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Department of Computer Science And Technology20151|PageMr.DivyangGorM.Sc.(CA)(2ndSemester) 040020206:ComputerOrientedOperationsResearchMehtodsQuestionBank Unit:1IntroductionofOperationsResearchandLinearProgrammingQ:1ShortAnswerQuestions:1.Writethedefinitionofoperationresearch.2.Writethedefinitionofsolution,basicsolution.3.WhatisLinearprogrammingproblem?4.Howwillyouconstructamathematicalmodel.5.Writedownanytwoscopesofoperationresearch.6.Describethephaseformulatingtheproblem.7.Definei]Solutionii]Basicsolution.8.Definefeasiblesolution.9.DefineLPPinthemathematicalform.10.Giveanyfourmodelsofoperationsresearch.11.Listdifferentactivitiesofmarketing.12.Listdifferentactivitiesofpersonnelmanagement.13.Whatismodel?14.StateanyfourapplicationofOR.15.AdvantagesofORstudy.16.DisadvantagesofORstudy.17.Defineunboundedsolution.18.DefinefeasibleandInfeasiblesolution.19.Whatisextremepoint?20.Drawgraphfor3a+5b≥20,Wherea,b≥0.

21.Statethedifferentscopeofoperationresearch.22.Whatarevariousphasesofoperationresearch?23.Whatismodel?Listoutthemodel.Q:2LongAnswerQuestions.1.AfirmmanufacturestwoproductsAandbonwhichtheprofitsearnedperunitareRs3andRs4respectively.EachproductisprocessedontwomachinesM1andM2.ProductArequiresoneminuteofprocessingtimeonM1andtwominutesonM2whileBrequiresoneminuteonM1andoneminuteonM2.MachineM1isavailablefornotmorethan7hours,whilemachineM2isavailablefor10h oursduringanywor kingday.Formulatethen umberofu nitsofproductsA andBtobe manufacturedtogetmaximumprofit.2.TheABCCompanyhasbeenaproducerofpicturetubesfortelevisionsetsandcertainprintedcircuitsforradios.ThecompanyhasjustexplainedintofullscaleproductionandmarketingofAMandAM-FMradios.Ithasbuiltanewplantthatcanoperate48hoursperweek.ProductionofanAMradiointhenewplantwillrequire2hoursandproductionofanAM-FMradiowillrequire3hours.EachAMradiowillcontributeRs.40toprofitswhileanAM-FMradiowillcontributeRs.80to

Department of Computer Science And Technology20154|PageMr.DivyangGor8.MaximizationofobjectivefunctioninLPPmeansA)ValueoccursatallowablesetdecisionB)highestvalueischosenamongallowabledecisionC)noneoftheaboveD)alloftheabove9.AlternativesolutionexistinalinearprogrammingproblemwhenA)oneoftheconstraintisredundantB)objectivefunctionisparalleltooneoftheconstraintsC)twoconstraintsareparallelD)alloftheabove10.LinearprogrammingprobleminvolvingonlytwovariablescanbesolvedbyA)BigMmethodB)SimplexmethodC)GraphicalmethodD)noneofthese11.ThelinearfunctionofthevariableswhichistobemaximizeorminimizeiscalledA)ConstraintsB)ObjectivefunctionC)DecisionvariableD)Noneoftheabove12.AphysicalmodelisanexampleofA)AniconicmodelB)AnanaloguemodelC)AverbalmodelD)Amathematicalmodel13.Ifthevalueoftheobjectivefunctionzcanbeincreasedordecreasedindefinitely,suchsolutioniscalledA)BoundedsolutionB)UnboundedsolutionC)SolutionD)Noneoftheabove14.AmodelisA)AnessenceofrealityB)AnapproximationC)AnidealizationD)Alloftheabove15.ThefirststepinformulatingalinearprogrammingproblemisA)IdentifyanyupperorlowerboundonthedecisionvariablesB)StatetheconstraintsaslinearcombinationsofthedecisionvariablesC)UnderstandtheproblemD)Identifythedecisionvariables16.ConstraintsinanLPmodelrepresentsA)LimititationsB)RequirementsC)balancinglimitationsandrequirementsD)allofabove17.ThebestuseoflinearprogrammingistofindoptimaluseofA)moneyB)ManpowerC)Machine

Department of Computer Science And Technology20156|PageMr.DivyangGorQ:5Fillintheblanks.1.Thegraphicalmethodcanonlybeusedwhenthereare_____decisionvariables.2.Theterm__________impliesthatoneormorevariablesinthesolutionandtheprofitcanbeinfinitelylarge.3.Whentheslopeoftheobjectivefunctionisthesameastheslopeofoneormoreconstraints,wemayhave__________.4.TofindtheoptimalsolutiontoanLPproblemwhenusingthegraphicalmethod,wemustfirstidentifythe_________.5.The__________probleminvolvesade cisionastowhichproductst oproduceg ivenlimitedresources.6.The__________isthatregionwhichsatisfiesallconstraints.7.The__________representsallpointsthatresultinaspecifiedprofit.8.Animportantfunctionofsensitivityanalysisisto__________.9.Isoprofitmethodinvolvesgraphing_______profitlines.10.The__________foraconstraintisthevalueofoneadditionalunitofascarceresource.11._____isthefirststepinformulatinganLPproblem.12.LPtheorystatesthattheoptimalsolutiontoanyproblemwilllieat____________.13.A___________ofasystemoftwoequationsintwovariablesisanorderedpairthatmakesbothequationstrue.14.A___________ofasystemoflinearinequalitiesisanorderedpairthatisasolutionofeachinequalityinthesystem.15.Thegraphofthesystemofconstraintsinlinearprogrammingiscalledthe__________.16._________istheprocessofoptimizingalinearobjectivefunctionsubjecttoasystemoflinearinequalities.17.Agraphicalsolutionislimitedtosolvinglinearprogrammingproblemswithonly___decisionvariables.18.Theoptimalsolutiontoalinearprogrammingmodelalwaysoccursata(an)_________pointofthefeasibleregion.19.Multipleop timalsolutionscanocc urwhentheobjectivefunctionli neis___ _______toaconstraintline.20.The_______________prope rt yoflinearprogrammingmodel sindicat esthatthedecisio nvariablescannotberestrictedtointegervaluesandcantakeonanyfractionalvalue.Unit:2SimplexMethodforSolutionofLPPQ:1Shortanswerquestion.1.Definesurplusvariables.2.Whatisthecriterionfortheenteringvariableandoutgoingvariable?3.Defineartificialvariables.4.Defineslackvariables.5.WhenisBigMmethoduseful?6.Whatistheconditionforoptimalityinsimplextable?7.Whatistheconditionforenteringvariableinsimplextable?8.WritethestandardformofLPPforthefollowingLPP:

