系统工程作业.docx

系统工程作业.docx

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系统工程作业

Selectionandreconstructionofthesupplychainbasedondynamicprogrammingandnetworkoptimization

Abstract:

Thispaperfirstintroducedthebasictheoryofanalytichierarchyprocess,networkoptimizationanddynamicprogramming,andthenanalyzedtheindustrysupplynetworkandenterprisesupplychainaswellassupplychainoptimization,proposedthebasicassumptionsandoptimizationstepsinthepracticalapplication.Finally,anexamplewasgivenandprovedthefeasibilityandtheeffectivenessofthemethod.

Keyword:

networkoptimization;industrysupplychain;enterprisesupplychain;dynamicprogramming,AHP

1Introductiontothebasictheory

1.1Dynamicprogramming

Seekingtheshortestpathisanimportantbranchofoperationsresearchandhasbeenwidelyusedinpractice.Sucheffectivewayshasbeenofferedinoperationsresearchabouthowtofindtheshortestpathinthenetworkasdynamicprogramming，networkdiagramsandsoon.Inthepaper,wemainlyuseAHPandthedynamicprogrammingmethodfortheshortestpathinthesupplychain.Tobeginwith,thebasicprinciplesofdynamicprogrammingareintroducedasfollows:

Thetwobasicequationsrepresenttherecurrencerelationinthedynamicprogramming,inwhichkisdescribedasstagevariable,

asthereachablestateset,

asthedecisionvariablesinkstage,

asthesetofpossibledecisions,

asthedistancefrom

to

astheshortestdistancefrom

inkstagetotheend.Optcanbetakenasminormaxaccordingtothepracticalmeaningofdifferentproblemsandtheindexfunctionalsobetakenasdistance,time,profits,costs,productionorresourceconsumptionindifferentcases.

1.2Analytichierarchyprocess

ThefamousoperationsresearchexpertinAmericanT.L.SaatyputforwardthedecisionmethodAHPinthe1970sbasedonMultipletargetsandmultiplecriteria,whichdividedacomplexproblemintoseveralcomponentsorfactorswhichcomposeahierarchicalstructureaccordingtothegovernrelationsamongthem.Then,multiplecomparisonresultsindicatetherelativeimportanceofcomponents.Afterthat,referringtorelatedexperts’determination,therelativeimportanceorderofvarioussubstituteschemeswouldbeobtained.Inthewholeprocess,thismethodreflectsthethinkingcharacteristics“analysis-determination–synthesis”.AHPmethodcanberoughlydividedintothefollowingfivesteps.

1.2.1Tomakethefactorsofthissystemandtheirrelationshipclearandcreateahierarchicalstructureofthesystem

Toclassifythebasicfactorsastheircharacteristicsinthissystemandanalyzetherelationshipofthesefactors,thenconstructthesystemhierarchicalstructure,asshowninthefigure1.

Fig.1Thesystemhierarchicalstructure

1.2.2Toconstructthemultiplecomparisonmatrix

Aftercomparingwiththetwofactorsonthesamelevelabouttheimportancetooneuppercriterion,establishthejudgmentmatrixforeachlevel.Intheadjacentlevels,theupperistarget,andthelowerisfactors.Meanwhile,thejudgmentresultcanbequantifiedby“1-9”scalemethodwhichhasbeenshownintable1.

1.2.3Tocalculaterelativeimportance

TocalculatetherelativeimportancevectorWi,andtheunifiedrelativeimportancevectorWi0,totheuppercriterionforeachfactor,inthisstep,thearithmeticmethodisalwaysadoptedtocalculateWiandWi0.Theresultisshownasfollowingequalities.

Tab.1Meaningsofscale

Ratioscale

meanings

1

Comparingthetwoelements,theyhavethesameimportance

3

Comparingthetwoelements,theformeroneisweaklymoreimportantthantheother

5

Comparingthetwoelements,theformeroneisintensivelymoreimportantthantheother

7

Comparingthetwoelements,theformeroneisobviouslymoreimportantthantheother

9

Comparingthetwoelements,theformeroneisextremelymoreimportantthantheother

2,4,6,8

Indicatetheabovementionedadjacentjudgments’middlevalue

1.2.4Todoconsistencytest

Inordertotesttheconsistencyofmatrix,wedefinetheConsistencyIndexofthematrixasC.I.:

Whentheyareexactlyconsistent,thevalueofC.I.is0.WiththeC.I.greater,theconsistencyofthematrixisgoingtobeworse.Inordertoovercometheshortcoming,weintroduceAverageRandomConsistencyIndex（R.I.）toreviseC.I..Forthematrixof1to9,theR.I.isshownintable2:

Tab.2TheAverageRandomConsistencyIndexR.I.

order

1

2

3

4

5

6

7

8

9

R.I.

0

0

0.58

0.90

1.12

1.24

1.32

1.41

1.46

TheC.R.iscalledtherandomconsistencyratioofthematrix;andwhenC.R.<0.10,ornearto0.1,thematrixhasbeenconsideredasthesatisfiedconsistency;otherwisereadjustmentneedstobedone.

