数据模型与决策运筹学课后习题和案例答案

21CHAPTER2LINEARPROGRAMMINGBASICCONCEPTSREVIEWQUESTIONS211PONDEROSAINDUSTRIALUSESLINEARPROGRAMMINGMONTHLYTOGUIDETHEPRODUCTMIXDECISION212OVERALLPROFITABILITYHASINCREASEDBY20BETTERUTILIZATIONOFRAWMATERIAL,CAPITALEQUIPMENT,ANDPERSONNELALSORESULTED213THEGOALWASTOIMPROVETHEUTILIZATIONOFRESERVATIONPERSONNELBYMATCHINGWORKSCHEDULESTOCUSTOMERNEEDS214UNITEDAIRLINESSAVEDMORETHAN6MILLIONANNUALLYINDIRECTSALARYANDBENEFITCOSTSCUSTOMERSERVICEALSOIMPROVEDANDWORKLOADSWEREREDUCEDFORSUPPORTSTAFF215THESDMSYSTEMISUSEDTOCOORDINATETHESUPPLY,DISTRIBUTIONANDMARKETINGOFEACHOFCITGOSMAJORPRODUCTSTHROUGHOUTTHEUNITEDSTATES216CITGOSAVEDABOUT14MILLIONANNUALLYININTERESTEXPENSESIMPROVEMENTSINCOORDINATION,PRICING,ANDPURCHASINGDECISIONSADDEDATLEAST25MILLIONMORETOANNUALPROFITS221THEYPROVIDETHEHIGHESTQUALITYAVAILABLEINTHEINDUSTRYFORTHEMOSTDISCRIMINATINGBUYERS2221SHOULDTHECOMPANYLAUNCHTHETWONEWPRODUCTS2WHATSHOULDBETHEPRODUCTMIXFORTHETWONEWPRODUCTS223THEGROUPWASASKEDTOANALYZEPRODUCTMIX224WHICHCOMBINATIONOFPRODUCTIONRATESFORTHETWONEWPRODUCTSWOULDMAXIMIZETHETOTALPROFITFROMBOTHOFTHEM2251AVAILABLEPRODUCTIONCAPACITYINEACHOFTHEPLANTS2HOWMUCHOFTHEPRODUCTIONCAPACITYINEACHPLANTWOULDBENEEDEDBYEACHPRODUCT3PROFITABILITYOFEACHPRODUCT2311WHATARETHEDECISIONSTOBEMADE2WHATARETHECONSTRAINTSONTHESEDECISIONS3WHATISTHEOVERALLMEASUREOFPERFORMANCEFORTHESEDECISIONS232WHENFORMULATINGALINEARPROGRAMMINGMODELONASPREADSHEET,THECELLSSHOWINGTHEDATAFORTHEPROBLEMARECALLEDTHEDATACELLSTHECHANGINGCELLSARETHECELLSTHATCONTAINTHEDECISIONSTOBEMADETHEOUTPUTCELLSARETHECELLSTHATPROVIDEOUTPUTTHATDEPENDSONTHECHANGINGCELLSTHETARGETCELLISASPECIALKINDOFOUTPUTCELLTHATSHOWSTHEOVERALLMEASUREOFPERFORMANCEOFTHEDECISIONTOBEMADE22233THEEXCELEQUATIONFOREACHOUTPUTCELLCANBEEXPRESSEDASASUMPRODUCTFUNCTION,WHEREEACHTERMINTHESUMISTHEPRODUCTOFADATACELLANDACHANGINGCELL2411GATHERTHERELEVANTDATA2IDENTIFYTHEDECISIONSTOBEMADE3IDENTIFYTHECONSTRAINTSONTHESEDECISIONS4IDENTIFYTHEOVERALLMEASUREOFPERFORMANCEFORTHESEDECISIONS5CONVERTTHEVERBALDESCRIPTIONOFTHECONSTRAINTSANDMEASUREOFPERFORMANCEINTOQUANTITATIVEEXPRESSIONSINTERMSOFTHEDATAANDDECISIONS242ALGEBRAICSYMBOLSNEEDTOBEINTRODUCEDTOREPRESENTSTHEMEASUREOFPERFORMANCEANDTHEDECISIONS243ADECISIONVARIABLEISANALGEBRAICVARIABLETHATREPRESENTSADECISIONREGARDINGTHELEVELOFAPARTICULARACTIVITYTHEOBJECTIVEFUNCTIONISTHEPARTOFALINEARPROGRAMMINGMODELTHATEXPRESSESWHATNEEDSTOBEEITHERMAXIMIZEDORMINIMIZED,DEPENDINGONTHEOBJECTIVEFORTHEPROBLEMANONNEGATIVITYCONSTRAINTISACONSTRAINTTHATEXPRESSTHERESTRICTIONTHATAPARTICULARDECISIONVARIABLEMUSTBEGREATERTHANOREQUALTOZEROALLCONSTRAINTSTHATARENOTNONNEGATIVITYCONSTRAINTSAREREFERREDTOASFUNCTIONALCONSTRAINTS244AFEASIBLESOLUTIONISONETHATSATISFIESALLTHECONSTRAINTSOFTHEPROBLEMTHEBESTFEASIBLESOLUTIONISCALLEDTHEOPTIMALSOLUTION251TWO252THEAXESREPRESENTPRODUCTIONRATESFORPRODUCT1ANDPRODUCT2253THELINEFORMINGTHEBOUNDARYOFWHATISPERMITTEDBYACONSTRAINTISCALLEDACONSTRAINTBOUNDARYLINEITSEQUATIONISCALLEDACONSTRAINTBOUNDARYEQUATION254THECOEFFICIENTOFX1GIVESTHESLOPEOFTHECONSTRAINTBOUNDARYLINETHECONSTANTTERMGIVESTHEVALUEWHERETHELINEINTERCEPTSTHEX2AXIS255THEEASIESTWAYTODETERMINEWHICHSIDEOFTHELINEISPERMITTEDISTOCHECKWHETHERTHEORIGIN0,0SATISFIESTHECONSTRAINTIFITDOES,THENTHEPERMISSIBLEREGIONLIESONTHESIDEOFTHECONSTRAINTWHERETHEORIGINISOTHERWISEITLIESONTHEOTHERSIDE261THESOLVERDIALOGUEBOX262THEADDCONSTRAINTDIALOGUEBOX263THEASSUMELINEARMODELOPTIONANDTHEASSUMENONNEGATIVEOPTION271CLEANINGPRODUCTSFORHOMEUSE272TELEVISIONANDPRINTMEDIA273DETERMINEHOWMUCHTOADVERTISEINEACHMEDIUMTOMEETTHEMARKETSHAREGOALSATAMINIMUMTOTALCOST274THECHANGINGCELLSAREINTHECOLUMNFORTHECORRESPONDINGADVERTISINGMEDIUM23275THEOBJECTIVEISTOMINIMIZETOTALCOSTRATHERTHANMAXIMIZEPROFITTHEFUNCTIONALCONSTRAINTSCONTAINRATHERTHAN276NO277CLOSERTOTHEORIGIN281NO282THEGRAPHICALMETHODHELPSAMANAGERDEVELOPAGOODINTUITIVEFEELINGFORTHELINEARPROGRAMMINGIS2831WHERELINEARPROGRAMMINGISAPPLICABLE2WHEREITSHOULDNOTBEAPPLIED3DISTINGUISHBETWEENCOMPETENTANDSHODDYSTUDIESUSINGLINEARPROGRAMMING4HOWTOINTERPRETTHERESULTSOFALINEARPROGRAMMINGSTUDYPROBLEMS21ATHETWOFACTORSTHATOFTENHINDERTHEUSEOFOPTIMIZATIONMODELSBYMANAGERSARECULTURALDIFFERENCESANDRESPONSETIMECULTURALDIFFERENCESCAUSEMANAGERSANDMODELDEVELOPERSTOOFTENHAVEAHARDTIMEUNDERSTANDINGEACHOTHERRESPONSETIMEISOFTENSLOWDUETOTHETIMETOTRANSLATE,FORMULATE,ANDSOLVETHEMANGERSPROBLEMUSINGOPTIMIZATIONSYSTEMSBTHECOMPANYSHIFTEDFROMANEMPHASISONTHEMANUFACTUREOFTHICKERPLYWOODSTOTHINNERPLYWOODSCPONDEROSAPLANSTOUSEOPTIMIZATIONINTHEUSEOFTIMBERFOROTHERPRODUCTSALSOINADDITION,OPTIMIZATIONMAYBEUSEDFORRAWMATERIALANDINVENTORYMANAGEMENTANDFORFINANCIALPLANNING22ATHESHIFTSCHEDULESATAIRPORTSANDRESERVATIONOFFICESWEREDONEBYHANDPRIORTOTHISSTUDYBTHEPROJECTREQUIREMENTSWEREITODETERMINETHENEEDSFORINCREASEDMANPOWER,IITOIDENTIFYEXCESSMANPOWERFORREALLOCATION,IIITOREDUCETHETIMEREQUIREDFORPREPARINGSCHEDULES,IVTOMAKEMANPOWERALLOCATIONMOREDAYANDTIMESENSITIVE,ANDVTOQUANTIFYTHECOSTASSOCIATEDWITHSCHEDULINGCFLEXIBILITY,SUCHASTHENUMBEROFSTARTTIMES,THEPREFERREDSHIFTLENGTHS,THELENGTHOFBREAKS,THEPREFERREDDAYSOFFCOMBINATIONS,ETCWERECONSIDEREDTHISVERSATILITYWASNECESSARYTOSATISFYTHEGROUPCULTUREATEACHOFFICE,WHICHWASNECESSARYTOGATHERFIELDSUPPORT24DBENEFITSINCLUDEDISIGNIFICANTLABORCOSTSAVINGS,IIIMPROVEDCUSTOMERSERVICE,IIIIMPROVEDEMPLOYEESCHEDULES,IVQUANTIFIEDMANPOWERPLANNINGANDEVALUATION23ADURINGTHEYEARSPRECEDINGTHISSTUDY,THEPRICEOFCRUDEOILINCREASEDTENFOLDANDSHORTTERMINTERESTRATESMORETHANTRIPLEDBCITGOSDISTRIBUTIONNETWORKOFPIPELINES,TANKERS,ANDBARGESSPANNEDTHEEASTERNTWOTHIRDSOFTHEUNITEDSTATESTHEYMARKETTHEIRPRODUCTSINALLOFTHE48CONTIGUOUSSTATESCAN11WEEKPLANNINGHORIZON,PARTITIONEDINTOSIXONEWEEKPERIODSANDONEFIVEWEEKPERIOD,WASUSEDDCITGOUSEDANIBM4381TYPICALRUNTIMESFORMODELGENERATION,SOLUTION,ANDREPORTSWERETWOMINUTES,HALFAMINUTE,ANDSEVENMINUTES,RESPECTIVELYETHEFOURTYPESOFMODELUSERSWERETHEPRODUCTMANAGERS,THEPRICINGMANAGER,THEPRODUCTTRADERS,ANDTHEBUDGETMANAGERPRODUCTMANAGERSCOMPAREDTHEMODELRECOMMENDATIONSTOTHEACTUALOPERATIONALDECISIONSTODETERMINETHEEXISTENCEANDCAUSEOFDISCREPANCIESTHEYALSOUSEDTHEMODELSWHATIFCAPABILITIESTOGENERATEECONOMICALLYVIABLEALTERNATIVESTOCURRENTANDFORECASTEDOPERATIONSTHEPRICINGMANAGERUSEDTHEMODELTOSETRANGESFORTERMINALPRICESFOREACHPRODUCTANDTOHELPSETPRICESANDRECOMMENDVOLUMESFORBULKSALESMADETOREDUCEEXCESSINVENTORIESPRODUCTTRADERSUSEDTHEMODELTODETERMINEWHICHSIDEOFTHETRADINGBOARDTHEYSHOULDBEONFOREACHPRODUCTTHEYALSOUSEDTHEMODELSWHATIFCAPABILITIESTODETERMINETHESENSITIVITYOFSPOTPRICESTOTHEREQUIREDPURCHASESORSALESVOLUMESASPRICESFLUCTUATEDDURINGTHEWEEKTHEBUDGETMANAGERUSEDTHEFINANCIALSUMMARYREPORTTOGENERATEVARIOUSCOMPONENTSOFTHEMONTHLYANDQUARTERLYBUDGETSFTHEMAJORREPORTSGENERATEDBYTHESDMSYSTEMAREIINFEASIBILITYREPORT,IIINTRANSIT,TERMINAL,EXCHANGE,INVENTORYREPORTS,IIISPOTRECOMMENDATIONREPORT,IVPURCHASES,SALES,TRADESREPORTS,VWHOLESALEREPORT,VIVOLUMESUMMARYREPORT,VIIFINANCIALSUMMARYREPORTGTHEEDUCATIONOFTHEUSERSWASACHALLENGEINADDITIONTOTHECOLLECTION,VALIDATION,ANDCORRECTIONOFINPUTDATAFORTHEMODELANOTHERCHALLENGECONCERNEDTHEFORECASTINGSALESVOLUMESANDWHOLESALESPRICESCITGOFORECASTEDFORMONTHLYANDQUARTERLYBUDGETS,WHILESDMSYSTEMSNEEDEDWEEKLYFORECASTSHDIRECTBENEFITSWEREITHEREDUCTIONINCITGOSPRODUCTINVENTORYWITHNODROPINSERVICELEVELS,ANDIIOPERATIONALDECISIONMAKINGIMPROVED25INDIRECTBENEFITSWEREITHEESTABLISHMENTOFACORPORATEDATABASE,WHICHPROVIDEDCOMMON,UPTODATE,ONLINE,OPERATIONALINFORMATIONFORCURRENTDECISION,SUPPORTIITHEUTILIZATIONOFASINGLEFORECASTTHROUGHOUTTHEDIFFERENTDEPARTMENTS,WHICHKEPTTHEENTIREORGANIZATION,FOCUSED,IIITHECLOSEDLOOPPLANNINGPROCESSFOSTEREDBYTHECONTINUALFEEDBACKPROVIDEDBYTHEPROJECTMANAGER,WHENCOMPARINGACTUALDECISIONTOMODELRECOMMENDEDDECISION,IVINCREASEDINTERDEPARTMENTALCOMMUNICATION,ANDVTHEINSIGHTGAINEDFROMTHEMODELINGPROCESSITSELF24ABMAXIMIZEP600D300W,SUBJECTTOD42W123D2W18ANDD0,W0COPTIMALSOLUTIOND,WX1,X24,3P33002625AOPTIMALSOLUTIOND,WX1,X2167,650P3750BOPTIMALSOLUTIOND,WX1,X2133,700P390027COPTIMALSOLUTIOND,WX1,X2100,750P4050DEACHADDITIONALHOURPERWEEKWOULDINCREASETOTALPROFITBY15026AB28CDEACHADDITIONALHOURPERWEEKWOULDINCREASETOTALPROFITBY15027ABLETAUNITSOFPRODUCTAPRODUCEDBUNITSOFPRODUCTBPRODUCEDMAXIMIZEP3,000A2,000B,SUBJECTTO2AB2A2B23A3B4ANDA0,B029COPTIMALSOLUTIONA,BX1,X20667,0667P33333328AASINTHEWYNDORGLASSCOPROBLEM,WEWANTTOFINDTHEOPTIMALLEVELSOFTWOACTIVITIESTHATCOMPETEFORLIMITEDRESOURCESLETX1BETHEFRACTIONPURCHASEDOFTHEPARTNERSHIPINTHEFIRSTFRIENDSVENTURELETX2BETHEFRACTIONPURCHASEDOFTHEPARTNERSHIPINTHESECONDFRIENDSVENTURETHEFOLLOWINGTABLEGIVESTHEDATAFORTHEPROBLEMRESOURCEUSAGEPERUNITOFACTIVITYAMOUNTOFRESOURCE12RESOURCEAVAILABLEFRACTIONOFPARTNERSHIPINFIRSTFRIENDSVENTURE101FRACTIONOFPARTNERSHIPINSECONDFRIENDSVENTURE011MONEY500040006000SUMMERWORKHOURS400500600UNITPROFIT45