Department of Computer Science And Technology20157|PageMr.DivyangGor12

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Maximize1325

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Department of Computer Science And Technology201513|PageMr.DivyangGor16.Theproblemhas__________solutionifthevalueofatleastoneartificialvariablepresentinthebasisisnon-zeroandtheoptimalityconditionissatisfied.17.Topreparealess-than-or-equalconstraintforuseinasimplextable,wemustadda(n)__________variable.18.Toprepareagreater-than-or-equalconstraintforuseinasimplextable,wemustadd__________.Unit:3TransportationandAssignmentProblem(TP&AP)Q:1Shortanswerquestions.1.WhatisTransportationproblem?2.StatethemathematicalformulationforT.P.3.WhatisanAssignmentProblem?4.WhatisthedifferencebetweenAssignmentProblemandTransportationProblem?5.StatethemathematicalformulationforA.P.6.WhatistheTravellingsalesmanproblem?7.WritestepsforNorth-WestCornerMethod.8.WritestepsforMatrixMinimaMethod.9.Whatisdifferencebetweentransportationproblemandassignmentproblem?13.WritethestepsforsolvingaA.P.byHungarianmethod14.Writethestepsfortransportationalgorithm.15.Definefeasiblesolution.16.Whatisbasicfeasiblesolution?17.Defineoptimalsolution.18.Statedifferentmethodstoobtaintheinitialbasicfeasiblesolution.19.Whatarethepropertiesofnon-degeneratesolution?20.HowdotheMODIandstepping-stonemethodsdiffer?4/RQJDQVZHUTXHVWLRQV1.ThreefertilizersfactoriesX,YandZlocatedatdifferentplacesofthecountryproduce6,4and5lakhtonesof urearespectively. Underthe directiveofth ecentralgovernment,theyareto bedistributedto3StatesA,BandCas5,3and7lakhrespectively.Thetransportationcostpertonesinrupeesisgivenbelow:ABCX111716Y151214Z201215FindoutsuitabletransportationpatternatminimumcostbyNorthWestCornermethodandLeastCostmethod.2.DetermineanIBFSbyVogel'sApproximationmethod.SourceD1D2D3D4SupplyS1193050107S2703040609S3408702018

Department of Computer Science And Technology201514|PageMr.DivyangGorDemand587143.Adepartmentalhasfiveemployeeswithfivejobstobeperformed.Thetime(inhours)eachmenwilltaketoperformeachjobisgivenintheeffectivenessmatrix.Howshoul dthejobsbeallocat ed,oneper employee,soa stomini mizethetotalman-hours.Employeesjobs12345a105131516b3918136c107222d7119712e79104124.Acitycorporationhasdecidedtocarryoutroadrepairsonmainfourarteriesofthecity.ThegovernmenthasagreedtomakeaspecialgrantofRs50lakhtowardsthecostwithaconditionthatrepairsaredoneatthelowestcostandquickesttime.Iftheconditionswarrant,asupplementarytokengrantwill alsobecons ideredfavorably. Thecorporation hasfloate dtendersandfivecontractorshavesentintheirbids.Inordertoexpeditework,oneroadwillbeawardedtoonlyonecontractor.CostofRepairs(Rsinlakh)ContractorsR1R2R3R4R5C1914191513C2717201918C3918211817C41012181918C51015211615Findthebestwayofassigningtherepairworktothecontractorsandthecosts.Ifitisnecessarytoseeksupplementarygrants,whatshouldbetheamountsought?5.AcompanyhasfactoriesatF1,F2&F3whichsupplywarehousesayW1,W2andW3.Weeklyfactorycapacities are200,160and90unitsrespecti vely.Wee klywarehousesrequirementsare180,120and150unitsrespectively.Unitshippingcosts(inrupees)areasfollows:WarehouseFactoryw1w2w3SupplyF1162012200F214818160F326241690Demand180120150Determinetheoptimumdistributionforthiscompanytominimizetheshippingcost.6.ObtaintheinitialsolutiontoaboveTPusingnorthwestcornermethod.D1D2D3D4SupplyO1641514O2892716O343625Dem.6101547.ObtaintheinitialsolutiontobellowTPusingleastcostmethod.ABCDSupplyI635422II592715III57868Demand7121798.ObtaintheinitialsolutiontoBelowTPusingleastcostmethod.

