Research of Resources Leveling based on the latest finished Time

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1、ResearchofResourcesLevelingbasedonthelatestfinishedTime-Scaled Network Diagram LIUjian,LUOyong,TONGdai,LIhuiSchoolofTransportationandAutomotiveEngineering,Xihuauniversity,China.Box610039,Tel:086-028-81276516;email:tranjian@tom.comAbstract:Anewmodeltoreso

2、lvetheproblemsinhighwayresourceslevelingunderfixedtimeispresented.Themodelbasedonthelatestfinishedtime-scaled network diagram presentsthehighestprioritywiththechangevalueofminimumvariancebetweenresourcedemandbeforeandaftermovingwhenanodehavemanynon-key-w

3、ork-process.Anexampledemonstratesthemodelcandiminishthequantityofoptimizationwork.KeyWords:networkplanning;resourcesleveling;optimization;latestfinishedtime.1.IntroductionThecommonlyusedoptimizedmethodsforresourcelevelingandfixedcompletiontimeareminimumv

4、arianceandExtremevalueandsooninnetworkplanning[1-5].Thereducedvariancemethodbasedontheearliesttime-scaled network diagramisoneofthem.ThePaper[6]presentsConstraintConditionofminimumvarianceforitsimperfect,theoptimizationmethodofpaper[7]isabouttheright-mov

5、ingdistance.ThesemethodscouldoptimizesomeproblemsofresourcelevelingindifferentEnvironment,butitmaynotgettheoptimalsolutionbecausetheyarebasedontheearliesttime-scaled network diagram.Forshortcomingofabovemethods,thenewmethodbasedonthelatestfinishedtime-sc

6、aled network diagramisdeveloped,andconfirmedtobeefficiencybyanexample.在网络计划优化中，对工期固定下的资源均衡问题，常用优化方法有基于资源强度图的削峰填谷法、最小方差法等[1-5]。“缩方差法”就是其中的一种，是基于最早时标网络图的优化方法。文献[6]针对“缩方差法”的不完善，对其进行优化，并提出使用“缩方差法”的限制条件，以达到最优的效果。文献[7]运用后移差法为优化方法。这些方法在不同环境中的应用都能对资源均衡问题进行一定程度上的

7、优化，但是这些方法都是建立在节点最早实现时间时标网络基础上的，有时并不一定能够得到最优解。本文尝试在原有的“缩方差法”基础上用逆向的思维对其进行改进，使用按节点最迟时间绘制的时标网络对工期固定下的资源均衡问题进行优化，并提出利用最小方差变化值作为同一节点有多个非关键工序进行的优先调整原则。2逆向缩方差法资源均衡优化模型分析2modelanalysis2.1优化模型2.1OptimizationModel2.1.1节点只有一个非关键工序可以调整2.1.1thenodewithanon-key-work-p

8、rocesses-unitwhichmaybeadjustedThedegreeofimbalancemaybemeasuredbythevarianceorleveldifferencewhichistheproblemsofobjectoptimizationindifferentpointsofview,sotheirsolutionisdifferent.Themodelofthispaperisbasedontheminimumv