthecostofleftoverinventory(the“toomuch”cost)plustheopportunitycostoflostsales(the“toolittle”cost):Themaximumprofitistheprofitwithoutanymismatchcosts,i.e.,everyunitissoldandtherearenolostsales:ThemismatchcostcanalsobeevaluatedwithMismatchcost=Maximumprofit–Expectedprofit Whenisthemismatchcosthigh?Mismatchcostasapercentofthemaximumprofitwheref(z)=densityfunctionoftheNormaldistribution(InExcelf(z)=normdist(z,0,1,0))Themismatchcostishighwhen(f(z)/F(z))and(s/m)arehigh. LowcriticalratioshighmismatchcostsThemismatchcostishighwhen(f(z)/F(z))ishigh……(f(z)/F(z))ishighwhenthecriticalratioislow: 变差系数反映预测质量，提高预测精确性，可有更高利润。关键比例小的产品，剩余成本高，容易过时的和容易腐败的产品采购少。若残值为零，关键比例即为毛利率，故食堂原材料备料库存少（毛利低，积压成本大），餐厅备料较充分，过期库存多。 不同的不匹配成本与运营管理模式MTS—报童模型不匹配成本为过量或不足，MTS适合于关键比例高、需求变动小MTO—排队系统不匹配成本为生产闲置、顾客排队MTO适合于短途运输、短提前期、机器或劳动力便宜中间状态为使用反应性能力进行快速响应两种反应性能力：第二次订购能力无限但较第一次订购昂贵的反应性能力第二次订购能力有限的反应性能力 SomeU.S.airlineindustryobservationsSincederegulation(1978)137carriershavefiledforbankruptcy.From95-99(theindustry’sbest5yearsever)airlinesearned3.5centsoneachdollarofsales:TheUSaverageforallindustriesisaround6cents.From90-99theindustryearned1centper$ofsales.Carrierstypicallyfill72.4%ofseatsandhaveabreak-evenloadof70.4%. MatchingsupplytodemandwhensupplyisfixedExamplesoffixedsupply:Travelindustries(fixednumberofseats,rooms,cars,etc).Advertisingtime(limitednumberoftimeslots).Telecommunicationsbandwidth.SizeoftheMBAprogram.Doctor’savailabilityforappointments.Revenuemanagementisasolution:Ifadjustingsupplyisimpossible–adjustthedemand!Segmentcustomersintohighwillingnesstopayandlowwillingnesstopay.Limitthenumberofticketssoldatalowprice,i.e.,controltheaveragepricebychangingthemixofcustomers. RevenuemanagementandmarginarithmeticSmallchangesinrevenuecanhaveabigimpactonprofit,especiallyforhighgrossmarginandlownetprofit%industries: EnvironmentssuitableforrevenuemanagementThesameunitofcapacity(e.g.,airlineseat)canbeusedtodeliverservicestodifferentcustomersegments(e.g.,businessandleisurecustomers)atdifferentprices.Highgrossmargins(sothatthevariablecostofadditionalsalesislow).Perishablecapacity(itcannotbestored)andlimitedcapacity(allpossiblecustomerscannotalwaysbeserved).Capacityissoldinadvanceofdemand.Thereisanopportunitytosegmentcustomers(sothatdifferentpricescanbecharged)anddifferentsegmentsarewillingtopaydifferentprices.Itisnotillegalormorallyirresponsibletodiscriminateamongcustomers. RevenueManagement:Bookinglimitsandprotectionlevels预定限额和保留水平 PracticalproblemTheParkHyattPhiladelphiaattheBellevue.118King/Queenrooms.HyattoffersarL=$159(lowfare)discountfareforamid-weekstaytargetingleisuretravelers.RegularfareisrH=$225(highfare)targetingbusinesstravelers.Demandforlowfareroomsisabundant.LetDbeuncertaindemandforhighfarerooms.SupposeDhasPoissondistributionwithmean27.3.Assumemostofthehighfare(business)demandoccursonlywithinafewdaysoftheactualstay.Objective:Maximizeexpectedrevenuesbycontrollingthenumberoflowfareroomsyousell. YieldmanagementdecisionsThebookinglimitisthenumberofroomsyouarewillingtosellinafareclassorlower.Theprotectionlevelisthenumberofroomsyoureserveforafareclassorhigher.LetQbetheprotectionlevelforthehighfareclass.Qisineffectwhileyouselllowfaretickets.Sincethereareonlytwofareclasses,thebookinglimitonthelowfareclassis118–Q:Youwillsellnomorethan118-Qlowfareticketsbecauseyouareprotecting(orreserving)Qseatsforhighfarepassengers.0118QseatsprotectedforhighfarepassengersSellnomorethanthelowfarebookinglimit,118-Q TheconnectiontothenewsvendorAsingledecisionismadebeforeuncertaindemandisrealized.Thereisanoveragecost:IfDQthenyouprotectedtoofewrooms(youunderprotected)……sosomeroomscouldhavebeensoldatthehighfareinsteadofthelowfare.ChooseQtobalancetheoverageandunderagecosts. OptimalprotectionlevelOveragecost:IfDQweprotectedtoofewrooms.D–Qroomscouldhavebeensoldatthehighfarebutweresoldinsteadatthelowfare,soCu=rH-rLOptimalhighfareprotectionlevel:Optimallowfarebookinglimit=118–Q*ChoosingtheoptimalhighfareprotectionlevelisaNewsvendorproblemwithproperlychosenunderageandoveragecosts. HyattexampleCriticalratio:Poissondistributionwithmean27.3:Answer:24roomsshouldbeprotectedforhighfaretravelers.Similarly,abookinglimitof118-24=94roomsshouldbeappliedtolowfarereservations. RelatedcalculationsHowmanyhigh-faretravelerswillberefusedareservation?Expectedlostsales=4.10.Howmanyhigh-faretravelerswillbeaccommodated?Expectedsales=Expecteddemand-Lostsales=27.3-4.1=23.2Howmanyseatswillremainempty?Expectedleftoverinventory=Q-Expectedsales=24-23.2=0.8.Whatistheexpectedrevenue?$225xExp.sales+$159xBookinglimit=$20,166.Note:withoutyieldmanagementworstcasescenariois$159x118=$18,762. RevenueManagement:Overbooking Uglyreality:cancellationsandno-showsApproximately50%ofreservationsgetcancelledatsomepointintime.Inmanycases(carrentals,hotels,fullfareairlinepassengers)thereisnopenaltyforcancellations.Problem:thecompanymayfailtofilltheseat(room,car)ifthepassengercancelsattheverylastminuteordoesnotshowup.Solution:sellmoreseats(rooms,cars)thancapacity.Danger:somecustomersmayhavetobedeniedaseateventhoughtheyhaveaconfirmedreservation. Hyatt’sProblemTheforecastforthenumberofcustomersthatdonotshowup(X)isPoissonwithmean8.5.Thecostofdenyingaroomtothecustomerwithaconfirmedreservationis$350inill-willandpenalties.Howmanyrooms(Y)shouldbeoverbooked(soldinexcessofcapacity)?Newsvendorsetup:Singledecisionwhenthenumberofno-showsinuncertain.UnderagecostifX>Y(insufficientnumberofseatsoverbooked).OveragecostifXYthenwecouldhavesoldX-Ymorerooms……tobeconservative,wecouldhavesoldthoseroomsatthelowfare,Cu=rL.Overagecost:ifX