Department of Computer Science And Technology201515|PageMr.DivyangGorD1D2D3D4SupplyO112346O243208O3022110Demand46869.ABCDSupplyI153334II331215III022312IV272419Demand21251717ObtaintheinitialsolutiontoaboveTPusingnorthwestcornermethod.10.IIIIIIIVSupplyA2116151311B1718142313C3227184119Demand6101215ObtaintheinitialsolutiontoaboveTPusingVogel'sapproximationmethod.11.D1D2D3D4SupplyO1121430O2332150O3425920Demand20403010ObtaintheinitialsolutiontoaboveTPusingVogel'sapproximationmethod12.IIIIIIIVSupplyA231176B10611C58151010Demand753217ObtaintheoptimalsolutiontoaboveTP.13.abcSupplyI10988II107107III11979IV1214104Demand10108ObtaintheinitialsolutiontoaboveTPusingnorthwestcornermethod.14.WarehousesW1W2W3W4SupplyF1193050107F2703040609F3408702018Demand58714ObtaintheoptimalsolutiontoaboveTP.15.SolvethefollowingAssignmentProblem

Department of Computer Science And Technology201516|PageMr.DivyangGorPQRSA22302115B1833931C44252421D2330281416.SolvethefollowingAssignmentProblemIIIIIIIV11110185214131219353424151817917.SolvethefollowingAssignmentProblemABCDEF11313162319921119261617183121149610471591414135913128141118.SolvethefollowingAssignmentProblemPQRSA5347B2376C4152D681219.Findtheassignmentofsalesmentovariousdistrictswhichwillresultminimumcost.SalesmanDistrict1234A16101411B14111515C15151312D1312141520.Solvethefollowingassignmentproblemsoastominimizethetime(indays)requiredtocompleteallthetask.persontask12345A6581116B11316110C1611888D91412101621.Anautomobiledealerwishestoputfourrepairmentofourdifferentjobs.Therepairmenhavesomewhatdifferentkindsofskillsandtheyexhibitdifferentlevelsofefficiencyfromonejobtoanother.Thedealerhasestimatedthenumberofmanhoursthatwouldberequiredforeachjob-mancombination.Thisisgiveninthematrixform.Findtheoptimumassignmentthatwillresultinminimummanhoursneeded.ABCD1532827926364574577822.Solvethefollowingtransportationproblemtofinditsoptimalsolution:(MODI)

Department of Computer Science And Technology201517|PageMr.DivyangGorW1W2W3W4SupplyP119030050010070P270030040060090P3400100400200180Demand50807014034023.Findinitialbasicfeasiblesolutionby'Vogel'sMethod'and'NorthWestCornerMethod'.DestinationSource1234supplyI2116151311II1718142313III3227184119Demand61012154324.Solvethefollowingtransportationproblemtofinditsoptimalsolution:(MODI)ABCAvailableI50302201II90451703III250200504Required422Q:3MultipleChoiceQuestions:1.Theinitialsolutionofatransportationproblemcanbeobtainedbyapplyinganyknownmethod.However,theonlyconditionisthat(a)thesolutionbeoptimal(b)therimconditionaresatisfied.(c)thesolutionnotbedegenerate.(d)alloftheabove.2.Thedummysourceordestinationinatransportationproblemisaddedto(a)satisfyrimcondition.(b)preventsolutionfrombecomingdegenerate.(c)ensurethattotalcostdoesnotexceedalimit.(d)alloftheabove.3.Theoccurrenceofdegeneracywhilesolvingatransportationproblemmeansthat(a)totalsupplyequalstotaldemand(b)thesolutionsoobtainedisnotfeasible.(c)thefewallocationsbecomenegative.(d)noneoftheabove.4.Anal ternativeoptimalsolutiontoaminimizat iontr ansportationproblemexistswheneveropportunitycostcorrespondingtounusedroutesoftransportationis:(a)positiveandgreaterthanzero.(b)positivewithatleastoneequaltozero.(c)negativewithatleastoneequaltozero.(d)alloftheabove.5.OnedisadvantageofusingNorth-WestCornerRuletofindinitialsolutiontothetransportationproblemisthat(a)itiscomplicatedtouse.(b)itdoesnottakeintoaccountcostoftransportation.(c)itleadstodegenerateinitialsolution(d)alloftheabove.6.Thesolutiontoatransportationproblemwithm-rowsandn-columnsisfeasibleifnumberofpositiveallocationsare(a)m+n(b)mxn(c)m+n-1(d)alloftheabove.7.ThecalculationofopportunitycostintheMODImethodisanalogoustoa(a)cj-zjvaluefornon-basicvariablecolumnsinthesimplexmethod.

