運(yùn)籌學(xué)實(shí)驗(yàn)報告-lingo軟件地使用-習(xí)題代碼

1、WORD格式運(yùn) 籌 學(xué)實(shí)驗(yàn)報告*：學(xué)號：班級：專業(yè)資料整理WORD格式相關(guān)問題說明：一、 實(shí)驗(yàn)性質(zhì)和教學(xué)目的本實(shí)驗(yàn)是運(yùn)籌學(xué)課內(nèi)安排的上機(jī)操作實(shí)驗(yàn)。目的在于了解、熟悉計算機(jī)Lingo 軟件在運(yùn)籌學(xué)模型求解中的作用，激發(fā)學(xué)習(xí)興趣，提高學(xué)習(xí)效果，增強(qiáng)自身的動手能力，提高實(shí)際應(yīng)用能力。二、 實(shí)驗(yàn)根本要求要求學(xué)生：1. 實(shí)驗(yàn)前認(rèn)真做好理論準(zhǔn)備，仔細(xì)閱讀實(shí)驗(yàn)指導(dǎo)書；2. 遵從教師指導(dǎo)，認(rèn)真完成實(shí)驗(yàn)任務(wù)，按時按質(zhì)提交實(shí)驗(yàn)報告。三、 主要參考資料1 LINGO軟件2. LINGO8.0及其在環(huán)境系統(tǒng)優(yōu)化中的應(yīng)用，*大學(xué)，20053. 優(yōu)化建模與 LINDO/LINGO軟件，清華大學(xué)， 20054運(yùn)籌學(xué)編寫組主

2、編，運(yùn)籌學(xué)修訂版，清華大學(xué)，19905藍(lán)伯雄主編，管理數(shù)學(xué)下運(yùn)籌學(xué)，清華大學(xué)，19976胡運(yùn)權(quán)主編，運(yùn)籌學(xué)習(xí)題集修訂版，清華大學(xué)，19957胡運(yùn)權(quán)主編，運(yùn)籌學(xué)教程第二版，清華大學(xué)，2003專業(yè)資料整理WORD格式實(shí)驗(yàn)內(nèi)容1、線性規(guī)劃問題：max z8 x16x2專業(yè)資料整理WORD格式s.t.9x18 x2127 x111 x2249x111x213x1 , x20專業(yè)資料整理WORD格式(1) 給出原始代碼； (2) 計算結(jié)果 (包括靈敏度分析，求解結(jié)果粘貼 )；(3) 答復(fù)以下問題 (手寫 )：a) 最優(yōu)解及最優(yōu)目標(biāo)函數(shù)值是多少；b) 資源的對偶價格各為多少，并說明對偶價格的含義；c) 為

3、了使目標(biāo)函數(shù)值增加最多， 讓你選擇一個約束條件，將它的常數(shù)項(xiàng)增加一個單位，你將選擇哪一個約束條件？這時目標(biāo)函數(shù)值將是多少？d) 對 x2的目標(biāo)函數(shù)系數(shù)進(jìn)展靈敏度分析；e) 對第 2 個約束的約束右端項(xiàng)進(jìn)展靈敏度分析；f ) 結(jié)合此題的結(jié)果解釋“ Reduced Cost的含義。對偶價格就是說約束方程右端變量增加1 對目標(biāo)函數(shù)值的影響答案： 1代碼max =8*x1+6*x2;9*x1+8*x2<=12;7*x1+11*x2<=24;9*x1+11*x2<=13;x1>=0;x2>=0; 2計算結(jié)果Global optimal solution found.Obje

4、ctive value:10.66667Total solver iterations:2VariableValueReduced CostX11.3333330.000000X20.0000001.111111RowSlack or SurplusDual Price110.666671.00000020.0000000.8888889314.666670.00000041.0000000.00000051.3333330.00000060.0000000.000000專業(yè)資料整理WORD格式 1專業(yè)資料整理WORD格式Ranges in which the basis is unchang

5、ed:Objective Coefficient RangesCurrentAllowableAllowableVariableCoefficientIncreaseDecreaseX18.000000INFINITY1.250000X26.0000001.111111INFINITYRighthand Side RangesRowCurrentAllowableAllowableRHSIncreaseDecrease212.000001.00000012.00000324.00000INFINITY14.66667413.00000INFINITY1.00000050.01.333333IN

