订货、运货优化LINGO程序

模型解释：a、当n=12时没有满足所有约束条件的方程的解，再给n逐步加1再次运行程序，直到n=16，程序才可以运行出满足所有约束条件的解。（运行LINGO程序结果见附2）b、 数据处理：由于货物件数取整数，所以为了满足供货要求，对订货数量按进1法取整。c、 结果表示：（1）订货方案：（1.1）从每个工厂分别订每种货物的数量。一年共取货16次，每次从A1厂订货物M1数量工工A1BjCkM1=113件……j=1k=1列表如下：数量M1M2M3M4M5M6M7M8M9M10A1113--1784719763--1257875A212569--63--8412577--75A3--1575094--6372--15794（1.2）各种货物总量:数量M1M2M3M4M5M6M7M8M9M10MQ2382252282041972091972022342442）从工厂到仓库运货方案：（2.1）从每个工厂到各个仓库运输的10种货物总数量。（例如从A1工厂送到B2仓库中的货物为A1-B2：563件）数量B1B2B3B4B5A1--63200240A200--6170A3006840--（2.2）各个仓库中所存不同货物数量。（例如：B2仓库中存货物B2-M1为30件）数量M1M2M3M4M5M6M7M8M9M10B10000000000B217222500020900028B3670421651970002160B400187000197019217B500039000202003）从仓库到个分店的运货方案：（3.1）从每个仓库到各个分店的送货量。（例如：从B3仓库送到C1店的货物数量B3-C1为106件）数量C1C2C3C4C5C6C7C8B100000000B2--1680--03040162B30--279300--0--106B4015100153--314--B520600000035（3.2）每个分店所存各类货物的数量。（例如：C1店存货物Cl-M1为4件）数量M1M2M3M4M5M6M7M8M9M10C141950713382551038C2650327532251375032C31032255038--505025--C419251325105032109425C525--1071319--25650C6321363--251063631325C75075610663632763C89413323263610133213按上述分配方案可得：一次订货后的总花费为p=959543.179+10000=969543.179元。模型检验、结果分析及改进：（1） 模型检验：将上述优化方案各个数值代入目标函数中计算解得P=970790，比求解结果大，正是由于用了进一法确定货物数量。通过表中的分配数据可看出此程序与实际情况很吻合，不失为一个好的数学模型。（2） 结果分析：根据（附2）中LOINGO程序的运行结果分析报告中的数值，从工厂订货方案的缩减成本系数值取零，为最优解；而从工厂到仓库的运货方案及从仓库到各个分店的运货方案中并不是所有的缩减成本系数值为0，所以此模型满足了货物需求量花费最少的优化配置，而并未同时满足运输货物花费最少的最优化，在LINGO求解报告中可看出运输费上还有很大的优化空间，此无疑为模型明显的缺点。究其原因是我们在模型假设中假设订货数量=需求数量，为满足此等式条件，限制运货方案的不等式条件就需作出让步，而我们当初作此假设，目的是为了在下次订货时达到零库存，从而充分利用仓库容量，而且充分利用最大流动资金上限。（3） 模型改进：通过“结果分析”中指出的问题，对已建立模型目标函数的约束条件上进行改进，即将假设订货数量=需求数量改为“>=”剩余条件，通过计算机程序达到解决方案的优化。模型应用及推广：（1） 应用：优化问题现已成为各个领域中最常遇到的一类问题，本题模型涉及到订货方案、两次运货方案的多重优化，环环相扣，若不应用一定的数学模型去优化设计，很难找到最节约的实施方案，从而也决定了，此模型在生产、生活中的重要性，尤其是今年来日新月异的物流行业更是广泛用之。本模型为求解方便，假设了每个订货周期各个分店的销售量一样，这很不合实际。因此在实际中应用时，要考虑到销售淡季与旺季的差别，以此平均值为参考，结合销售分店的销售业绩做合理的改变，使模型能够真正用来解决实际问题。