运筹学实验报告线性规划问题建模与求解.docx
运筹学一实验报告系（部）专业班级姓名学号实验基地（实验室）实验项目线性规划问题建模与求解实验日期实验成绩_指导教师第一部分：实验目的1）了解线性规划问题建模思路，并能够根据实际问题进行建模。2）学会利用EXCEL与Lingo两种软件进行线性规划问题的求解。习题：某农场I、II、In等耕地的面积分别为IOoa机2、300加小和200万小，计划种植水稻、大豆和玉米，要求三种作物的最低收获量分别为190000依、130000口和350000依。I、II、III等耕地种植三种作物的单产如表所示。若三种作物的售价分别为水稻1.20元4g,大豆1.50元/依，玉米0.80元见g。那么，（1）如何制订种植计划，才能使总产量最大？（2）如何制订种植计划，才能使总产值最大？表不同等级耕地种植不同作物的单产（单位:必/加/）I等耕地II等耕地III等耕地水稻11OOO95009OOO大豆8OOO68006OOO玉米14OOO12OOO10OOO第二部分：实验内容小结（心得及体会）实验过程与结果：利用EXCEL求解（/）如何制订种植计划，才能使总产量最大？一、建立模型设X）表示为i种作物在j等耕地种植的面积（i=l表示水稻，i=2表示大豆，i=3表示玉米；j=l表示I等耕地，j=2表示11等耕地，j=3表示Hl等耕地）。Z表示总产量。maxZ=IlOOOX11+9500Xp+90Xf，+8000X,+6800X+6000X2,+14000X+12000Xv+1OOOOX33'XjXJX产。xi2÷x22÷x32=300x.3+x23+x33=200S.t.11OOOX11+9500X12+9000X,3>=1900008000X,+6800X”+6000X”>=13000014000X31+12000Xv+lOOOOX33>=350000Xij>=0(i=l,2,3；j=l,2,3)K3U：XA=B3S8S2-C3SCS2*D3SDS2-E3SES2+F3SFS2-G3SGS2-H3SHS2*I3SS2÷J3SJS2决策变急约束1Xll xl2 X13IlOOO950090001000OOlO0 11000095 000080000006800006000 0)3132-目标正数140001200010000Q,!右端1000101003001020140000 1200000130000I(XXX)03500初求解弁JSXas目玩|$K$Isl81：最大值(M)。最小值(NC)目忘值:M通过更改可变单元假SB$2:5J$2S最守约电但)SB$2：$J$2>=0$K$4:$K$6<=$L$4:$L$6%DC（八）$K$7:$K$9>=$L$7:$L$9更改9t(D)S三三()*S三L)口便无融兖非比KQQ雌孵方法：(D里纯送性规划yJSlS(P)求*8方法力光滑非法性疑划求策间照挣GRG非线性引孥，力帆胧求第间畸推单纯锄期2划引孳,并为三洸港规把姆司筋弃演化引擎，超勤（三）I5R½)I关闭(Q)0021,11111C21.666671003001572222g½S1109500908068600014000120100L6892222.2221右第10000100110101001030030000101001200200110009500900000000190000190000000806860000130(XX)13000000014000120100006572222222350000DEFGHIxl3x21x22x23x31x32x33=B3*$BS2.C3$C$2*D3-$D$2-E3$E$2-F3$F$2-G3.$G$2-H3*$H$273$I$2J3.SJ$2受函123456策标束京京京束束决目约约约约约约23456789三、实验分析从表中可以看出，水稻只在In等耕地上种植21.1hm2；大豆只在11I等耕地上种植21.7hm2；玉米在I等耕地种植100hm2,II等耕地种植300hm2,III等耕地种植157.2hm2O可以获得最大总产量6892222kg。(2)如何制订种植计划，才能使总产值最大？一、建立模型设X表示为i种作物在j等耕地种植的面积(i=l表示水稻，i=2表示大豆，i=3表示玉米；j=l表示I等耕地，j=2表示II等耕地，j=3表示III等耕地)。z表示总产值。maxz=(11000X+9500X,+9000X,)*1.2+(8000X1+6800X+6000X”)*1.5+(14000X31+l2000Xn+10000X3)*0.8r.÷x21÷x31<=1x12÷x22÷x32<=3XJX23+X33<=200s.t.<IloOOXJ9500X÷9000X.>=190000K4123456789108000X,+6800X,+6000X”>=13000014000X31+12000Xp+10000X33>=350000X>=0(i=l,2,3；j=l,2,3)IJJ、人=B43B2*C4C3C2*D4O3O2E4E3E2F4*F3F2G4G3G2*H4H3H2*143*i2J4J3)2决策变量售价目标语数约束1ABn-12110CDEFGHIxl2xl3x21X22x23Rlx32一1212151515080895009(XX)800068600014(XX)120001001008目标的数100000右端11003001100950090006000008000680060000000000001400012000I(KX)O00=B5SBS2*CSSCS2*D5SDS2*E5SES2÷F5SFS2*G5SGS2*H5SHS2*I5SS2*)5S)S2XllX121.21.2110009500IlOOOO009500009000000800681900130000350000x31×32x330.80.808目标函数1400012000100000ol0I右逑10IlooOl100300xl3x21x22×231.2151.51.5900080006800600000000600000014000120100000190000130000350000S三三6:CD|$K$4IBBi»(&!)oa(N0目标m通3»改可变单元SB$2:$J$2蜀SB$23J$2>=01KS5KS7V=SLS5LS7$«8：$«10>«SLSftiLSIO*w三<便无妁荣交量为非负效的透择茨18方法:Sfl5(2)为光湖反性规划到三E三SGRG非域性不颦.为E性猊我刻S问题理维炎雄在规划引挈.并加洸清规a求解殡斑择演化引宓*j(ii)I碎(三)-IBCDEFGIH_J_JKXllX12xl3x2lx22'x23x3lx32x3358.7530020016250025001.21.2121.51.51.50.80.80.8目标函数Il(X)O950090008000680060001400012000100(X)6830500I0018C0001000I00I00I030000I00I00I200Il(XX)O95009000000000llll2500000800068006000000130000000000140001200010000350000A=B4*B3*B2+C4C3(右迭1003002001900001300350000W逢123456策价标束束束束束束决等目约约约约约约12345678910三、实验分析从表中可以看出，水稻在I等耕地种植58.75hn,11等耕地种植300h,III等耕地种植200hm2；大豆只在In等耕地上种植16.25hm2；玉米只在I等耕地上种植25ho可以获得最大总产值6830500元。利用lingo软件求解(/)如何制订种植计划，才能使总产量最大？文件内容如下：max11000x11+9500x12+9000x13+8000x21+6800x22+6000x23+14000x31+12000x32+10000x33STxll+x21+x31<=100×12+x22+x32<=300xl3+x23+x33<=20011000x11+9500x12+9000x13>=1900008000x21+6800x22+6000x23>=13000014000x31+12000x32+10000x33>=350000然后进行求解运行，可以得如下结果：Globaloptimalsolutionfound.6892222.0.0000005Objectivevalue:Infeasibilities:Totalsolveriterations:VariableValueReducedCostXll0.0000001777.778X120.0000001444.444X1321.111110.000000X210.000000666.6667X
