Mathematicalmethodsonmanagementproblems(1)

　,　　,　　,　　

( School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China )

Mathematicalmethodsonmanagementproblems(1)

ZHANGShengkai,LIUChao,LIUYan,ZHANGFengrong

(SchoolofInformationScienceandEngineering,DalianPolytechnicUniversity,Dalian116034,China)

Abstract:One-time management sequencing problem is studied, that is serviced-elements served by service-elements will be completed in one time. This method is applied for the actual situation to solve the underground parking service model for dealing with the parking problem. A suggestion is put forward that through the entrance of the conversion or reserved variable lane lifting, the utilization efficiency of underground parking will be enhanced.

Key words:serviced-elements; underground parking; utilization efficiency

0Introduction

Withthespeedingupoftheprogressofhumanscience,technologyandindustrialization,urbanizationlevelaregettinghigherandhigher.Therapidgrowthinthenumberofurbanpopulationmakesthecitylandexpand,butatpresenttheexpansionspeedinsomecitiesisfarbehindthegrowthrateofurbanpopulation,hinderingthedevelopmentofthecity.Inordertoexpandlivingspaceinalimitedlandresources,increasingurbanbuildingcapacitymustbeasolutionofthecitythree-dimensionalredevelopment,althoughtheconstructionofhigh-risebuildingsandurbanairtrafficnetwork,makethecapacityofurbanconstructionincrease.Meanwhile,italsohasanegativeimpactontheurbanlandscapeandecology,andevencausetheweakeningofthecitypartoftheregionalbusinessenvironmentorloss,bringinconveniencetopeoplelivingincities,atthesametime,italsobringsvariouskindssecurityissues.Theprogressivedevelopmentofurbanundergroundspacecanexpandthelivingspaceandincreasethecapacityofurbanconstruction.

Inthispaper,wefirstintroducetacticiansoftheK-Sbestservicemodelofschedulingproblem,someundergroundparkingareanalyzed,inordertocontrolthevehicledistributionandstrengthensafetymanagement.

1TheoptimumservicesequencingproblemsformodelK-S

Thelossofserviced-elementsisstudied.Theparametersaredifferentfromreferences1to3,thearticlehadgivenamethodoftheoptimumsequencing.

SupposethatthereexistK-serviced-elementsgroups:

{M1, M2, …, Mk}

{J1,J2,…,Js}

(1)

iscalledtheexpectedvalue.

Obviously,everyexpectedvalueisonlycorrespondingtoaserviceofserviced-elementisservedbyservice-element,andbetweenserviced-elementandservice-elementareonetoonecorresponding.

(2)

i=1, 2, …, k; j=1, 2, …, s

Definition 2 The set

(3)

(4)

iscalledanexpectedsumofEij.Themaximumexpectedsuminallexpectedsumsisasfollows:

(5)

iscalledmaximumexpectedsumofEijforeachfixedk,thefeasiblelineisonlydefinedby(3).

Definition5ForM(J),iftotalexpectedsumismaximum,thenM(J)iscalledanoptimumservicesequencingproblemiscalledanoptimumsequencing.

Obviously,theoptimumservicesequencingisexistence.

Definition6IfJjisservicedbyMi,alltheelementsofJjareservedbysomeelementsofMi,theM(J)isoptimumservicesequencingifandonlyifM(J)isModelK-Soptimumservice.

TheoremIForserviceM(J),ifallelementsofJjarecompletelyservedbyelementsofMi(i=1,2,…,k;j=1,2,…,s), M(J)isoptimumservicesequencingifandonlyifM(J)isModelK-Soptimumservice.

Proof10Themaximumexpectedsumcanbefoundanditisuniqueexistence.

TakingamaximumnumeralineverycolumnofEij,thesumofallmaximumnumeralsineverycolumnsofEijisthemaximumexpectedsum,thatis

(6)

(7)

From(6)subtract(7),then

thatis

(8)

Sufficiencyandnecessityofthetheoremhadbeenprovedasfollows.

Inordertoprovetheresult,nexttwocasesasfollowingwillbediscussed.

First,thematrixofM(J)isgivenby:

(9)

ThemaximumexpectedsumsofEwith(9)isgivenby:

(10)

(11)

Therefore, (11)correspondingtoservicemustbeoptimumservice.

(12)

andbecauseM(J)isoptimumservice,therefore,wehavetakenequality,ofcourse,therequirementofModelK-SSequencingissufficedbyaboveproof.

Intheproofprocessoftheorem1,wecanseeittobeanoptimumsequencingMethodandtheMethodisclearapplication.