Department of Computer Science And Technology201518|PageMr.DivyangGor(b)valueofavariableinb-columnofthesimplexmethod.(c)variableinxb-column.(d)alloftheabove.8.Ifweweretouseopportunitycostvalueforanunusedcelltotestoptimality,itshouldbe(a)equaltozero.(b)mostnegativenumber.(c)mostpositivenumber.(d)alloftheabove.9.AnassignmentproblemisconsideredasaparticularcaseofaTransportationproblembecause(a)thenumberofrowsequalscolumns(b)allxij=0(c)allrimconditionsare1(d)allofabove.10.Forasalesmanwhohastovisitncities,followingarethewaysofhistourplan(a)n!(b)(n+1)!(c)(n-1)!(d)n11.Everybasicfeasiblesolutionofageneralassignmentproblemhavingasquarepay-offmatrixofordernshouldhaveassignmentsequalto(a)2n+1(b)2n-1(c)m+n+1(d)M+n12.Thepurposeofadummyroworcolumninanassignmentproblemisto(a)obtainbalancebetweentotalactivitiesandtotalresources(b)preventasolutionfrombecomingdegenerate(c)provideameansofrepresentingadummyproblem(d)noneoftheabove.13.TheHungarianmethodforsolvinganassignmentproblemcanalsobeusedtosolve(a)atransportationproblem(b)atravelingsalesmanproblem(c)both(i)and(ii)(d)only(ii)14.Anoptimalofanassignmentproblemcanbeobtainedonlyif(a)eachrowandcolumnhasonlyonezeroelement(b)eachrowandcolumnhasatleastonezeroelement(c)thedataarearrangementinasquarematrix(d)nonoftheabove15.Themethodusedforsolvinganassignmentproblemiscalled(a)reducedmatrixmethod(b)MODImethod(c)Hungarianmethod(d)noneoftheabove16.Whichmethodusuallygivesaverygoodsolutiontotheassignmentproblem?(a)northwestcornerrule(b)Vogel'sapproximationmethod(c)MODImethod(d)stepping-stonemethod17.Thetransshipmentmodelisanextensionofthetransportationmodelinwhichintermediatetransshipmentpointsare______betweenthesourcesanddestinations.(a)decreased(b)deleted(c)subtracted(d)added18.Intheprocessofevaluatinglocationalternatives,thetransportationmodelmethodminimizesthe(a)totaldemand(b)totalsupply(c)totalshippingcost(d)numberofdestinations19.Inanassignmentproblem,(a)oneagentcandopartsofseveraltasks(b)onetaskcanbedonebyseveralagents(c)eachagentisassignedtoitsownbesttask(d)noneoftheabove

Department of Computer Science And Technology201519|PageMr.DivyangGor20.Inatransportationproblem,itemsareallocatedfromsourcestodestinations(a)atamaximumcost(b)ataminimumcost(c)ataminimumprofit(d)ataminimumrevenueQ:4TrueorFalse1.Timeseriesmethodstendtobemostusefulforshort-rangeforecasting.2.Anexponentialsmoothingforecastwillreactmorestronglytoimmediatechangesinthedatathanthemovingaverage.3.Longer-periodmovingaveragesreactmorequicklytorecentdemandchangesthandoshorter-periodmovingaverages.4.TheDelphi methodforacquiring informedjudgmentsan dopinions fromknowledgeableindividualsusesaseriesofquestionnairestodevelopaconsensusforecastaboutwhatwilloccurinthefuture.5.Timeseriesmethodsassumethatwhathasoccurredinthepastwillcontinuetooccurinthefuture.6.Theoperatingcharacteristicsofaqueuingsystemprovideinformationratherthananoptimizationofaqueuingsystem.7.Queuinganalysisisadeterministictechnique.8.Acerealcompanythatisplanningonmarketinganewlow-cholesterolcerealshouldbeconcernedaboutthestatesofnature--thatistheprobabilitythatpeoplewillstayinterestedineatinghealthyfoods.9.Theexpectedopportunitylosscriterionwillalwaysresultinthesamedecisionastheexpectedvaluecriterion.10.Transportationroblemsandassignmentproblemsbothoftheseproblemtypescouldnotbesolvedusingsimplexalgorithm.11.Vogel'sapproximationmethodtacklestheproblemoffindingagoodinitialsolutionbytakingintoaccountthecostsassociatedwitheachroutealternative.12.Theoptimalsolutionofatransportationmodelprovidesashippingpatternwiththelowesttotalshippingcost.13.Inatransportationproblem,numberofsourcesmustbesameasnumberofdestinations.14.Inatransportationproblem,thetotaldemandofdestinationsmustbeidenticaltothetotalcapacityofsources,otherwiseQMcannotsolveit.15.Intheassignmentmodel,eachpersoncanbeassignedtooneandonlyonejob.16.theassignmentmodel,eachjobwillbedonebyoneandonlyoneperson.17.Theassignmentproblemcanbeviewedasaspecialtransportationprobleminwhicheverysourcehascapacity1andeverydestinationhasdemand1.18.Thetransportationproblemcanbeviewedasanassignmentproblemandsolvedbyusingtheassignmentmodel.19.Demandsofdestinationsis(are)theinput(s)forsolvingatransportationproblem.20.Inthedata-enteringtableofQM'stransportationmodel,asourcetakesarow.Q:5Fillintheblanks.1.Inthedata-enteringtableofQM'stransportationmodel,asourcetakesa________.2.IntheresultofQM'stransportationmodel,ifitshowsthatSource2shouldship45unitstoa"dummy"destination,thenitmeansthat___________.3.Dummysourceordummydestinationwilloccurinthecaseof____________.4.Inatransportationproblem,wemustmakethenumberof__________and__________equal.

