Journal of Convergence Information Technology Volume 4, Number 3, September 2009 Extensive Analysis and Prediction of Optimal Inventory levels in supply chain management based on Particle Swarm Optimization Algorithm P. Radhakrishnan*1, Dr. V. M. Prasad*2 and Dr. M. R. Gopalan*3 *1Assistant professor in CSE, PSG Institute of advance studies Coimbatore, Tamil Nadu, India. radhakrish.phd@gmail.com *2Associate Professor, JNTU School of Management Studies Hyderabad, Andhra Pradesh, India. *3Director Research, IFIM Business School Bangalore, Karnataka, India doi: 10.4156/jcit.vol4.issue3.3 Abstract Efficientinventorymanagementisacomplex process which entails the management of the inventory inthewholesupplychain.Thedynamicnatureofthe excessstocklevelandshortagelevelfromoneperiod to another is a serious issue. In addition, consideration ofmultipleproductsandmoresupplychainmembers leadstoverycomplexinventorymanagementprocess. Moreover,thesupplychaincostincreasesbecauseof theinfluenceofleadtimesforsupplyingthestocksas wellastherawmaterials.Abetteroptimization methodologywouldconsiderallthesefactorsinthe prediction of the optimal stock levels to be maintained in order to minimize the total supply chain cost.Here, weareproposinganoptimizationmethodologythat utilizestheParticleSwarmOptimizationalgorithm, oneofthebestoptimizationalgorithms,toovercome theimpasseinmaintainingtheoptimalstocklevelsat each member of the supply chain. Keywords Supplychainmanagement,supplychaincost, Inventory,leadtime,optimization,Particleswarm optimization (PSO) 1.Introduction Themanufacturingenterprisesareunder competitive pressure dueto the remarkable changesin themarketscenarioeffectedbyuniversalcompetition, shorter product life cycles, active variations in demand patternsandproductvarietiesandenvironmental standards[1].Thecompetitivenessofabusiness enterprise in the modern market place is established by thetraitssuchasdeclineinleadtimesandexpenses, fortificationofcustomerservicelevelsandsuperior productquality[2]. Thecompanyisforcedtopay due attentiontotheirsupplychainsduetotheaforesaid features.Asupplychaindenotesacompanyorgroup thatoffersgoodsandservicestothemarket. Otherwise,agroupofseveralunitsthatfunctionin orderto1)acquirerawmaterials,(2)convertthese unprocessedsuppliesintospecificendproducts,and (3) distributetheendproductstoretailersorend users can be referred as a supply chain [7]. Purchase of raw resources/materials and converting them into usable outputs at asingle ormultiple plants, transportingthemtodiversewarehousesforstorage andsubsequentdeliveryofthesametothespecific retailers or customers are the processes performed by a conventional supply chain management [2].Supplychainmanagementaimsatintegratingand coordinatingtheactivitiesofthesuppliers, manufacturers,warehousesandstorestoensure appropriate manufacture and delivery of the outputsto theexactplaceattherighttimeandtominimizethe entiresupplychaincostandalsotoensuremeeting servicelevelrequirements.Theproducerisdeemedto bethemanagerofthesupplychainastheyare responsibleforobtainingrawresources,changing it to endproducts,deliveringthecompletedgoodstothe customers.Themanagementofvaryingdemandsisa massiveissueencounteredbythecommonsupply chainsintendingtocuttheexpensesofsupplychains inadditiontoadvancingcustomerserviceintensities [9]. Thereareseriousissuesinthemanagement of the supplychainduetotherisingsupplychainintricacy owingtotheshorterproductlifecyclescausinghigh uncertainty in demands, affecting global markets. From theoperationalpointofview,Informationsharing, coordination,monitoring;anduseofoperationtools arethefourimportanttopicsthataredealtwith by the researchers [8]. Thehighexpectationincustomerservicelevelsof latehasforcedtheorganizationstomanagetheir 25Extensive Analysis and Prediction of Optimal Inventory levels in supply chain management based on Particle Swarm Optimization Algorithm P. Radhakrishnan, Dr. V. M. Prasad and Dr. M. R. Gopalan supplychainsefficiently[5].Theexcessorlackof inventorieshasresultedinthehighsupplychaincost fortheorganizations.Hence,theinventory optimization in supply chain management has emerged as one of the most recent and important issue. Thestockofitems/componentsaccumulatedbyan organizationforprospectiveexploitationisknownas inventory.Theinspectionandmanagementofthe inventoryisfacilitatedbyasetofprocedurescalled