6、FINITY60.00.0INFINITY(3)a)b)c)d)e)f)2、運(yùn)輸問題： 6 個發(fā)點(diǎn) 8 個收點(diǎn)的最小費(fèi)用運(yùn)輸問題。產(chǎn)銷量及單位運(yùn)價如下表。銷地cijBBBBBBBB產(chǎn)12345678量產(chǎn)地A 16297425955A 24553853247A 35213748342A 47679927152A 52365726541A 65922814332銷量6055514341524338(1) 給出原始代碼； (2) 計算結(jié)果 (決策變量求解結(jié)果粘貼 )6 8Min Z =Cij Xij6 i 1 j 1Xij <=bjj=1.8銷量約束i1專業(yè)資料整理WORD格式 2專業(yè)資料整理

7、WORD格式8Xij = ai i=1.6產(chǎn)量約束j1Xij 0 i=1.6；j=1.8代碼：model:!6 發(fā)點(diǎn) 8 model :!6 發(fā)點(diǎn) 8收點(diǎn)運(yùn)輸問題;sets :warehouses/wh1.wh6/: capacity;vendors/v1.v8/: demand;links(warehouses,vendors): cost, volume;endsetsmin=sum(links: cost*volume);! 目標(biāo)函數(shù) ;for(vendors(J):sum(warehouses(I): volume(I,J)<=demand(J);! 需求約束 ;for(ware

8、houses(I):sum(vendors(J): volume(I,J)=capacity(I);! 產(chǎn)量約束 ;! 這里是數(shù)據(jù) ;data :capacity=55 47 42 52 41 32;demand=60 55 51 43 41 52 43 38;cost=6 2 9 7 4 2 5 94553853252137483767992712365726559228143;enddataend答案Global optimal solution found.Objective value:473.0000Infeasibilities:0.000000Total solver itera

9、tions:9Model Class:LPTotal variables:48Nonlinear variables:0Integer variables:0專業(yè)資料整理WORD格式 3專業(yè)資料整理WORD格式Total constraints:15Nonlinear constraints:0Total nonzeros:144Nonlinear nonzeros:0VariableValueReduced CostCAPACITY( WH1)55.000000.000000CAPACITY( WH2)47.000000.000000CAPACITY( WH3)42.000000.00000

10、0CAPACITY( WH4)52.000000.000000CAPACITY( WH5)41.000000.000000CAPACITY( WH6)32.000000.000000DEMAND( V1)60.000000.000000DEMAND( V2)55.000000.000000DEMAND( V3)51.000000.000000DEMAND( V4)43.000000.000000DEMAND( V5)41.000000.000000DEMAND( V6)52.000000.000000DEMAND( V7)43.000000.000000DEMAND( V8)38.000000

11、.000000COST( WH1, V1)6.0000000.000000COST( WH1, V2)2.0000000.000000COST( WH1, V3)9.0000000.000000COST( WH1, V4)7.0000000.000000COST( WH1, V5)4.0000000.000000COST( WH1, V6)2.0000000.000000COST( WH1, V7)5.0000000.000000COST( WH1, V8)9.0000000.000000COST( WH2, V1)4.0000000.000000COST( WH2, V2)5.0000000

12、.000000COST( WH2, V3)5.0000000.000000COST( WH2, V4)3.0000000.000000COST( WH2, V5)8.0000000.000000COST( WH2, V6)5.0000000.000000COST( WH2, V7)3.0000000.000000COST( WH2, V8)2.0000000.000000COST( WH3, V1)5.0000000.000000COST( WH3, V2)2.0000000.000000COST( WH3, V3)1.0000000.000000COST( WH3, V4)3.0000000

13、.000000COST( WH3, V5)7.0000000.000000COST( WH3, V6)4.0000000.000000COST( WH3, V7)8.0000000.000000專業(yè)資料整理WORD格式 4專業(yè)資料整理WORD格式COST( WH3, V8)3.0000000.000000COST( WH4, V1)7.0000000.000000COST( WH4, V2)6.0000000.000000COST( WH4, V3)7.0000000.000000COST( WH4, V4)9.0000000.000000COST( WH4, V5)9.0000000.000

14、000COST( WH4, V6)2.0000000.000000COST( WH4, V7)7.0000000.000000COST( WH4, V8)1.0000000.000000COST( WH5, V1)2.0000000.000000COST( WH5, V2)3.0000000.000000COST( WH5, V3)6.0000000.000000COST( WH5, V4)5.0000000.000000COST( WH5, V5)7.0000000.000000COST( WH5, V6)2.0000000.000000COST( WH5, V7)6.0000000.000

