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

1、精選優(yōu)質(zhì)文檔-傾情為你奉上運(yùn) 籌 學(xué)實(shí) 驗(yàn) 報 告姓 名： 學(xué) 號： 班 級： 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)基本要求要求學(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1LINGO軟件2. LINGO8.0及其在環(huán)境系統(tǒng)優(yōu)化中的應(yīng)用，天津大學(xué)出版社，20053. 優(yōu)化建模與LINDO/LINGO軟件，清華大學(xué)出版社，2005

2、4運(yùn)籌學(xué)編寫組主編，運(yùn)籌學(xué)（修訂版），清華大學(xué)出版社，19905藍(lán)伯雄主編，管理數(shù)學(xué)（下）運(yùn)籌學(xué)，清華大學(xué)出版社，1997 6胡運(yùn)權(quán)主編，運(yùn)籌學(xué)習(xí)題集（修訂版），清華大學(xué)出版社，1995 7胡運(yùn)權(quán)主編，運(yùn)籌學(xué)教程（第二版），清華大學(xué)出版社，2003專心-專注-專業(yè)實(shí)驗(yàn)內(nèi)容1、線性規(guī)劃問題：(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) 回答下列問題(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

3、是多少？d) 對x2的目標(biāo)函數(shù)系數(shù)進(jìn)行靈敏度分析；e) 對第2個約束的約束右端項(xiàng)進(jìn)行靈敏度分析；f ) 結(jié)合本題的結(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. Objective value: 10.66667 Total solver iterations: 2 Variable

4、 Value Reduced Cost X1 1. 0. X2 0. 1. Row Slack or Surplus Dual Price 1 10.66667 1. 2 0. 0. 3 14.66667 0. 4 1. 0. 5 1. 0. 6 0. 0.Ranges in which the basis is unchanged: Objective Coefficient Ranges Current Allowable Allowable Variable Coefficient Increase Decrease X1 8. INFINITY 1. X2 6. 1. INFINITY

5、 Righthand Side Ranges Row Current Allowable Allowable RHS Increase Decrease 2 12.00000 1. 12.00000 3 24.00000 INFINITY 14.66667 4 13.00000 INFINITY 1. 5 0.0 1. INFINITY 6 0.0 0.0 INFINITY(3)a)b)c)d)e)f) 2、運(yùn)輸問題：已知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 cij產(chǎn)地B1B2B3B4B5B6B7B8產(chǎn)量A16297425955A24553853247A352137

6、48342A47679927152A52365726541A65922814332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) Min Z = Cij Xij Xij <=bj （j=1.8） 銷量約束 Xij = ai （i=1.6） 產(chǎn)量約束 Xij 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):

7、cost, volume;endsets min=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(warehouses(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 9 4 5 5 3 8 5 3

8、2 5 2 1 3 7 4 8 3 7 6 7 9 9 2 7 1 2 3 6 5 7 2 6 5 5 9 2 2 8 1 4 3;enddataend答案Global optimal solution found. Objective value: 473.0000 Infeasibilities: 0. Total solver iterations: 9 Model Class: LP Total variables: 48 Nonlinear variables: 0 Integer variables: 0 Total constraints: 15 Nonlinear constr

9、aints: 0 Total nonzeros: 144 Nonlinear nonzeros: 0 Variable Value Reduced Cost CAPACITY( WH1) 55.00000 0. CAPACITY( WH2) 47.00000 0. CAPACITY( WH3) 42.00000 0. CAPACITY( WH4) 52.00000 0. CAPACITY( WH5) 41.00000 0. CAPACITY( WH6) 32.00000 0. DEMAND( V1) 60.00000 0. DEMAND( V2) 55.00000 0. DEMAND( V3)

10、 51.00000 0. DEMAND( V4) 43.00000 0. DEMAND( V5) 41.00000 0. DEMAND( V6) 52.00000 0. DEMAND( V7) 43.00000 0. DEMAND( V8) 38.00000 0. COST( WH1, V1) 6. 0. COST( WH1, V2) 2. 0. COST( WH1, V3) 9. 0. COST( WH1, V4) 7. 0. COST( WH1, V5) 4. 0. COST( WH1, V6) 2. 0. COST( WH1, V7) 5. 0. COST( WH1, V8) 9. 0.