inventorysystems.Atvariousstagesalongthe productionanddistributionsupplychain, items/components/productscangetaccumulated resultinginstockpileofinventory[3].Theinventory system is expected to decide the quantity of eachitem tobestoreddependinguponthestatusofthestock levelandasaresult,itemmayhavetobeorderedor manufactured.Theimprovementofinventorycontrolandits managementoveranextendedsupplynetworkis facilitatedbythesystematicapplicationofinventory optimizationtechniquesandtechnologies.Theinventoryoptimizationapproachshoulddwelluponimportant aspects such as the enhancement in customer service,reductionofleadtimesandcostsand managing the fluctuating market demand[3][10][11].Eventhoughthetotalsupplychaincostis minimized,thechiefconcernfortheinventoryand supplychainmanagersistheassessmentofthe accurateamountofinventorytobekeptateachpoint in the supply chain free of surpluses and scarcities. The accurateassessmentofmostdesirableinventoryis crucial,aslackofinventoryleadstolostsales,while overloadofinventorymaywellresultinfutilestorage costs [14]. Afactorymaymanufacture certainnumber of products, each supply chain member may consume a feworalltheproductsandeachproductmaybe manufacturedusingcertainnumberofrawmaterials sourcedfromdifferentsuppliers.Allthese considerationsposeadditionalchallengeinextracting theexactlistofproductsandthestocklevelsthat influence the supply chain cost heavily.Inourpaper,weareproposingamethodologythat considerssomeoftheabovefactorssuchthatthe resultinganalysispavesthewayforminimizingthe supplychaincost.Thesupplychaincostcanbe minimized by maintaining optimal stock levels at each oneofthesupplychainmembers.Suchoptimalstock levelscanbepredictedbyanalyzingthepastrecords. The minimization of supply chain cost will be realistic onlyiftheoptimallevelispredictedwiththe knowledgeoftheleadtimesofthestocks.Hencewe aredevelopingamethodologythatanalyzesthepast recordsandprojectstheemergingexcess/shortage stocklevelsthataretobeconsideredtofinally ascertaintheoptimalstocklevelsthathavetobe maintainedbyeachoneofthesupplychainmembers. WeareusingParticleSwarmOptimizationalgorithm, whichisconsideredtobeoneofthebestoptimization algorithmsinEvolutionarycomputation,forour analysispurposes.Thestocklevelsthatareobtained fromtheanalysisarethestocklevelsthatcontribute moretotheincreaseintotalsupplychaincostandis theessentialinformationrequiredforsupplychain inventory optimization. The organization of rest of the paper is as follows; a briefreviewofrelatedresearchesoninventory optimizationisprovidedinSection2;Section3 introducestheparticleswarmoptimizationalgorithm. TheproposedpredictionanalysisbyParticleSwarm optimizationalgorithmwithrequiredillustrationsand mathematical formulations are covered in section 4 and Section5discussestheimplementationoftheresults. Section 6 summarizes the discussions dealtwith in the paperandsection7isconstitutedbythereferred articles. 2.Related Works Leeetal.[6]introducedasupplychainmodel functioning under periodic review base-stock inventory systemtoassistthemanufacturingmanagersatHPto administermaterialintheirsupplychains.Asearch routinefacilitatedtheachievementoftheinventory levels across supply chain members. Astudyandevaluationsoftheperformance measures employed in supply chain models as well as a frameworkforthebeneficialselectionofperformance measurement systemsformanufacturing supply chains was displayed by Beamon et al. [7].ASystemDynamicssimulationmodelofatypical retail supply chainwas developed by Barlas et al [13]. Thecreationofinventorypoliciesthatsimultaneously enhancetheretailer'srevenueandreducecostsisthe objectiveoftheirsimulation.Thestudyofthe implicationsofdifferentdiversificationstrategieswas also the aim of their research. Buffett et al. [14] proposed a technique to utilize in supply-chainmanagementthatsupportsthedecision-makingprocessforpurchasesofdirectgoods.The projectionsforfuturepricesanddemandarethebasis ofthecreationofRequestforQuotations(RFQs) whichacceptthequotesthatoptimizethelevelof inventory each day, besides minimizing the cost.Theimpactsofneighborhoodstopologieson particleswarmoptimizationforcomplexfunctions werediscussedbyWeiJianet.al[15]. Theyillustrated theconvergencefeaturesaffectedbyconstant parameters on particle swarm optimization. To prevent prematurephenomenonoftheoriginalalgorithm,they 26Journal of Convergence Information Technology Volume 4, Number 3, September 2009 introducedthevelocityandpositiondisturbances.A valvewasalsointroducedandtheselectioncriteria were discussed. An algorithm based on the particle swarm paradigm to address nonlinear constrained optimization problems wasproposedbyA.I.deFreitasVazet.al[16].The relaxationofthedominanceconceptintroducedinthe multi-objectiveoptimizationisthebasisofthe algorithm.Theselectionofthebestparticleposition andthebesteverparticleswarmpositionwas performed using the concept. Pardoeetal.