（2） 推广：此模型是再不允许缺货、订货资金流动上限受限制的情况下建立的，如若允许缺货或资金流动不受限制的情况下，可抓住主要影响因素，作出合理的假设，对模型的目标函数或约束条件进行修改，从而立即得到新的模型。（附2）LINGO程序:!目标函数为每次订货的总花费PT（1为订货费）万元；min=100*m1+210*m3+250*m4+290*m5+300*m6+430*m8+450*m9+500*m10+90*mm1+180*mm2+240*mm4+305*mm6+380*mm7+435*mm8+490*mm10+170*mmm2+210*mmm3+245*mmm4+285*mmm6+400*mmm7+450*mmm9+480*mmm10 !订货成本费pl；+10*b2+14*b3+17*b4+13*b5+10*bb1+8*bb2+9*bb4+16*bb5+15*bbb1+16*bbb2+9*bbb3+15*bbb4 !从工厂到仓库的运输费p2;+40*mq1+70*mq2+90*mq3+100*mq4+120*mq5+120*mq6+150*mq7+160*mq8+180*mq9+200*mq10 !库存费p3;+3*c11+2*c12+3*c13+6*c14+3*c15+c16+4*c17+5*c18+3*c22+3*c23+5*c25+2*c26+5*c27+3*c28+5*c31+2*c33+5*c34+5*c36+4*c38+4*c41+c42+4*c43+4*c44+2*c45+2*c47+2*c51+2*c52+5*c53+3*c54+5*c55+2*c56+5*c57+2*c58;!从仓库到各个分店的运输费；!一次订货费资金限制；100*m1+210*m3+250*m4+290*m5+300*m6+430*m8+450*m9+500*m10+90*mm1+180*mm2+240*mm4+305*mm6+380*mm7+435*mm8+490*mm10+170*mmm2+210*mmm3+245*mmm4+285*mmm6+400*mmm7+450*mmm9+480*mmm10+10*b2+14*b3+17*b4+13*b5+10*bb1+8*bb2+9*bb4+16*bb5+15*bbb1+16*bbb2+9*bbb3+15*bbb4+40*mq1+70*mq2+90*mq3+100*mq4+120*mq5+120*mq6+150*mq7+160*mq8+180*mq9+200*mq10+3*c11+2*c12+3*c13+6*c14+3*c15+c16+4*c17+5*c18+3*c22+3*c23+5*c25+2*c26+5*c27+3*c28+5*c31+2*c33+5*c34+5*c36+4*c38+4*c41+c42+4*c43+4*c44+2*c45+2*c47+2*c51+2*c52+5*c53+3*c54+5*c55+2*c56+5*c57+2*c58<=990000;!订货次数去定n=16;n=16;!各个工厂的生产量限制；n*m1<=2000;n*m3<=3000;n*m4<=1000;n*m5<=3200;n*m6<=1000;n*m8<=2000;n*m9<=1500;n*m10<=1500;n*mm1<=2000;n*mm2<=1300;n*mm4<=1000;n*mm6<=1500;n*mm7<=2000;n*mm8<=1500;n*mm10<=1200;n*mmm2<=2500;n*mmm3<=800;n*mmm4<=1500;n*mmm6<=1000;n*mmm7<=1400;n*mmm9<=2500;n*mmm10<=1500;！每物资需求量限制；m1+mm1=3800/n;mm2+mmm2=3600/n;m3+mmm3=3640/n;m4+mm4+mmm4=3250/n;m5=3140/n;m6+mm6+mmm6=3340/n;mm7+mmm7=3140/n;m8+mm8=3230/n;m9+mmm9=3740/n;m10+mm10+mmm10=3900/n;！等量限制：从各个厂订货总量等于各个厂存入五个仓库中的数量；m1+m3+m4+m5+m6+m8+m9+m10=b2+b3+b4+b5;mm1+mm2+mm4+mm6+mm7+mm8+mm10=bb1+bb2+bb4+bb5;mmm2+mmm3+mmm4+mmm6+mmm7+mmm9+mmm10=bbb1+bbb2+bbb3+bbb4;！