11、 COST( WH2, V1) 4. 0. COST( WH2, V2) 5. 0. COST( WH2, V3) 5. 0. COST( WH2, V4) 3. 0. COST( WH2, V5) 8. 0. COST( WH2, V6) 5. 0. COST( WH2, V7) 3. 0. COST( WH2, V8) 2. 0. COST( WH3, V1) 5. 0. COST( WH3, V2) 2. 0. COST( WH3, V3) 1. 0. COST( WH3, V4) 3. 0. COST( WH3, V5) 7. 0. COST( WH3, V6) 4. 0. COST(

12、 WH3, V7) 8. 0. COST( WH3, V8) 3. 0. COST( WH4, V1) 7. 0. COST( WH4, V2) 6. 0. COST( WH4, V3) 7. 0. COST( WH4, V4) 9. 0. COST( WH4, V5) 9. 0. COST( WH4, V6) 2. 0. COST( WH4, V7) 7. 0. COST( WH4, V8) 1. 0. COST( WH5, V1) 2. 0. COST( WH5, V2) 3. 0. COST( WH5, V3) 6. 0. COST( WH5, V4) 5. 0. COST( WH5,

13、V5) 7. 0. COST( WH5, V6) 2. 0. COST( WH5, V7) 6. 0. COST( WH5, V8) 5. 0. COST( WH6, V1) 5. 0. COST( WH6, V2) 9. 0. COST( WH6, V3) 2. 0. COST( WH6, V4) 2. 0. COST( WH6, V5) 8. 0. COST( WH6, V6) 1. 0. COST( WH6, V7) 4. 0. COST( WH6, V8) 3. 0. VOLUME( WH1, V1) 0. 4. VOLUME( WH1, V2) 55.00000 0. VOLUME(

14、 WH1, V3) 0. 7. VOLUME( WH1, V4) 0. 5. VOLUME( WH1, V5) 0. 2. VOLUME( WH1, V6) 0. 0. VOLUME( WH1, V7) 0. 3. VOLUME( WH1, V8) 0. 8. VOLUME( WH2, V1) 0. 1. VOLUME( WH2, V2) 0. 2. VOLUME( WH2, V3) 0. 2. VOLUME( WH2, V4) 43.00000 0. VOLUME( WH2, V5) 0. 5. VOLUME( WH2, V6) 0. 2. VOLUME( WH2, V7) 4. 0. VO

15、LUME( WH2, V8) 0. 0. VOLUME( WH3, V1) 0. 4. VOLUME( WH3, V2) 0. 1. VOLUME( WH3, V3) 42.00000 0. VOLUME( WH3, V4) 0. 2. VOLUME( WH3, V5) 0. 6. VOLUME( WH3, V6) 0. 3. VOLUME( WH3, V7) 0. 7. VOLUME( WH3, V8) 0. 3. VOLUME( WH4, V1) 0. 5. VOLUME( WH4, V2) 0. 4. VOLUME( WH4, V3) 0. 5. VOLUME( WH4, V4) 0.

