運籌學建模煉油廠生產(chǎn)計劃安排

1、煉油廠生產(chǎn)計劃安排摘要本文主要論述了煉油廠生產(chǎn)計劃的優(yōu)化問題，在該廠的生產(chǎn)能力和市場條件的限制下，通過對煉油廠生產(chǎn)流程的分析，得到了總利潤與成品油產(chǎn)量的函數(shù)關系，以及成品油產(chǎn)量所需滿足的約束條件，從而將問題轉化為線性規(guī)劃問題，然后轉換建立了一個模型。模型將總利潤作為目標函數(shù)，將煉油廠生產(chǎn)所受到的生產(chǎn)能力、原料供應和市場需求方面的限制條件轉化為目標函數(shù)的約束條件，最后利用lindo軟件編程實現(xiàn)求解。一、問題的提出煉油廠通過不同渠道購買原油1和原油2,原油經(jīng)過分儲、重整、裂解和調和處理，所得到油和煤油可以直接用于銷售。(1)分儲分儲是將每一種原油根據(jù)沸點不同分解為輕石腦油、中石腦油、重石腦油、輕油

2、、重油和殘油。每桶原油可以產(chǎn)生的各種油分儲見表1。表1原油分儲得到的油分(桶/桶)輕石腦油中石腦油重石腦油輕油重油殘油原油10.100.200.200.120.200.13原油20.150.250.180.080.190.12(2)重整石腦油進入重整過程產(chǎn)生辛烷值為115的重整汽油，經(jīng)過重整得到的重整汽油見表2。表2石腦油經(jīng)過重整后提到的重整汽油(桶/桶)輕石腦油中石腦油重石腦油重整汽油0.60.520.45(3)裂解輕油和重油經(jīng)過催化裂解過程而產(chǎn)生裂化油和裂化汽油，輕油和重油裂解產(chǎn)生的產(chǎn)品見表3。表3輕油重油裂解產(chǎn)生的產(chǎn)品(桶/桶)裂解油裂解汽油輕油0.680.28重油0.750.20(4)

3、調合汽油、航空煤油和煤油都可以利用石腦油、輕油、重油和裂解油等調合而成，而航空煤油的蒸汽壓必須不超過每平方厘米1公斤，而輕油、重油、裂解油和殘油的蒸汽壓見表4。表4各種油品的蒸汽壓(公斤/平方厘米)裂解渣油蒸汽1.00.61.50.05壓煤油的相關數(shù)據(jù)如下：假定煤油由輕油、裂解油、重油和渣油按10:4:3:1調合而成。每天原油1的可供應量為20,000桶；每天原油2的可供應量為30,000桶；每天最多可分儲45,000桶原油；每天最多可重整10,000桶石腦油；每天最多可裂解處理8,000桶；每天生產(chǎn)的潤滑油必須在500桶至IJ1,000桶之間；高檔發(fā)動機油的產(chǎn)量必須是普通發(fā)動機油產(chǎn)量的40%

4、。各種產(chǎn)品的利潤見表5所示。表5各種最終產(chǎn)品的利潤(元/桶)高檔發(fā)動機油普通發(fā)動機油燃料油煤油潤滑油利潤0.70.60.40.350.15提出問題：應如何制定煉油廠的生產(chǎn)計劃，以得到最大利潤。假定所有變量之間相互關系均為線形關系。二、模型假設(1)該煉油廠的所有原材料和產(chǎn)品在運輸和加工過程中的損耗忽略不計；(2)由原料加工成產(chǎn)品時，產(chǎn)品的體積是原料體積之和；(3)生產(chǎn)普通發(fā)動機油和高檔發(fā)動機油時，只要辛烷值達到要求即可，5種原材料不需要都用到；(4)生產(chǎn)飛機燃料時，只要蒸發(fā)壓達到要求即可，4種原材料不需要都用到；(5)該煉油廠生產(chǎn)的所有產(chǎn)品品質都是一樣的，不生產(chǎn)不同品質的產(chǎn)品；(6)該煉油廠所