Department of Computer Science And Technology201520|PageMr.DivyangGor5.Thenetcostofshippingoneunitonaroutenotusedinthecurrenttransportationproblemsolutioniscalledthe__________.6.Theprocedureusedtosolveassignmentproblemswhereinonereducestheoriginalassignmentcoststoatableofopportunitycostsiscalled__________.7.Themethodoffindinganinitialsolutionbaseduponopportunitycostsiscalled__________.8.__________occurswhenthenumberofoccupiedsquaresislessthanthenumberofrowsplusthenumberofcolumnsminusone.9.BothtransportationandassignmentproblemsaremembersofacategoryofLPproblemscalled______.10.TheequationRi+Kj=Cijisusedtocalculate__________.11.Thetransportationproblemistotransportvariousamountsofasinglehomogenouscommodity,thatareinitiallystoredatvariousorigins,todifferentdestinationsinsuchawaythatthetotaltransportationcostis__________.12.Inabalancedm×ntransportationproblemí µ!!!!!=_____,whereai'sarecapacitiesofthesourcesandbjsarerequirementsofthedestinations.13.Thetransportationproblemcanberegardedasageneralizationofthe_____.14.Afeasiblesolutionofmbyntransportationproblemissaidtobenon-degeneratebasicsolutionifnumberofpositiveallocationsisexactlyequalto_______.15.Bynorth-westcornerrulewealwaysgeta_______basicfeasiblesolution.16.Theoptimal itytestisapplicabletoaF.S.c onsistingof_______ allocations inindependentpositions.17.Inatransportationproblemthesolutionundertestwillbeoptimalanduniqueifallthecellevaluationsare_____.18.Invogel'sapproximationmethodthedifferencesofthesmallestandsecondsmallestcostsineachrowandcolumnarecalled______.19.Incom putationalprocedureofoptimalitytest wechoosethatuiorvj=0f or whichthecorrespondingroworcolumnhasthe________numberofindividualallocations.20.Theiterativeprocedureofdetermininganoptimalsolutionofaminimizationtransportationproblemisknownas_______.Unit:4GamesTheoryandSequencingProblemsQ:1ShortAnswerQuestions.1.Defineterms:Activity,Event,MergeEvent,BurstEvent,Totalfloat,Freefloat,Criticalpath,criticalactivity2.StateRulesforNetworkDiagram.3.WhatisSequencingproblems?4.Whatisdummyactivity?5.Whatissuccessoractivity?6.WritesimilaritiesanddifferencesbetweenPERTandCPM.7.WriteapplicationsofPERT/CPMtechniques.8.WriteusesofPERT/CPMtechniques.9.WritethestepsforProcessingnjobsthroughtwomachines.10.DefineCompetitivegame11.Definepayoffmatrix12.DefinepureStrategies

Department of Computer Science And Technology201521|PageMr.DivyangGor13.DefineMixedStrategies14.Definesaddlepoint15.Defineoptimalstrategies16.Whatistwo-personzerosumgame?givingasuitableexample.17.Giveminimaxprincipleusedinthetheoryofgames.18.Explainmaximinprincipleusedinthetheoryofgames.19.Whatisgameingametheory?20.Whatarethepropertiesofagame?21.Explainthe"beststrategy"onthebasisofminimaxcriterionofoptimality.22.Writethenotationoft!",T,I!".23.ExplainNumberofMachines.24.DefineProcessingTime.25.DefineProcessingOrder.26.DefineIdletimeonaMachine.27.DefineTotalElapsedTime.28.Determinethevalueofthegame.29.Determinethevalueofthegame.Q:2LongAnswerQuestions.1.Statethemajorlimitationsofthegametheory.2.Explainthedifferencebetweenpurestrategyandmixedstrategy.3.Whataretheassumptionsmadeinthetheoryofgame?4.Explainfourelementsthatcharacterizeasequencingproblem.5.Explaintheprincipalassumptionsmadewhiledealingwithsequencingproblem.6.Givethreedifferentexamplesofsequencingproblemsfromyourdailylife.7.Writeashortnoteonthe"sequencingdecisionproblemfornjobsontwomachines".8.Acompanymanagementandthelabourunionarenegotiatingaanewthreeyearsettlement.Eachofthesehas4strategies:I:HardandaggressivebargainingII:-ReasoningandlogicalapproachIII:-LegalisticstrategyIV:-ConciliatoryapproachThecosttothecompanyaregivenforeverypairofstrategychoice.UnionStrategiesCompanyStrategiesIIIIIIIVI20151235II2514810III402105IV-54110PlayerAPlayerBB!B!A!26A!-24PlayerAPlayerBB!B!B!A!-12-2A!64-6

Department of Computer Science And Technology201522|PageMr.DivyangGor9.Findtherangeofvaluesofpandqthatwillrendertheentryasaddlepointforthegame.10.Forwhatvalueofλ,thegamewithfollowingpay-offmatrixisstrictlydeterminable?11.Determinewhichofthefollowingtwo-personzero-sumgamesarestrictlydeterminableandfair.Givetheoptimumstrategiesforeachplayerinthecaseofitbeingstrictlydeterminable.a)b)12.Solvethefollowinggamesbyusingmaximumprinciple,whosepayoffmatrixaregivenbelow:Includeinyouranswer:(i)strategyselectionforeachplayer,(ii)thevalueofthegametoeachplayer.Doesthegamehaveasaddlepoint?a)PlayerAPlayerBB!B!B!A!245A!107qA!4P6PlayerAPlayerBí µ!í µ!í µ!í µ!Λ62í µ!-1λ-7í µ!-24λPlayerAPlayerBí µ!í µ!í µ!12í µ!4-3PlayerAPlayerBí µ!í µ!í µ!-52í µ!-7-4PlayerAPlayerBí µ!í µ!í µ!í µ!í µ!1734í µ!5645í µ!7203