15、000COST( WH5, V8)5.0000000.000000COST( WH6, V1)5.0000000.000000COST( WH6, V2)9.0000000.000000COST( WH6, V3)2.0000000.000000COST( WH6, V4)2.0000000.000000COST( WH6, V5)8.0000000.000000COST( WH6, V6)1.0000000.000000COST( WH6, V7)4.0000000.000000COST( WH6, V8)3.0000000.000000VOLUME( WH1, V1)0.0000004.0

16、00000VOLUME( WH1, V2)55.000000.000000VOLUME( WH1, V3)0.0000007.000000VOLUME( WH1, V4)0.0000005.000000VOLUME( WH1, V5)0.0000002.000000VOLUME( WH1, V6)0.0000000.000000VOLUME( WH1, V7)0.0000003.000000VOLUME( WH1, V8)0.0000008.000000VOLUME( WH2, V1)0.0000001.000000VOLUME( WH2, V2)0.0000002.000000VOLUME(

17、 WH2, V3)0.0000002.000000VOLUME( WH2, V4)43.000000.000000VOLUME( WH2, V5)0.0000005.000000VOLUME( WH2, V6)0.0000002.000000VOLUME( WH2, V7)4.0000000.000000VOLUME( WH2, V8)0.0000000.000000VOLUME( WH3, V1)0.0000004.000000VOLUME( WH3, V2)0.0000001.000000VOLUME( WH3, V3)42.000000.000000VOLUME( WH3, V4)0.0

18、000002.000000專業(yè)資料整理WORD格式 5專業(yè)資料整理WORD格式VOLUME( WH3, V5)0.0000006.000000VOLUME( WH3, V6)0.0000003.000000VOLUME( WH3, V7)0.0000007.000000VOLUME( WH3, V8)0.0000003.000000VOLUME( WH4, V1)0.0000005.000000VOLUME( WH4, V2)0.0000004.000000VOLUME( WH4, V3)0.0000005.000000VOLUME( WH4, V4)0.0000007.000000VOLUM

19、E( WH4, V5)0.0000007.000000VOLUME( WH4, V6)14.000000.000000VOLUME( WH4, V7)0.0000005.000000VOLUME( WH4, V8)38.000000.000000VOLUME( WH5, V1)41.000000.000000VOLUME( WH5, V2)0.0000001.000000VOLUME( WH5, V3)0.0000004.000000VOLUME( WH5, V4)0.0000003.000000VOLUME( WH5, V5)0.0000005.000000VOLUME( WH5, V6)0

20、.0000000.000000VOLUME( WH5, V7)0.0000004.000000VOLUME( WH5, V8)0.0000004.000000VOLUME( WH6, V1)0.0000004.000000VOLUME( WH6, V2)0.0000008.000000VOLUME( WH6, V3)0.0000001.000000VOLUME( WH6, V4)0.0000001.000000VOLUME( WH6, V5)0.0000007.000000VOLUME( WH6, V6)32.000000.000000VOLUME( WH6, V7)0.0000003.000

21、000VOLUME( WH6, V8)0.0000003.000000RowSlack or SurplusDual Price1473.0000-1.000000219.000000.00000030.0000000.00000049.0000000.00000050.0000000.000000641.000000.00000076.0000000.000000839.000000.00000090.0000001.000000100.000000-2.000000110.000000-3.000000120.000000-1.000000130.000000-2.000000140.00

22、0000-2.000000150.000000-1.000000專業(yè)資料整理WORD格式 6專業(yè)資料整理WORD格式3、一般整數(shù)規(guī)劃問題：某效勞部門各時段每 2h 為一時段需要的效勞員人數(shù)見下表。按規(guī)定，效勞員連續(xù)工作 8h即四個時段為一班?，F(xiàn)要求安排效勞員的工作時間，使效勞部門效勞員總數(shù)最少。時 段12345678效勞員最少數(shù)目10891113853(1) 給出原始代碼； (2) 計算結(jié)果 (決策變量求解結(jié)果粘貼 )model :sets :time/x1.x8/: required,start;endsetsdata :! 每天所需的最少職員數(shù) ; required = 10 8 9 11

23、 13 8 5 3;enddata! 最小化每周所需職員數(shù) ; min=sum(time: start); for(time (J):sum(time(I) | I #le# 4:start(wrap(J+I+2,8) >= required(J);end結(jié)果Global optimal solution found.Objective value:23.00000Total solver iterations:3VariableValueReduced CostREQUIRED( X1)10.000000.000000REQUIRED( X2)8.0000000.000000REQUI