[17]presentedTacTex-06,asupply chainmanagementagentcomprisingofpredictive, optimizing,andadaptivecomponents.TacTex-06 predictsthefutureoftheeconomy,suchastheprices thatwillbeprofferedbycomponentsuppliersandthe degreeofcustomerdemandandsubsequentlyensures maximum profit by strategizing its future actions. Caldeira et al. [18] proposed the accomplishment of Beam-ACOinsupply-chainmanagement.Thesupply andlogisticagentsofasupplychainareoptimized usingtheBeam-ACO.Theoptimizationofthe distributedsystemisfacilitatedbyastandardACO algorithm.Thelocalandglobalresultsofthesupply chain are improved by the application of Beam-ACO. Theinvestigationsontheapplicationofparticle swarmoptimization(PSO)tosolveshortestpath(SP) routingproblemswereperformedbyAmmarW. Mohemmedet.al[12].Aheuristicoperatorthat reducesthepossibilityofloop-formationinthepath construction process for particle representation in PSO was incorporated in a modified priority-based encoding proposed by the authors. Adominancevariationwhichenablesafiner neighborhoodhandlingincriterionspacewas introducedbyGerardDupontet.al[4].Several enhancements to particle swarm optimizer dealing with multi-objective problems were proposed. 3.Particle Swarm Optimization In1995,KennedyandEberhartin,inspiredbythe choreography of a bird flock, first proposed the Particle SwarmOptimization(PSO).Incomparisonwiththe evolutionaryalgorithm,PSO,relativelyrecently devisedpopulation-basedstochasticglobal optimizationalgorithmhasmanysimilaritiesandthe robustperformanceoftheproposedmethodovera varietyofdifficultoptimizationproblemshasbeen proved[24].InaccordancewithPSO,eitherthebest localorthebestglobalindividualaffectsthebehavior ofeachindividualinordertohelpitflythrougha hyperspace [19].Simulationofsimplifiedsocialmodelshasbeen employedtodevelopParticleSwarmOptimization techniques.Thefollowingarethefeaturesofthe method [20]: Theresearchesonswarmssuchasfishschooling and bird flocking are the basis of the method. Thecomputationtimeisshortanditrequireslittle memory as it is based on a simple concept. Nonlinearoptimizationproblemswithcontinuous variablesweretheinitialfocusofthismethod. Nevertheless,problemswithdiscretevariablescanbe treatedbyeasyexpansionofthemethod.Hence,the mixedintegernonlinearoptimizationproblemswith bothcontinuousanddiscretevariablescanbetreated with this method. InadditiontoPSO,wehaveseveralevolutionary paradigmswhichincludeGeneticalgorithms(GA), Geneticprogramming(GP),Evolutionarystrategies (ES)andEvolutionaryprogramming(EP).Biological evolutionissimulatedbytheseapproacheswhichare basedonpopulation[21].GeneticalgorithmandPSO are two widely used types of evolutionary computation among the various types of EC paradigms [22].PSO and evolutionary computation techniques such asGeneticAlgorithms(GA)havemanysimilarities betweenthem.Apopulationofrandomsolutionsis used to initialize the system which updates generations to search for optima. Nevertheless, PSO does not have evolution operators such as crossover and mutation that are available in GA.InPSO,thepotentialsolutions,calledparticles follow the current optimum particles to fly through the problemspace.Everyparticlerepresentsacandidate solution to the optimization problem. The best position visitedbytheparticleandthepositionofthebest particleintheparticlesneighborhoodinfluenceits position. Particleswouldretainpartoftheirpreviousstate usingtheirmemory.Theparticlesstillrememberthe bestpositionstheyeverhadevenasthereareno restrictions for particles toknow the positions of other particlesinthemultidimensionalspaces.Aninitial randomvelocityandtworandomlyweighted influences namely individuality (the tendency to return totheparticlesbestpreviousposition),andsociality (the tendency to move towards the neighborhoods best previous position) form each