Department of Computer Science And Technology201523|PageMr.DivyangGorb)c)d)Q:3MultipleChoiceQuestions.1. Twopersonzero-sumgamemeansthatthe(a)Sumoflossestooneplayerisequaltothesumofgainstoother(b)Sumoflossestooneplayerisnotequaltothesumofgainstoother(c)Both(a)and(b)(d)Noneoftheabove2. Gametheorymodelsareclassifiedbythe(a)Numberofplayers(b)sumofallpayoffs(c)Numberofstrategies(d)alloftheabove3. Agameissaidtobefairif(a)bothupperandlowervaluesofthegamearesameandzero(b)upperandlowervaluesofthegamearenotequal(c)uppervalueismorethanlowervalueofthegame(d)noneoftheabove4. Whathappenswhenmaximinandminimaxvalueofthegamearesame?(a)nosolutionexists(b)solutionismixed(c)saddlepointexists(d)noneoftheabove5. Amixedstrategygamecanbesolvedby(a)algebraicmethod(b)matrixmethodPlayerAPlayerBí µ!í µ!í µ!í µ!í µ!í µ!-20053í µ!32122í µ!-4-30-26í µ!53-426PlayerAPlayerBí µ!í µ!í µ!í µ!í µ!3-506í µ!-4-212í µ!5423PlayerAPlayerBí µ!í µ!í µ!í µ!í µ!-53110í µ!5546í µ!4-20-5

Department of Computer Science And Technology201525|PageMr.DivyangGor20. Unforeseenfactorsthepreventtheplansfromactuallyhappeningare(a)equipmentmaydevelopafault(b)specificationsmaybechanged(c)additionalordermayarrivetobeaddedtoschedules(d)alloftheaboveQ:4Fillintheblanks.1. Agameissaidbe_______ifloweranduppervaluesofthegamearesameaswellaszero.2. Acourseofactionthatputsanyplayerinthemostpreferredpositionirrespectiveofthecourseofactionchosenbythecompetitoriscalled________.3. Ifagameinvolvesmorethantwoplayers,thenitiscalleda________game.4. Thepurestrategyontheonlycourseofactionthatis_______beingchosenbyaplayer.5. Therulesof_______areusedtoreducethesizeofthepayoffmatrix.6. The________isusedtodeterminetheprobabilityofusingdifferentstrategiesbyboththeplayers.7. The________isusedtofindtheoptimalstrategyforeachplayerinapayoffmatrixofsize2X2withoutsaddlepoint.8. The________isusefulforgamewherepayoffmatrixisofsize2XnormX2.9. The________methodisusefulforgamewithlargerpayoffmatrixwithoutsaddlepoint.10. Theconceptof________isusedinsimplifyingthesolutionofarectangulargame.Q:5TrueofFalse.1. Inarowpersonzero-sumgame,asaddlepointalwaysexists.2. Ifthereareonlytwostrategies,thepayoffmatrixhasasaddlepoint.3. Inapurestrategygame,eachplayeralwaysplaysjustonestrategy.4. Inamixedstrategygame,eachplayerrandombychoosesthestrategytobeused.5. Amixedstrategygameisbasedontheassumptionthatplayersactirrationally.6. Thestrategyforaplayerisacourseofactionthattheadoptsforeachplayoff.7. Thevalueofthegameistheexpectedoutcomeperplaywhenplayersfollowtheiroptimalstrategy.8. Thepayoffisaquantitativemeasureofsatisfactionthataplayergetsattheendoftheplay.9. Ifthemaximinvalueissameastheminimaxvalue,thanthegameissaidtohaveasaddlepoint.10. Agamesaidtobestrictlydeterminableifloweranduppervaluesofthegameareequal.Unit:5ProjectScheduling(CPMandPERT)Q:1ShortAnswerQuestions.1.Defineterms:Activity,Event,MergeEvent,BurstEvent,Totalfloat,Freefloat,Criticalpath,criticalactivity2.StateRulesforNetworkDiagram.3.WhatisSequencingproblems?4.Whatisdummyactivity?5.Whatissuccessoractivity?6.WritesimilaritiesanddifferencesbetweenPERTandCPM.7.WriteapplicationsofPERT/CPMtechniques.

Department of Computer Science And Technology201526|PageMr.DivyangGor8.WriteusesofPERT/CPMtechniques.9.WritethestepsforProcessingnjobsthroughtwomachines.Q:2LongAnswerQuestions.1.DrawtheNetworkDiagramforthefollowingactivitiesandfindthecriticalpath.JobABCDEFGHIJKJobtime(days)13810911108671418Immediatepredecessors-ABCBED,FEHG,IJ2.AprojecthasthefollowingtimeSchedule.ConstructaPERTnetworkandcomputeCriticalPathanditsduration.AlsocalculateTotalfloat,Freefloat.Activity1-21-32-43-43-54-95-6TimeinWeeks4111654Activity5-76-87-88-98-109-10TimeinWeeks8121873.Aprojectschedulehasthefollowingcharacteristics.ConstructthePERTnetworkandfindthecriticalpathandtimedurationoftheproject.Activity1-21-41-72-33-64-54-85-66-97-88-9Time221415843354.WritedowntheproceduretoobtainoptimumcompletiontimeusingCriticalPathmethod.5.FindthecriticalpathandcalculatetheTotalfloatandFreefloatforthefollowingPERTdiagram.6.Asmallmaintenanceprojectconsistsofthefollowing12jobsJobsDurationindaysJobsDurationindaysJobsDurationindays1-223-556-1042-374-637-942-435-858-913-436-789-107Drawthearrownetworkoftheproject.Determinethecriticalpath.7715135126716898101234567981025421243857692843524