Next,weapplythismodeltotheundergroundparkinglot,theparkingcapacityisdefinedfromthepointofviewofsecurityduringdisasters,thenweanalysisthenumberofvehiclesandparkingserviceinthepeak.

2.1Naturalconditions

DalianVictoryShoppingPlazaisoneofAsia’slargestundergroundshoppingmalls,dailypassengerflowisalsothelowest15to18millionpassengers,holidays, 20to25millionpeopleorevenmore.Itwaslistedasoneofthekeyunitsoffire.

DalianVictoryShoppingPlazaisalarge-scalecomprehensiveshoppingplacesandundergroundshoppingsquareconstructionisasthemainbody,coveringareaof27 000m2,andthebuildingareais140 000m2,with8channels, 67inwardandoutwarddirects, 28groundescape, 2substations.

2.2Theorganization

Basedontheprinciplesof“Whoisincharge,whoisresponsible”and“Whoisonguard,whoisresponsible”,toestablishperfectcompulsorydisasterpreventionorganization,about218personsoftheobligatoryfirebrigade, 116personsofcompulsoryevacuation, 30personsofemergencyteams,thecompanyisoncall24hoursofstay,dealingwithemergencies.

2.3Specificworkingmeans

(1)Trainingeducation:Newhiresandoverallregionalopeningmustconductfirecontrolsafetytraining.

(2)Dailywatchandmonthlytest.

(3)Funding:Fundingisthebasicconditionoffirecontrolwork,thecompanyinvests400 000RMBayearastheequipmentmaintenancecostsonfireshutter,emergencyexitandsmokeexhaustsystems,etc.

(4)TheVictoryPlazaonline:Educationalfilmprojectshavebeenmade,broadcastinginthe170unitsinternalnetworkTVinthePlaza.

(5)Broadcastandpropaganda.

(6)Mechanismperfection:Enrichtheperfectemergencyfireevacuationinadvance.

(7)Specialprojects:Thecompanyhasstrengthenedfiresafetyinspections,andhasenhancedawarenessoffireprevention.

3Servicemodelintheapplicationsofundergroundparkinglot

Withthedevelopmentofeconomy,privatecarownershipishigherandhigher. “Parkingdifficult”isoneoftheprominentcontradictionofcitytraffic[4].Now,almosteverycityaremoreorlessbuiltundergroundparkinglots.Andtheundergroundcarparkbuiltinthedepartmentstore,multi-storeyresidentialandpublicbuildings,somebuiltinthecitysquareandpark.Becauseofundergroundparkinggaragebringsmanybenefits:doesnotusethelimitedland;willnotaffecttheurbanlandscapeasthecolorfulvehiclecolors;suitableforparkingmanagement[5-6].

Inordertostudytheproblemofconvenient,forundergroundmall,parking,accesstothevehicleandevensomeconsumerplacesthesubwayorimportandpersonnelandsoon,wearecollectivelyreferredtoastheelements.Foraunitofplace,intotheelementsdenotedbyx,outoftheelementdenotedasy,atacertaintimeinterval[0,t],anytimetk∈[0,t]whentheelementxisdenotedasxk,similarlytotheelementsyisdenotedasyk, (k=0,1,2,…).NowsupposethataunitofE1inthetimeinterval[0,t]fromafinitesequenceoft1, t2, …, tn, tk∈[0, t].Thecorrespondingxsequencex1, x2, …, xn,thesamey1, y2, …, yn,ifwewanttostudyatatimetm, tm∈[0,t], (1≤m≤n),thesubintervaltime[0,tm],theunitforthesumofnetexistingelementsis

(13)

whereV0istheunitE1originalelementssum,thenumberofelementsintheoutputperunittimeisP1,whereP1isaconstant,sototheE1attimetk∈[0,t],theS1elementsalltherequiredoutputtimeis

(14)

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管理问题的数学方法应用(1)

张 盛 开,刘 超,刘 燕,张 凤 荣

( 大连工业大学 信息科学与工程学院, 辽宁 大连116034 )

摘要：研究了一个时间管理排序问题，即每一个服务单位在单位时间内只能服务一个被服务单位，同时被服务单位在单位时间内，只能被一个服务单位所服务，并且一经服务又必须一次服务完毕。将此方法应用到实际情况中，用以解决地下停车服务模型处理停车问题。最后，提出了通过入口的转换或预留可变车道的建议，用以提高地下停车场的利用效率。

关键词：服务单位；地下停车场；利用效率

中图分类号：TB114.1

文献标志码：A

Receivedby: 2015-12-22.

Firstauthor:ZHANGShengkai,Male,Professor.