24、RED( X3)9.0000000.000000REQUIRED( X4)11.000000.000000REQUIRED( X5)13.000000.000000REQUIRED( X6)8.0000000.000000REQUIRED( X7)5.0000000.000000REQUIRED( X8)3.0000000.000000START( X1)13.000000.000000START( X2)0.0000000.000000START( X3)0.0000000.000000START( X4)2.0000000.000000START( X5)8.0000000.000000S

25、TART( X6)0.0000000.000000START( X7)0.0000000.000000專業(yè)資料整理WORD格式 7專業(yè)資料整理WORD格式START( X8)0.0000000.000000RowSlack or SurplusDual Price123.00000-1.00000020.000000-1.00000030.0000000.00000044.0000000.00000052.0000000.00000060.000000-1.00000077.0000000.00000085.0000000.00000097.0000000.0000004、指派問題：如下效率矩

26、陣，求極大化指派問題。B1B2BBB534A 14871512A 279171410A 3691287A 46714610A 56912106(1) 給出原始代碼； (2) 計算結(jié)果 (決策變量求解結(jié)果粘貼 )model :!5 個工人， 5 個工作的分配問題;sets :workers/w1.w5/;jobs/j1.j5/;links(workers,jobs): cost,volume;endsets! 目標(biāo)函數(shù) ;min=sum(links: cost*volume);! 每個工人只能有一份工作;for(workers(I):sum(jobs(J): volume(I,J)=1;);!

27、每份工作只能有一個工人;for(jobs(J):sum(workers(I): volume(I,J)=1;);data :cost= 4 8 7 15 127917141069128767146106912106；專業(yè)資料整理WORD格式 8專業(yè)資料整理WORD格式enddataend答案Global optimal solution found.Objective value:34.00000Total solver iterations:10VariableValueReduced CostCOST( W1, J1)4.0000000.000000COST( W1, J2)8.00000

28、00.000000COST( W1, J3)7.0000000.000000COST( W1, J4)15.000000.000000COST( W1, J5)12.000000.000000COST( W2, J1)7.0000000.000000COST( W2, J2)9.0000000.000000COST( W2, J3)17.000000.000000COST( W2, J4)14.000000.000000COST( W2, J5)10.000000.000000COST( W3, J1)6.0000000.000000COST( W3, J2)9.0000000.000000C

29、OST( W3, J3)12.000000.000000COST( W3, J4)8.0000000.000000COST( W3, J5)7.0000000.000000COST( W4, J1)6.0000000.000000COST( W4, J2)7.0000000.000000COST( W4, J3)14.000000.000000COST( W4, J4)6.0000000.000000COST( W4, J5)10.000000.000000COST( W5, J1)6.0000000.000000COST( W5, J2)9.0000000.000000COST( W5, J

30、3)12.000000.000000COST( W5, J4)10.000000.000000COST( W5, J5)6.0000000.000000VOLUME( W1, J1)0.0000003.000000VOLUME( W1, J2)0.0000005.000000VOLUME( W1, J3)1.0000000.000000VOLUME( W1, J4)0.00000013.00000VOLUME( W1, J5)0.00000011.00000VOLUME( W2, J1)0.0000000.000000VOLUME( W2, J2)1.0000000.000000VOLUME(

31、 W2, J3)0.0000004.000000VOLUME( W2, J4)0.0000006.000000VOLUME( W2, J5)0.0000003.000000專業(yè)資料整理WORD格式 9專業(yè)資料整理WORD格式VOLUME( W3, J1)1.0000000.000000VOLUME( W3, J2)0.0000001.000000VOLUME( W3, J3)0.0000000.000000VOLUME( W3, J4)0.0000001.000000VOLUME( W3, J5)0.0000001.000000VOLUME( W4, J1)0.0000001.000000VO

32、LUME( W4, J2)0.0000000.000000VOLUME( W4, J3)0.0000003.000000VOLUME( W4, J4)1.0000000.000000VOLUME( W4, J5)0.0000005.000000VOLUME( W5, J1)0.0000000.000000VOLUME( W5, J2)0.0000001.000000VOLUME( W5, J3)0.0000000.000000VOLUME( W5, J4)0.0000003.000000VOLUME( W5, J5)1.0000000.000000RowSlack or SurplusDual