等量限制：从各个工厂订的同种货物数量之和等于所定此种货物的总数量;m1+mm1=mq1;mm2+mmm2=mq2;m3+mmm3=mq3;m4+mm4+mmm4=mq4;m5=mq5;m6+mm6+mmm6=mq6;mm7+mmm7=mq7;m8+mm8=mq8;m9+mmm9=mq9;m10+mm10+mmm10=mq10;！容量限制；1.5*b1m1+b1m2+1.5*b1m3+2*b1m4+1.5*b1m5+0.5*b1m6+1.5*b1m7+2*b1m8+b1m9+0.5*b1m10<=800;1.5*b2m1+b2m2+1.5*b2m3+2*b2m4+1.5*b2m5+0.5*b2m6+1.5*b2m7+2*b2m8+b2m9+0.5*b2m10<=600;1.5*b3m1+b3m2+1.5*b3m3+2*b3m4+1.5*b3m5+0.5*b3m6+1.5*b3m7+2*b3m8+b3m9+0.5*b3m10<=1000;1.5*b4m1+b4m2+1.5*b4m3+2*b4m4+1.5*b4m5+0.5*b4m6+1.5*b4m7+2*b4m8+b4m9+0.5*b4m10<=700;1.5*b5m1+b5m2+1.5*b5m3+2*b5m4+1.5*b5m5+0.5*b5m6+1.5*b5m7+2*b5m8+b5m9+0.5*b5m10<=800;！等量限制：各个仓库中的各类货物之和等于从三个工厂存入该仓库的货物量；b1m1+b1m2+b1m3+b1m4+b1m5+b1m6+b1m7+b1m8+b1m9+b1m10=bb1+bbb1;b2m1+b2m2+b2m3+b2m4+b2m5+b2m6+b2m7+b2m8+b2m9+b2m10=b2+bb2+bbb2;b3m1+b3m2+b3m3+b3m4+b3m5+b3m6+b3m7+b3m8+b3m9+b3m10=b3+bbb3;b4m1+b4m2+b4m3+b4m4+b4m5+b4m6+b4m7+b4m8+b4m9+b4m10=b4+bb4+bbb4;b5m1+b5m2+b5m3+b5m4+b5m5+b5m6+b5m7+b5m8+b5m9+b5m10=b5+bb5;！等量限制：不同仓库的同种货物之和等于该种货物总量；b1m1+b2m1+b3m1+b4m1+b5m1=mq1;b1m2+b2m2+b3m2+b4m2+b5m2=mq2;b1m3+b2m3+b3m3+b4m3+b5m3=mq3;b1m4+b2m4+b3m4+b4m4+b5m4=mq4;b1m5+b2m5+b3m5+b4m5+b5m5=mq5;b1m6+b2m6+b3m6+b4m6+b5m6=mq6;b1m7+b2m7+b3m7+b4m7+b5m7=mq7;b1m8+b2m8+b3m8+b4m8+b5m8=mq8;b1m9+b2m9+b3m9+b4m9+b5m9=mq9;b1m10+b2m10+b3m10+b4m10+b5m10=mq10;！等量限制：各个仓库的库存数量等于从该仓库向各个分店送货数量之和；bb1+bbb1=c11+c12+c13+c14+c15+c16+c17+c18;b2+bb2+bbb2=c22+c23+c25+c26+c27+c28;b3+bbb3=c31+c33+c34+c36+c38;b4+bb4+bbb4=c41+c42+c43+c44+c45+c47;b5+bb5=c51+c52+c53+c54+c55+c56+c57+c58;！等量限制：各个分店所需亚要的同种货物之和等于该货物总量；c1m1+c2m1+c3m1+c4m1+c5m1+c6m1+c7m1+c8m1=mq1;c1m2+c2m2+c3m2+c4m2+c6m2+c7m2+c8m2=mq2;c1m3+c2m3+c3m3+c4m3+c5m3+c6m3+c7m3+c8m3=mq3;c1m4+c2m4+c3m4+c4m4+c5m4+c7m4+c8m4=mq4;c1m5+c2m5+c3m5+c4m5+c5m5+c6m5+c7m5+c8m5=mq5;c1m6+c2m6+c4m6+c5m6+c6m6+c7m6+c8m6=mq6;c1m7+c2m7+c3m7+c4m7+c6m7+c7m7+c8m7=mq7;c1m8+c2m8+c3m8+c4m8+c5m8+c6m8+c7m8+c8m8=mq8;c1m9+c2m9+c3m9+c4m9+c5m9+c6m9+c7m9+c8m9=mq9;c1m10+c2m10+c4m10+c5m10+c6m10+c7m10+c8m10=mq10;！