Department of Computer Science And Technology201527|PageMr.DivyangGor7.Aprojecthasthefollowingtimeschedule:ActivityTimeInmonthActivityTimeInmonthActivityTimeInmonth1-223-686-951-323-757-841-414-637-932-545-81ConstructPERTnetworkandcomputetotalfloatforeachactivity.FindCriticalpathwithitsduration.8.Installaionofairpopulation controleq uipments requiresfollowingactivites:Draw networkdiagramfromthefollowingactivitesandfindCiticalPathActivityABCDEFGHTime23244352ImmediatePredecessornonenoneABCCD,EF,G9.Drawnetworkdiagramfromfollowingdetailsandcalculatecriticalpathfromit.ActivityABCDEFGHIJTime151535812114314ImmediatePredecessor--AAB,CB,CEED,GF,H,I10.Drawnetworkdiagramfromfollowingdetails.ActivityABCDEFGHPredecessorActivity-AABB,CED,FG11.Listedinthetablearetheactivitesandsequencingnecessaryforamaintenancejobsontheheatexchangersinarefinery.ActivityABCDEFGHIJPredecessorActivity-ABBBCCF,GD,E,HI12.Determinethecriticalpathfromthefollowingnetworkdiagram.13.AprojectconsistsofaseriesortaskslabeledA,B.....,H,Iwiththefollowingrelationships(W

Department of Computer Science And Technology201528|PageMr.DivyangGorActivityDescriptionRequiredPredecessorDurationAProductdesign(None)5monthsBMarketresearch(None)1CProductionanalysisA2DProductmodelA3ESalesbrochureA2FCostanalysisC3GProducttestingD4HSalestrainingB,E2IPricingH1JProjectreportF,G,I1Q:3MultipleChoiceQuestions.1. Adummyactivityisrequiredwhena. Twoormoreactivitieshavethesamestartingevents.b. Twoormoreactivitieshavedifferentendingevents.c. Twoormoreactivitieshavethesameendingevents.d. Thenetworkcontainstwoormoreactivitiesthathaveidenticalstartingandendingevents.2. WhichofthefollowingisabasicassumptionofPERT?a. Thereisonlyonecompleteroutefromthestartofaprojecttotheendofaproject.b. Onlycriticalpathactivitiesinthenetworkmustbeperformed.c. Activitycompletiontimesareknownwithcertainty.d. Noactivityinthenetworkmustberepeated.3. PERTanalysiscomputesthevarianceofthetotalprojectcompletiontimeasa. Thesumofthevariancesofallactivitiesintheproject.b. Thesumofthevariancesofallactivitiesnotonthecriticalpath.c. Thevarianceofthefinalactivityoftheproject.d. Thesumofthevariancesofallactivitiesonthecriticalpath.4. Thecriticalpathofanetworkisthea. Pathwiththefewestactivities.b. Shortesttimepaththroughthenetwork.c. Longesttimepaththroughthenetwork.d. Pathwiththemostactivities.5. Dummyactivitiesa. arefoundinbothAOAandAONnetworks.b. areusedwhentwoactivitieshaveidenticalstartingandendingevents.c. haveadurationequaltotheshortestnon-dummyactivityinthenetwork.d. cannotbeonthecriticalpath.6. WhichofthefollowingisalimitationofPERTandCPM?a. Thegraphicalnatureofanetworkdelayscomprehensionoftheactivitylist'sinterrelationships.b. Theyareapplicabletoonlyanarrowvarietyofprojectsandindustries.c. Theycanbeusedonlytomonitorschedules.

Department of Computer Science And Technology201529|PageMr.DivyangGord. Thereisinherentdangeroftoomuchemphasisbeingplacedonthecriticalpath.7. TheEFofanactivityisthea. Max{EFofallimmediatepredecessors}.b. Min{LSofallimmediatefollowingactivities}.c. ES+Activitytime.d. LF-Activitytime.8. InaCPM/PERTnetworkadummyactivityisnecessarywhena. twoactivitieshavethesamestartingnodeb. twoactivitieshavethesameendingnodec. anodedoesnotactuallyconnecttoanothernoded. whentwoactivitiessharethesamestartingandendingnode9. Sharedslackinanactivitynetworkisdefinedasa. Theamountoftimeanactivitycanbedelayedwithoutdelayingtheentireproject.b. Theamountofslackthatanactivityhasincommonwithanotheractivity.c. Theamountofunusedresourcesforanactivity.d. Theamountbywhichatimeestimatecanbeinerrorwithoutaffectingthecriticalpathcomputations.10. Ifanactivityhaszeroactivityslackita. meansthattheprojectisexpectedtobedelayed.b. mustbeadummyactivity.c. isonthecriticalpath.d. alloftheabove11. Whichoftheseisnotcorrecta. PERTisprobabilisticinnature.b. CPMisdeterministicinnature.c. CPMisevent-oriented.d. CPMandPERTusesimilarterminologybutweredevelopedindependently.12. Whichofthefollowingisnotaruleofnetworkconstruction?a. Eachdefinedactivityisrepresentedbyoneandonlyonearrow.b. Anetworkshouldhaveonlyinitialandoneterminalnode.c. Identicalinitialandfinalnodescanidentifytwoactivities.d. Onlyasfewdummyactivitiesshouldbeincludedasiswarranted.13. WhichofthefollowingisnotcorrectinrespectofPERTcalculations?a. Expectedtimeofanactivityisaweightedaverageofthreetimesestimates,a,m,andbwithrespectiveweightsof1,4,and1.b. Thecompletiontimeofanactivityisassumedtofollownormaldistribution.c. Thestandarddeviationofactivitycompletiontimeisone-sixthoftheexcessofpessimisticoveroptimistictime.d. Thesumtotalofvariancesofcriticalactivitytimesgivesthevarianceoftheoverallprojectcompletiontime.14. Markthewrongstatement.a. Allactivitiesonacriticalpatharecriticalactivities.b. Aprojectnetworkmayhavenone,one,ormorecriticalpaths.c. Adelayincriticalactivitysurelydelaysthecompletionofproject.d. Eachcriticalactivityhasidenticalearliestandthelateststarttimes.15. CPMis:a. CriticalProjectManagement