004500BTHEDECISIONSTOBEMADEAREHOWMUCH,IFANY,TOPARTICIPATEINEACHVENTURETHECONSTRAINTSONTHEDECISIONSARETHATYOUCANTBECOMEMORETHANAFULLPARTNERINEITHERVENTURE,THATYOURMONEYISLIMITEDTO6,000,ANDTIMEISLIMITEDTO600HOURSINADDITION,NEGATIVEINVOLVEMENTISNOTPOSSIBLETHEOVERALLMEASUREOFPERFORMANCEFORTHEDECISIONSISTHEPROFITTOBEMADE210CFIRSTVENTUREFRACTIONOF1ST1SECONDVENTUREFRACTIONOF2ND1MONEY5000FRACTIONOF1ST4000FRACTIONOF2ND6000HOURS400FRACTIONOF1ST500FRACTIONOF2ND600NONNEGATIVITYFRACTIONOF1ST0,FRACTIONOF2ND0PROFIT4500FRACTIONOF1ST4500FRACTIONOF2NDDDATACELLSB2C2,B5C6,F5F6,ANDB11C11CHANGINGCELLSB9C9TARGETCELLF9OUTPUTCELLSD5D6ETHISISALINEARPROGRAMMINGMODELBECAUSETHEDECISIONSAREREPRESENTEDBYCHANGINGCELLSTHATCANHAVEANYVALUETHATSATISFYTHECONSTRAINTSEACHCONSTRAINTHASANOUTPUTCELLONTHELEFT,AMATHEMATICALSIGNINTHEMIDDLE,ANDADATACELLONTHERIGHTTHEOVERALLLEVELOFPERFORMANCEISREPRESENTEDBYTHETARGETCELLANDTHEOBJECTIVEISTOMAXIMIZETHATCELLALSO,THEEXCELEQUATIONFOREACHOUTPUTCELLISEXPRESSEDASASUMPRODUCTFUNCTIONWHEREEACHTERMINTHESUMISTHEPRODUCTOFADATACELLANDACHANGINGCELLFLETX1SHARETAKENINFIRSTFRIENDSVENTUREX2SHARETAKENINSECONDFRIENDSVENTUREMAXIMIZEP4,500X14,500X2,SUBJECTTOX11X215,000X14,000X26,000400X1500X2600HOURSANDX10,X20211GALGEBRAICVERSIONDECISIONVARIABLESX1,X2FUNCTIONALCONSTRAINTSX11X215,000X14,000X26,000400X1500X2600HOURSOBJECTIVEFUNCTIONMAXIMIZEP4,500X14,500X2,PARAMETERSALLOFTHENUMBERSINTHEABOVEALGEBRAICMODELNONNEGATIVITYCONSTRAINTSX10,X20SPREADSHEETVERSIONDECISIONVARIABLESB9C9FUNCTIONALCONSTRAINTSD4F7OBJECTIVEFUNCTIONF9PARAMETERSB2C2,B5C6,F5F6,ANDB11C11NONNEGATIVITYCONSTRAINTS“ASSUMENONNEGATIVITY”INTHEOPTIONSOFTHESOLVERHOPTIMALSOLUTIONX1,X20667,0667P600029AOBJECTIVEFUNCTIONZX12X2FUNCTIONALCONSTRAINTSX1X25X13X29NONNEGATIVITYCONSTRAINTSX10,X20BTHETOTALCOSTOFPARTBIS1640LENNYCOULDPAYANADDITIONAL16401512128INTOTALWAGESTOTHEBILINGUALOPERATORSWITHOUTINCREASINGTHETOTALOPERATINGCOSTBEYONDTHOSEFORTHESCENARIOWITHONLYMONOLINGUALOPERATORSTHEINCREASEOF128REPRESENTSAPERCENTAGEINCREASEOF128/1512847266HCREATIVECHAOSCONSULTANTSHASMADETHEASSUMPTIONTHATTHENUMBEROFPHONECALLSISINDEPENDENTOFTHEDAYOFTHEWEEKBUTMAYBETHENUMBEROFPHONECALLSISVERYDIFFERENTONAMONDAYTHA