2013年小美赛c题特等奖1162队B题

第二届“认证杯”数学中国数学建模国际赛承诺书我们仔细阅读了第二届“认证杯”数学中国数学建模国际赛的竞赛规则。我们完全明白，在竞赛开始后参赛队员不能以任何方式（包括电话、电子邮件、网上咨询等）与队外的任何人（包括指导教师）研究、讨论与赛题有关的问题。我们知道，抄袭别人的成果是违反竞赛规则的,如果引用别人的成果或其他公开的资料（包括网上查到的资料），必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。我们郑重承诺，严格遵守竞赛规则，以保证竞赛的公正、公平性。如有违反竞赛规则的行为，我们将受到严肃处理。我们允许数学中国网站()公布论文，以供网友之间学习交流，数学中国网站以非商业目的的论文交流不需要提前取得我们的同意。我们的参赛队号为：1162我们选择的题目是：PROBLEMB：HermitCrabsEvolveEmploymentPatternofHuman参赛队员(签名)：队员1：万方平队员2：姜冰心队员3：邢思雨参赛队教练员(签名)：第二届“认证杯”数学中国数学建模国际赛编号专用页参赛队伍的参赛队号：（请各个参赛队提前填写好）：1162竞赛统一编号（由竞赛组委会送至评委团前编号）：竞赛评阅编号（由竞赛评委团评阅前进行编号）：DiscussionoftheFeasibilityoftheVacancyChainDecember9,2013SummaryRousseauoncesaidManwasbornfree,andheiseverywhereinchains.However,itisnottryingtospreadapessimisticworldoutlook.Instead,itisthroughinteractionamongpeoplethatoursocietycanmakeprogress.Justlikehermitcrabswouldgrouptogethertoexchangeshellssothateveryindividualcangetalargersizeofhome.Ourhumansocietyalsoexistssimilarphenomenonwhichiscalledvacancychain.However,allo-catingshellsamongisrelativelyaeasyjob,howtoexchangejobamongpeopleisaratherdifficultproblem.Inordertoaddressproblemsabove.Weconcludethreesub-problemsanditssolutioninourpaper:1)Figureouttheconditionsneedtomeetsothatvacancychaincanfunctionasatooltooptimizeeveryindividualcanbenefit.2)Buildamodeltoevaluateonescompetenciesandproposeanalgorithmassocialstrategiestoexchangejobsinvacancychainssothateveryonebenefits.3)Developainequalitytoanswerhowmanyjobappli-cantsdoneedtosatisfybothemployersandemployeesandrunourmodeltopredictthechangeofHRexpendsforsomeenterprisecustomerswithinthenext5years.Inthefirstsub-problem,wediscussthedifferenteffectsofdifferen-torganizationalhierarchiesonvacancychains.Thenwesuccessfullyfig-ureoutthathierarchicalorganizationalformswithlessmiddlemanagersthanstraightpyramisaremostlikelytoberegulatedbyvacancychain-s.Andfortunately,mostenterprises’organizationalformsaresimilartoit.Thatistosay,vacancychaincanbeapplicabletomostcases.Next,insecondsub-problemsweproposealinearequationasaevaluatingfunctionandgetaoverallscoreforeveryindividualwhichrepresentsone’scom-petencies.Then,basedontheoverallscores,weuseagreedyalgorithmtoexchangejobsamongpeopleinvacancychain.Peoplesqualitieswillbecompatiblewiththejobrequirement.Inthiscaseeveryindividualwillgetthemostappropriatejob.Finally,inthethirdsub-problemsincevacancychainalsohasitscostlikereplacementcostandtrainingcost.Wewillnotallowthetotalcostoutweighitsbenefits.Sowewillproposeainequationthatneedtomeetsothatthecostwillnotoutweighthebenefits.Thatisto1Team#1162Page2of19say,wewillfigureouthowmanyjobapplicantsdoneedtosatisfybothem-ployeesandemployersatcertainsituations.Finally,wewillrunourmodeltoshowthechangeofHRexpendsforsomeenterprisescustomerswithinthenextfiveyears.Inthewholemodelingprocess,wegivefullconsiderationtovalidity,feasibilityandcost-efficiencyofourmodel.Team#1162Page3of19Contents1Introduction42Discussionofthefeasibilityofthevacancychain42.1Introduction...............................42.2Background...............................52.3Theinfluenceoforganizationalhierarchiesonvacancychain...52.3.1Modeloforganizationform..................52.3.2Analysis.............................62.3.3Conclusions...........................73AVacancychainmodel83.1Introduction...............................83.2Assumption...............................83.3Procedure................................83.3.1Analysis.............................83.3.2ModelSolution.........................93.3.3Analgorithmtoallocatejobsinvacancychain.......103.4Conclusions...............................114Practiceofmodel124.1Introduction...............................124.2Limitationofthenumberofpeopleinvacancychain........124.3ModelTesting..............................134.4Conclusions...............................165StrengthsandWeaknesses165.1Strengths.................................165.2Weaknesses...............................17References176Advertisement17Team#1162Page4of191IntroductionAsweknow,theconceptoftheterm-vacancychainisderivedfromthesci-entificobservationfromakindofphenomenainhermitcrabpopulation.Asthehermitcrabgrowsinsize,ithastofindalargershellandabandontheprevi-ousone.Severalhermitcrabspecies,bothterrestrialandmarine,usevacancychainstofindnewshells:whenanew,biggershellbecomesavailable,hermitcrabsgatherarounditandformakindofqueuefromlargesttosmallest.Whenthelargestcrabmovesintothenewshell,thesecondbiggestcrabmovesintothenewlyvacatedshell,therebymakingitspreviousshellavailabletothethirdcrab,andsoon.Sincethisbiologicaldiscovery,moremeaningshavebeenaddedtothetermofvacancychain.Nowadays,avacancychainisasocialstructurethroughwhichresourcesaredistributedtoconsumers.Inavacancychain,anewresourceunitthatarrivesintoapopulationistakenbythefirstindividualinline,whothenleaveshisorheroldunitbehind,thisoldunitistakenbyasecondindividual,leavinghisorheroldunitbehind,andsoforth.Usuallywhenavacancyoccursthebulkofthepeoplewhofillthepositionscomefromtheinsidetheinternallabormarketratherthanhiringsomeonenew.Theindividualsbeingmovedandorpromotedtoanewjoborpositionoftengainahigher