Department of Computer Science And Technology201530|PageMr.DivyangGorb. CriticalPathManagementc. CriticalPathMethodd. CrashProjectMethod16. Pickthewrongrelationship:a. Interferingfloat=Totalfloat-Freefloatb. Totalfloat=Freefloat+Independentfloatc. Totalfloat≥Freefloat≥Independentfloatd. Freefloat=Totalfloat-Headeventslack17. Thecriticalpathisthe__________paththroughthenetwork.a. longestb. shortestc. straightestd. noneoftheabove 18. Anactivitycannotbebegununtil_______.a. allactivitiespreviouslybegunhavebeencompletedb. itspredecessorshavebeencompletedc. itslateststarttimehavecompletedd. alloftheabove19. Arcsinaprojectnetworkindicatea. completiontimes.b. precedencerelationships.c. activities.d. thecriticalpath.20. Thecriticalpatha. isanypaththatgoesfromthestartingnodetothecompletionnode.b. isacombinationofallpaths.c. istheshortestpath.d. isthelongestpath.21. Activitiesfollowinganodea. canbeginassoonasanyactivityprecedingthenodehasbeencompleted.b. haveanearlieststarttimeequaltothelargestoftheearliestfinishtimesforallactivitiesenteringthenode.c. havealateststarttimeequaltothelargestoftheearliestfinishtimesforallactivitiesenteringthenode.d. Noneofthealternativesiscorrect.e. 22. Slackequals

Department of Computer Science And Technology201531|PageMr.DivyangGora. LF-EF.b. EF-LF.c. EF-LS.d. LF-ES.23. Activitieswithzeroslacka. canbedelayed.b. mustbecompletedfirst.c. lieonacriticalpath.d. havenopredecessors.Q:4Fillintheblanks.1. A(n)_______isapointintimethatmarksthebeginningorendofanactivity.2. _________isthetimeanactivitycanbedelayedwithoutaffectingthestarttimeofanyotheractivity.3. Theprocessofreducingtotaltimethatittakestocompleteaprojectbyemployingadditionalresourcesiscalled______.4. PERToftenassumesthatthetimeestimatesfollowthe_______probabilitydistribution.5. InPERT/CPM,a(n)_________isatime-consumingjobortask.6. InanAONnetworkrepresentation,the_______representstheactivities.7. _______assumesthatactivitytimesareprobabilistic,while______assumesthatactivitytimesaredeterministic.8. Theearlieststart(ES)ofanactivityisthe_________earliestfinish(EF)oftheimmediate__________.9. InCPM,weassumethatresourcesareexpendedina(n)_________.10. Majoreventsinaprojectsareoftenreferredtoas________.11. Ifwehaveaprojectthatwehavenotdonebefore,then_______isprobablytobepreferredover________asaprojectmanagementscheme.12. _______assumesthatactivitytimesareprobabilistic,while______assumesthatactivitytimesaredeterministic.13. InPERT/CPM,a(n)_________isatime-consumingjobortask.14. PERTstandsforProgramevaluationandReview_________.15. Thepathwiththelongestdurationinanetworkiscalled_______.16. PERTisa_______modelwhileCPMisadeterministicmodel.17. Thecriticalpathrepresentsthe______timerequiredtocompletetheproject.18. CPMstandsfor___________.Q:5TrueofFalse.1. PERTdiffersfromCPMinthatPERTprovidestimeversuscosttradeoffs.2. PERTuses threeactivity timevaluesto obtainanestimateofthemean activitytim eandpredictabilityofduration.3. Activitiesonthecriticalpathexhibitpositiveslacktimes.4. Theexpectedactivitytimeistheaverageofanactivity'soptimisticandpessimistictimes5. Dummyactivitiesarefoundinactivity-on-arc(AOA)conventionPERT/CPMnetworkmodels.

Department of Computer Science And Technology201532|PageMr.DivyangGor6. Thedummyactivityhasanexpectedtimeofzerobydefinition.7. Earlystarttime(ES)iscomputedfromrighttoleft(backwardpass).8. Theproject-groupapproachextendslittleornoformalauthoritytothe9. projectcoordinator.10. PERT,butnotCPM,hastheabilitytoconsidertheprecedencerelationshipsinaproject.11. Theshortestofallpathsthroughthenetworkisthecriticalpath.12. ThefundamentaldifferencebetweenPERTandCPMisthatPERTusesthebetadistributionforcrashingprojectswhileCPMusescostestimates.13. Slackistheamountoftimeanactivitycanbedelayedwithoutdelayingtheentireproject.14. Everynetworkhasatleastonecriticalpath.15. Thecriticalpathcanbedeterminedbyuseofeitherthe"forwardpass"orthe"backwardpass."16. ThePERTpessimistictimeestimateisanestimateoftheminimumtimeanactivitywillrequire.17. Thestandard deviationofproject durationistheaverageofth estandard deviationofallactivitiesonthecriticalpath.18. InPERTanalysis,theidentificationofthecriticalpathcanbeincorrectifanoncriticalactivitytakessubstantiallymorethanitsexpectedtime.19. PERTstandsforProgramEfficiencyandReviewTechniques.20. Therecanbemultiplecriticalpathsonthesameproject,allwithdifferentdurations.

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