33、 Price134.00000-1.00000020.000000-1.00000030.000000-7.00000040.000000-6.00000050.000000-5.00000060.000000-6.00000070.0000000.00000080.000000-2.00000090.000000-6.000000100.000000-1.000000110.0000000.0000005、一維資源分配問題：某工業(yè)部門根據(jù)國家方案的安排， 擬將某種高效率的設(shè)備五臺， 分配給所屬的甲、乙、丙三個工廠，各工廠假設(shè)獲得這種設(shè)備之后，可以為國家提供的盈利如下表所示。問：這五臺設(shè)備如何

34、分配給各工廠，才能使國家得到的盈利最大。工廠設(shè)備臺數(shù)甲 a乙 b丙 c000015542151526340404048060455907050(1) 給出原始代碼； (2) 計算結(jié)果 (決策變量求解結(jié)果粘貼 )代碼專業(yè)資料整理WORD格式 10專業(yè)資料整理WORD格式sets:R/1.6/:z;L/1.3/;c(R,L):x,y;endsetsdata:X=0005 5 415 15 2640 40 4080 60 4590 70 50;z=0 1 2 3 4 5;enddatamax = sum(c(i,j):X(i,j)*y(i,j);for(l(i):sum(c(j,k)|k#eq# 1

35、:y(j,k)=1);sum(c(i,j):y(i,j)*z(i)=5;for(c(i,j):B in(y(i,j);end答案Global optimal solution found.Objective value:90.00000Extended solver steps:0Total solver iterations:0VariableValueReduced CostZ( 1)0.0000000.000000Z( 2)1.0000000.000000Z( 3)2.0000000.000000Z( 4)3.0000000.000000Z( 5)4.0000000.000000Z( 6

36、)5.0000000.000000X( 1, 1)0.0000000.000000X( 1, 2)0.0000000.000000X( 1, 3)0.0000000.000000X( 2, 1)5.0000000.000000X( 2, 2)5.0000000.000000X( 2, 3)4.0000000.000000X( 3, 1)15.000000.000000X( 3, 2)15.000000.000000X( 3, 3)26.000000.000000X( 4, 1)40.000000.000000X( 4, 2)40.000000.000000X( 4, 3)40.000000.0

37、00000X( 5, 1)80.000000.000000專業(yè)資料整理WORD格式 11專業(yè)資料整理WORD格式X( 5, 2)60.000000.000000X( 5, 3)45.000000.000000X( 6, 1)90.000000.000000X( 6, 2)70.000000.000000X( 6, 3)50.000000.000000Y( 1, 1)0.0000000.000000Y( 1, 2)0.0000000.000000Y( 1, 3)0.0000000.000000Y( 2, 1)0.000000-5.000000Y( 2, 2)0.000000-5.000000Y(

38、 2, 3)0.000000-4.000000Y( 3, 1)0.000000-15.00000Y( 3, 2)0.000000-15.00000Y( 3, 3)0.000000-26.00000Y( 4, 1)0.000000-40.00000Y( 4, 2)0.000000-40.00000Y( 4, 3)0.000000-40.00000Y( 5, 1)0.000000-80.00000Y( 5, 2)0.000000-60.00000Y( 5, 3)0.000000-45.00000Y( 6, 1)1.000000-90.00000Y( 6, 2)0.000000-70.00000Y(

39、 6, 3)0.000000-50.00000RowSlack or SurplusDual Price190.000001.00000020.0000000.00000030.0000000.00000040.0000000.00000050.0000000.0000006、最短路問題：求從 V1至 V10的最短路。V4V7V 2V 5V 8V 1V 10V 9V3V6專業(yè)資料整理WORD格式 12專業(yè)資料整理WORD格式l 1,2=6,l1,3=5,l 2,4=3,l2,5=6,l 2,6=9,l3,4=7,l 3,5=5, l3,6=11, l4,7=9, l4,8=1,l 5,7=8,

40、l5,8=7,l 5,9=5,l6,8=4,l 6,9=10,l7,10=5,l 8,10=7, l 9,10=9 li,j表示 V i到 Vj之間的權(quán)重(1) 給出原始代碼； (2) 計算結(jié)果 (決策變量求解結(jié)果粘貼 )! 最短路問題 ; model :data : n=10; enddata sets :cities/1.n/: F;!10 個城市 ;roads(cities,cities)/1,21,32,42,52,63,43,53,64,74,85,75,85,96,86,97,108,109,10/: D, P;endsetsdata :D=6536 975 119187 54 10579;enddataF(n)=0;for(c