16、7. VOLUME( WH4, V5) 0. 7. VOLUME( WH4, V6) 14.00000 0. VOLUME( WH4, V7) 0. 5. VOLUME( WH4, V8) 38.00000 0. VOLUME( WH5, V1) 41.00000 0. VOLUME( WH5, V2) 0. 1. VOLUME( WH5, V3) 0. 4. VOLUME( WH5, V4) 0. 3. VOLUME( WH5, V5) 0. 5. VOLUME( WH5, V6) 0. 0. VOLUME( WH5, V7) 0. 4. VOLUME( WH5, V8) 0. 4. VOL

17、UME( WH6, V1) 0. 4. VOLUME( WH6, V2) 0. 8. VOLUME( WH6, V3) 0. 1. VOLUME( WH6, V4) 0. 1. VOLUME( WH6, V5) 0. 7. VOLUME( WH6, V6) 32.00000 0. VOLUME( WH6, V7) 0. 3. VOLUME( WH6, V8) 0. 3. Row Slack or Surplus Dual Price 1 473.0000 -1. 2 19.00000 0. 3 0. 0. 4 9. 0. 5 0. 0. 6 41.00000 0. 7 6. 0. 8 39.0

18、0000 0. 9 0. 1. 10 0. -2. 11 0. -3. 12 0. -1. 13 0. -2. 14 0. -2. 15 0. -1.3、一般整數(shù)規(guī)劃問題：某服務(wù)部門各時段（每2h為一時段）需要的服務(wù)員人數(shù)見下表。按規(guī)定，服務(wù)員連續(xù)工作8h（即四個時段）為一班?，F(xiàn)要求安排服務(wù)員的工作時間，使服務(wù)部門服務(wù)員總數(shù)最少。時 段12345678服務(wù)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); require

19、d = 10 8 9 11 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: 23.00000 Total solver iterations: 3 Variable Value Reduced Cost REQUIRED( X1) 10.00000 0. REQUIRED( X2) 8

20、. 0. REQUIRED( X3) 9. 0. REQUIRED( X4) 11.00000 0. REQUIRED( X5) 13.00000 0. REQUIRED( X6) 8. 0. REQUIRED( X7) 5. 0. REQUIRED( X8) 3. 0. START( X1) 13.00000 0. START( X2) 0. 0. START( X3) 0. 0. START( X4) 2. 0. START( X5) 8. 0. START( X6) 0. 0. START( X7) 0. 0. START( X8) 0. 0. Row Slack or Surplus

21、Dual Price 1 23.00000 -1. 2 0. -1. 3 0. 0. 4 4. 0. 5 2. 0. 6 0. -1. 7 7. 0. 8 5. 0. 9 7. 0.4、指派問題：已知如下效率矩陣，求極大化指派問題。B1B2B3B4B5A14871512A279171410A3691287A46714610A56912106(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;endset

22、s !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; ); !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 12 7 9 17 14 10 6 9 12 8 7 6 7 14 6 10 6 9 12 10 6；enddataend答案 Global optimal solution found. Objective value: 34.00000

23、 Total solver iterations: 10 Variable Value Reduced Cost COST( W1, J1) 4. 0. COST( W1, J2) 8. 0. COST( W1, J3) 7. 0. COST( W1, J4) 15.00000 0. COST( W1, J5) 12.00000 0. COST( W2, J1) 7. 0. COST( W2, J2) 9. 0. COST( W2, J3) 17.00000 0. COST( W2, J4) 14.00000 0. COST( W2, J5) 10.00000 0. COST( W3, J1)

24、 6. 0. COST( W3, J2) 9. 0. COST( W3, J3) 12.00000 0. COST( W3, J4) 8. 0. COST( W3, J5) 7. 0. COST( W4, J1) 6. 0. COST( W4, J2) 7. 0. COST( W4, J3) 14.00000 0. COST( W4, J4) 6. 0. COST( W4, J5) 10.00000 0. COST( W5, J1) 6. 0. COST( W5, J2) 9. 0. COST( W5, J3) 12.00000 0. COST( W5, J4) 10.00000 0. COST( W5, J5) 6. 0. VOLUME( W1, J1) 0. 3. VOLUME( W1, J2) 0. 5. VOLUME( W1, J3) 1. 0. VOLUME( W1, J4) 0. 13.00000 VOLUME( W1, J5)