1.2.5Tocalculatesyntheticweightandsortthesubstituteschemes

Tocalculatetheoverallimportanceofeachschemeandsortthefinalresult.

1.3Networkoptimization

Networkoptimizationistofindtheshortestpathofthenetworkintheinitialprogrammingandthenaccordingtotheprincipleofoptimalitytotakefullaccountoffactorssuchastime,resources,costssothattheselectedoptimalpathcanachievebestpossibleoptimizationssynthetically.

（1）Time-costoptimization,awaytoseekthelowesttotalcostsfortheshortesttimeconsideringtherelationshipbetweenthelogisticsprocessandfees,whichcanbeusedtomakelogisticsplansinthesupplychain.

（2）Time-resourceoptimization,awaytoseekminimumresourcesandminimumtimeconsideringtherelationshipbetweenthetimeandtheresourcesused,whichcanbeusedtomakeprocurementplansinthesupplychain.

（3）Syntheticoptimizationoftime,resources,costs,whichgivesfullconsiderationtotheoverallbalanceoftime,resourcesandcostinordertoachievetheultimategoalusingtheleastresourcesandtheminimumfeeintheshortestpossibletime.Thiswayhasbeenwidelyusedinsupplychainmanagement.

1.4Thesimilaritiesanddifferencesofthetheoryofgeneralnetworkoptimizationandsupplychainnetworkoptimization

Generalnetworkoptimizationreferstooptimizetheshortestpathinthenetworkwithcertainmethods,makingtheknownshortestpathtoachieveoptimal.

Supplychainnetworkoptimizationincludestwoideas:

（1）firstinlinewiththeprincipleofgeneralnetworkoptimization;

（2）usingtheshortestpathinindustrysupplynetworkasabenchmarktooptimizeothersupplychains.

2Overviewofthesupplychainnetwork

2.1Industrysupplynetworkandenterprisesupplychain

Industrysupplynetworkisalargeandcomplexnetworksystem,acombinationofalltherelevantenterprisesproducingthesameorsimilarproductsoralternativeproductsandusers.Inthesystem,therearemanydifferentsinglesupplychains,crossingeachothertoprovideservicesforthefinalconsumerssoastoachievetheultimateconsumerutilitymaximization,andthereexistsacompetitiverelationshipamongthesesinglesupplychains.

Enterprisesupplychainmeanssinglesupplychaingenerallyreferredto,akindofchainstructureornetworkstructurecomposedofrawmaterialsuppliers,manufacturers,distributors,retailersandcustomersbyconnectingwiththeupstreamanddownstreammembers.Soenterprisesupplychainisapartoftheindustrysupplychain.

2.2Optimalindustrysupplychain

Theso-calledindustryoptimalsupplychainistoseekthesupplychainwhichisoptimalintheindustrysupplychainnetworkorthebestinpracticeunderoneorseveralstandardsasoptimizationbenchmarkofothersupplychains.

2.3Enterprisesupplychainoptimization

Enterprisesupplychainoptimizationistolocatethedifferencesofenterprisesupplychainfromthebenchmark,theindustryoptimalsupplychain,thentoreducethembyoptimizingenterprisesupplychain,eventuallyreachingthestandardofthereferredsupplychaintoimproveeffectivenessandmarketcompetitivenessofthechain.Intheoptimizationprocess,themethodofpartiallycoordinated,overallintegratedandthereconstructionmethodcanbothbeusedtoarriveatthedestination.

3ApplicationofdynamicprogrammingandAHPinthesupplychainselectionandreconstruction

3.1Basicassumptions

Thesupplychainisalargeandcomplexsystem.inordertosimplifythestudy,weneedtodosomeassumptionsaboutthesupplychaintosimplifythesystemsothatthereadersareabletounderstandthenetworkoptimizationmethodmoreclearly.Thebasicassumptionsareasfollows:

（1）Thereareonlyaninitialrawmaterialsupplierandafinalconsumerinthenetwork;

（2）Supplynetworkconsistsofthreetierofsuppliers,atierofmanufacturersandtwotierofdistributors;

（3）Themanufactureristhecoreenterpriseofthesupplychain;

（4）Theindustrysupplynetworkprovidesonlyoneproduct;

（5）Theinternalcostsarealreadytheoptimalineachcompany,whichbecomesjustanodewithoutaccountingforthecosts,resources,timeandsoon.Inaddition,thecostsoffirstrawmaterialsarenottakenintoconsideration.

Fig.2Industrysupplynetwork

3.2Industrysupplynetwork

Aftertheabovebasicassumptions,supplynetworkofcertainindustryisdescribedasshowninfigure2andthisnetworkcanbeadirectedone（arrowsindicatethedirectionoflogistics）.Nodesinthegraphstandforeachbusiness,Efortheultimateconsumer,thearrowsfortransactioncostsortimebetweenthetwoconnectedpoints,thenumberinarrowlinesforthevalueofexpensesortime,forinstance

isthetransactioncostsbetweenAand

.Thepointsnotconnectedtoeachotherinthenetworksuchas

meansthatonepointdoesnotmeettherequirementsoftheotherandhavetostrivetobecomeoneoftheenterprises,orthatthestrengthoftheenterpriseissostrongthatitisno