等量限制：每个分店对不同货物需求总量等于从各个仓库中运输到该店的货物数量之和;c1m1+c1m2+c1m3+c1m4+c1m5+c1m6+c1m7+c1m8+c1m9+c1m10=c11+c31+c41+c51;c2m1+c2m2+c2m3+c2m4+c2m5+c2m6+c2m7+c2m8+c2m9+c2m10=c12+c22+c42+c52;c3m1+c3m2+c3m3+c3m4+c3m5+c3m7+c3m8+c3m9=c13+c23+c33+c43+c53;c4m1+c4m2+c4m3+c4m4+c4m5+c4m6+c4m7+c4m8+c4m9+c4m10=c14+c34+c44+c54;c5m1+c5m3+c5m4+c5m5+c5m6+c5m8+c5m9+c5m10=c15+c25+c45+c55;c6m1+c6m2+c6m3+c6m5+c6m6+c6m7+c6m8+c6m9+c6m10=c16+c26+c36+c56;c7m1+c7m2+c7m3+c7m4+c7m5+c7m6+c7m7+c7m8+c7m9+c7m10=c17+c27+c47+c57;c8m1+c8m2+c8m3+c8m4+c8m5+c8m6+c8m7+c8m8+c8m9+c8m10=c18+c28+c38+c58;！需求量限制c1m1=60/n;c1m2=300/n;c1m3=800/n;c1m4=100/n;c1m5=200/n;c1m6=600/n;c1m7=400/n;c1m8=80/n;c1m9=150/n;c1m10=600/n;c2m1=90/n;c2m2=800/n;c2m3=500/n;c2m4=1200/n;c2m5=500/n;c2m6=400/n;c2m7=200/n;c2m8=100/n;c2m9=800/n;c2m10=500/n;c3m1=150/n;c3m2=500/n;c3m3=400/n;c3m4=800/n;c3m5=600/n;c3m7=800/n;c3m8=800/n;c3m9=400/n;c4m1=300/n;c4m2=400/n;c4m3=200/n;c4m4=400/n;c4m5=150/n;c4m6=800/n;c4m7=500/n;c4m8=150/n;c4m9=1500/n;c4m10=400/n;c5m1=400/n;c5m3=150/n;c5m4=100/n;c5m5=200/n;c5m6=300/n;c5m8=400/n;c5m9=90/n;

c5m10=800/n;c6m1=500/n;c6m2=200/n;c6m3=1000/n;c6m5=400/n;c6m6=150/n;c6m7=1000/n;c6m8=1000/n;c6m9=200/n;c6m10=400/n;c7m1=800/n;c7m2=1200/n;c7m3=90/n;c7m4=150/n;c7m5=90/n;c7m6=1000/n;c7m7=90/n;c7m8=500/n;c7m9=100/n;c7m10=1000/n;c8m1=1500/n;c8m2=200/n;c8m3=500/n;c8m4=500/n;c8m5=1000/n;c8m6=90/n;c8m7=150/n;c8m8=200/n;c8m9=500/n;c8m10=200/n;end运行结果：Globaloptimalsolutionfound.959543.179Objectivevalue:959543.179Totalsolveriterations:VariableValueReducedCostM1112.50000.000000M3177.50000.000000M446.875000.000000M5196.25000.000000M662.500000.000000M8125.00000.000000

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