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快递公司送货策略优化模型摘要本文讨论了快递公司送货路线的优化设计问题,即在给定送货地点和给定设计规范的条件下,综合考虑最大载重范围、以及各快递员工作时限,建立了人员分配和路径优化的数学模型。在这个题目中两点之间的路线权值赋为这两点横纵坐标之和,如此便可以用MATLAB求出任意两配送点间的距离。针对问题一,我们以路程最短为目标,使公司获得最大效益并且快递员工作时间和每次出发的快件量越接近临界值越好,使其利用率最高。我们用以下方法即每一个行程的第一个送货点是距离总部最近的未服务的送货点,可得到一组运行路线,总的运行公里数,以及总费用。通过用TSP模型对每条路线的最短路处理,在之前的路线上进行修正,得到优化模型结果为最短时间为282699H,最短行程为506KM,需要6个业务员。针对问题二,在问题一的条件下,以给业务员的酬金最少为目标,结合业务员的安排和路线的选择,结果显示最优共安排了8业务员,跑9路线,其中1号业务员跑的路线为0138130和0247140,2号业务员跑的路线为0652018300,3号业务员的路线为0912190,4号业务员的路线为0101132230,5号业务员的路线为0161724280,6号业务员的路线为022290,7号业务员的路线为015270,8号业务员的路线为025260,时间为307668H,用为138307元针对问题三,因为所需的总时间不变,而每个业务员的工作时间增加为8小时,所以对其工作量重新安排,可将业务员减少到4人。关键字快递公司送货欧拉回路模型01规划TSP模型1、问题重述目前,快递行业正蓬勃发展,为我们的生活带来更多方便。一般地,所有快件到达某地后,先集中存放在总部,然后由业务员分别进行派送;对于快递公司,为了保证快件能够在指定的时间内送达目的地,必须有足够的业务员进行送货,但是,太多的业务员意味着更多的派送费用。假定所有快件在早上7点钟到达,早上9点钟开始派送,要求于当天17点之前必须派送完毕,每个业务员每天平均工作时间不超过6小时,在每个送货点停留的时间为10分钟,途中速度为25KM/H,每次出发最多能带25千克的重量。为了计算方便,我们将快件一律用重量来衡量,平均每天收到总重量为1845千克,公司总部位于坐标原点处(如图2),每个送货点的位置和快件重量见下表,并且假设送货运行路线均为平行于坐标轴的折线。(1)请你运用有关数学建模的知识,给该公司提供一个合理的送货策略(即需要多少业务员,每个业务员的运行线路,以及总的运行公里数);(2)如果业务员携带快件时的速度是20KM/H,获得酬金3元/KMKG;而不携带快件时的速度是30KM/H,酬金2元/KM,请为公司设计一个费用最省的策略;(3)如果可以延长业务员的工作时间到8小时,公司的送货策略将有何变化坐标KM坐标KM送货点快件量TXY送货点快件量TXY1832163521628215175861836541875111745547197815126308153419954531132622257727922682108239623242799141022476151910651402596151411411732610201712127146271221131358129286024201438101229812516204671430422818点的分布如下图510152025X5101520Y根据题意,得到运输情况及业务员工作信息如表1所示表1运输情况及业务员工作信息运输车载重量25KG平均每天收到总重量1845KG运输车途中平均速度25KM/H每个业务员每天平均工作时间X3543Y24711FORI14FORJ14DI,JABSXIXJABSYIYJENDENDDD0469404964059950MODELSETSCOUNTRY/1,2,3,4/JLSTEP/1,2,3,4/LINESTEP,COUNTRYXLINKSCOUNTRY,COUNTRYCENDSETSDATAJL591114C0469404964059950ENDDATAFORLINEBINXM1SIZESTEPFORCOUNTRYISUMSTEPNXN,I1FORSTEPNSUMCOUNTRYIXN,I1L1SUMCOUNTRYIX1,IXM1,IJLILXSUMSTEPN|NLTM1SUMLINKSI,JCI,JXN,IXN1,JMINL1LXENDLOCALOPTIMALSOLUTIONFOUNDOBJECTIVEVALUE3200000EXTENDEDSOLVERSTEPS13TOTALSOLVERITERATIONS223VARIABLEVALUEREDUCEDCOSTM140000000000000L119000000000000LX13000000000000JL150000000000000JL290000000000000JL311000000000000JL414000000000000X1,100000000000000X1,2000000002000000E05X1,300000000000000X1,410000000000000X2,100000005999994X2,200000000000000X2,310000001999996X2,400000005999986X3,1000000006000000E05X3,210000000000000X3,300000000000000X3,4000000002000000E05X4,110000000000000X4,200000001999998X4,300000005999992X4,400000006000002C1,100000000000000C1,240000000000000C1,360000000000000C1,490000000000000C2,140000000000000C2,200000000000000C2,340000000000000C2,490000000000000C3,160000000000000C3,240000000000000C3,300000000000000C3,450000000000000C4,190000000000000C4,290000000000000C4,350000000000000C4,400000000000000ROWSLACKORSURPLUSDUALPRICE1000000000000002000000060000013000000080000014000000060000035000000013999996000000050000027000000009999980800000000000000900000003000001103200000100000011000000010000001200000001000000第二条26713CLEARX10712Y5899FORI14FORJ14DI,JABSXIXJABSYIYJENDENDDD0410154081310805151350SETSCOUNTRY/1,2,3,4/JLSTEP/1,2,3,4/LINESTEP,COUNTRYXLINKSCOUNTRY,COUNTRYCENDSETSDATAJL681621C0410154081310805151350ENDDATAFORLINEBINXM1SIZESTEPFORCOUNTRYISUMSTEPNXN,I1FORSTEPNSUMCOUNTRYIXN,I1L1SUMCOUNTRYIX1,IXM1,IJLILXSUMSTEPN|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第三条981610CLEARX1091414Y2660FORI14FORJ14DI,JABSXIXJABSYIYJENDENDDD058650511850661160MODELSETSCOUNTRY/1,2,3,4/JLSTEP/1,2,3,4/LINESTEP,COUNTRYXLINKSCOUNTRY,COUNTRYCENDSETSDATAJL12152014C058650511850661160ENDDATAFORLINEBINXM1SIZESTEPFORCOUNTRYISUMSTEPNXN,I1FORSTEPNSUMCOUNTRYIXN,I1L1SUMCOUNTRYIX1,IXM1,IJLILXSUMSTEPN|NLTM1SUMLINKSI,JCI,JXN,IXN1,JMINL1LXENDLOCALOPTIMALSOLUTIONFOUNDOBJECTIVEVALUE4200000EXTENDEDSOLVERSTEPS6TOTALSOLVERITERATIONS270VARIABLEVALUEREDUCEDCOSTM140000000000000L126000000000000LX16000000000000JL112000000000000JL215000000000000JL320000000000000JL414000000000000X1,110000002000000X1,200000000000000X1,300000009999996X1,400000009999994X2,100000000000000X2,210000001999992X2,300000000000000X2,400000004000000X3,100000000000000X3,200000000000000X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