particles movement [23].Whentheneighborhoodofaparticleistheentire swarm,theglobalbestparticlereferstothebest positionintheneighborhoodandgbestPSOrefersthe resultingalgorithm.Generally,lbestPSOrefersthe algorithmincaseswhensmallerneighborhoodsare used [22].PSOusesindividualandgroupexperiencesto searchtheoptimalsolutions.Nevertheless,previous solutionsmaynotprovidethesolutionofthe optimizationproblem.Theoptimalsolutionis 27Extensive Analysis and Prediction of Optimal Inventory levels in supply chain management based on Particle Swarm Optimization Algorithm P. Radhakrishnan, Dr. V. M. Prasad and Dr. M. R. Gopalan deformedbyadjustingcertainparametersandputting randomvariables.Theabilityoftheparticlesto rememberthebestpositionthattheyhaveseenisan advantage of PSO [23]. 4. The Proposed Prediction Analysis Based OnParticleSwarmOptimization Algorithm. Themethodologyproposedherewillminimizethe totalsupplychaincostbypredictingoptimalstock levelsnotonlybyconsideringthepastrecordsofthe stocklevelsbutalsoconsideringtheleadtimeofthe products to reach each supply chain member from its previousstageaswellastheleadtimeinvolvedin supplyingtherawmaterialstothefactory.Usually, shortageforaparticularstockataparticularmember, excessstocklevelsataparticularmember,time requiredtotransportstockfromonesupplychain membertoanotheri.e.leadtimeofastockina member,timetakentosupplyrawmaterialstothe factorytomanufacturecertainproductsi.e.leadtime ofrawmaterialsusedinfactoryaresomeofthekey factorsthatplayavitalroleindecidingthesupply chaincost.Abetteroptimizationmethodologyshould considerallthesefactors.Inourmethodologywe consideralltheabovementionedkeyfactorsin predictingtheoptimalstocklevels.Also,different prioritiesareassignedtothosefactors.Asperthe priority given, the correspondingfactorswill influence the prediction of optimal stock levels. Hence as per the desiredrequirement,theoptimalstocklevelwillbe maintained by setting or changing the priority levels in the optimization procedure. Supplychainmodelisbroadlydividedintofour stagesinwhichtheoptimizationisgoingtobe performed. The supply chain model is illustrated in the figure 1. Figure 1: Four stage supply chain model Themembersparticipatinginthesupplychain modelarerawmaterialsources} , , , , {3 2 1 mr r r r ,a factoryf, i distributioncenters } , , , , {3 2 1 id d d d D = andthe agents} , , , , {3 2 1 id d d dA A A A A =, idAisthe number of agents for the distribution centerid. Hence, thetotalnumberofagentsinthesupplychainmodel can be arrived using formula28Journal of Convergence Information Technology Volume 4, Number 3, September 2009 ==imd AmA N1(1) where ANis the total number of agents used in the supply chain model. Thefactoryisassumedtobemanufacturing knumberofproducts.Thedatabaseholdsthe informationaboutthestocklevelsofeachproductin each of the supply chain member, lead time of products ineachsupplychainmemberandleadtimeofraw material.For lmembersfromfactorytoend-level-Agents,thereare 1 lleadtimesforaparticular productandthesetimesarecollectedfromthepast records. Similarly, the lead time for raw materials from mr tofisalsotakenfromtheearlierperiodandthus thedatabaseisconstituted.Eachandeverydataset recorded in the database is indexed by a Transportation Identification(TID).For pperiods,theTIDwill be} , , , , {3 2 1 pT T T T .ThisTIDwillbeusedasan index in mining the lead time information. Figure 2: Particle swarm optimization in optimizing the stock levels Now,theparticleSwarmOptimization(PSO)is utilizedtopredicttheoptimalstocklevelstobe maintainedinthefuturetominimizethesupplychain cost.Theproceduresinvolvedindeterminingthe optimal stock levels are illustrated in figure 2As the particle swarm optimization is more suitable forfindingthesolutionfortheoptimizationproblem withgeneralcharacteristicssuchasshorter computationtime,lessmemoryrequirementsetc.,we have utilized particle swarm optimization in finding the optimalstocklevelstobemaintainedineachmember ofthesupplychain.Theflowofmethodologyis discussed below. Theindividualsofthepopulationincluding searchingpoints,velocities, bestp and bestg are initializedrandomlybutwithinthelowerandupper boundsofthestocklevelsforallsupplychain members, which have to be specified initially.Hence the generated searching point individual is ][3 2 1 l k iS S S S P I =, pN i , 3 , 2 , 1 =(2) where, B U k B LP P P. .