5、生產(chǎn)的最終產(chǎn)品都能夠賣得出去；(7)該煉油廠所生產(chǎn)的最終產(chǎn)品的利潤是穩(wěn)定的。三、符號說明變量名物品名變量名物品名變量名物品名Z1原油1Z2原油2X1輕石腦油X2中石腦油X3重石腦油X7輕油X8重油X9渣油X11用于生產(chǎn)高檔發(fā)動機油的輕石腦油X12用于生產(chǎn)普通發(fā)動機油的輕石腦油X13用于生產(chǎn)重整汽油的輕石腦油X21用于生產(chǎn)高檔發(fā)動機油的中石腦油X22用于生產(chǎn)普通發(fā)動機油的中石腦油X23用于生產(chǎn)重整汽油的中石腦油X31用于生產(chǎn)高檔發(fā)動機油的重石腦油X32用于生產(chǎn)普通發(fā)動機重石腦油X33用于生產(chǎn)重整汽油的重石腦油X71用于裂解生產(chǎn)的輕油X72用于生產(chǎn)燃料油的輕油X73用于生產(chǎn)煤油的輕油X81用于裂解

6、生產(chǎn)的重油X82用于生產(chǎn)燃料油的重油X83用于生產(chǎn)煤油的重油X91用于生產(chǎn)煤油的渣油X92用于生產(chǎn)燃料油的渣油X93用于生產(chǎn)潤滑油的渣油X4重整汽油X5裂解汽油X6裂解油X41用于生產(chǎn)普通發(fā)動機油的重整汽油X41用于生產(chǎn)高檔發(fā)動機油重整汽油X51用于生產(chǎn)普通發(fā)動機油的裂解汽油X51用于生產(chǎn)高檔發(fā)動機油的裂解汽油X61用于生產(chǎn)煤油的裂解油X62用于生產(chǎn)燃料油的裂解油Y1高檔發(fā)動機油Y2普通發(fā)動機油y3煤油丫4燃料油丫5潤滑油四、模型建立1:問題整合原料油和中間產(chǎn)品到最終成品油的過程流程圖如下:原油輕石油精中石油精重石油精輕油重油殘渣V重整汽油裂化汽油裂化油V普通汽油燃料油V飛機燃料潤滑油煉油廠通

7、過不同渠道購買原油1和原油2,原油經(jīng)過蒸儲、重整、裂解、調和處理，所得到的產(chǎn)物可直接用于銷售。（1）蒸儲原油先進入蒸儲裝置，每桶原油經(jīng)蒸儲后的產(chǎn)品及份額見表1輕石腦油中石腦油重石腦油輕油重油渣油原油10.100.200.200.120.200.13原油20.150.250.180.080.190.12（2）重整石腦油部分直接用于發(fā)動機油混合，部分輸入重整裝置，可得辛烷值為115的重整汽油。經(jīng)過重整的重整汽油見表2。輕石腦油（桶）中石腦油（桶）重石腦油（桶）重整汽油（桶）0.60.520.45（3）裂解蒸儲所得的輕油和重油，一部分直接用于煤油和燃料油的混合，一部分經(jīng)過裂解裝置，可得裂解油和裂解汽

8、油，輕油和重油裂解所得產(chǎn)品見表3。裂解油（桶）裂解汽油（桶）輕油（桶）0.680.28重油（桶）0.750.20（4）調和發(fā)動機油，煤油，燃料油等可以利用石腦油、輕油、重油、裂解油等調和而成，而煤油的蒸汽壓必須不超過1kg/cm2.。輕油，重油，裂解油、渣油及煤油的蒸汽壓表見表4。輕油重油裂解油渣油煤油氣壓/,，2、(kg/cm)1.00.61.50.051.0輕石腦油、中石腦油等辛烷值輕石腦油中石腦油重石腦油重整汽油裂解汽油高檔發(fā)動機油普通發(fā)動機油908070115105>=94>=84其他相關數(shù)據(jù)如下燃料油中，輕油、重油、裂解油和渣油的比例應為10:3:4:1每天原油1可供應量

9、為20000桶。每天原油1可供應量為30000桶。蒸儲裝置能力每天最大為45000桶。重整裝置每天最多重整10000桶石腦油。裂化裝置能力最大為8000桶。潤滑油每天產(chǎn)量為500-1000桶之間。高檔發(fā)動機油產(chǎn)量不低于普通發(fā)動機油產(chǎn)量的40%。各種產(chǎn)品的利潤見表6高檔動機油（桶）普通發(fā)動機油（桶）煤油（桶）燃料油（桶）潤滑油（桶）利潤（元）7006004003501502:目標函數(shù)的建立Max=700yi+600y2+400丫3+350丫4+150丫5；3：約束條件分析各裝置投入產(chǎn)出關系如蒸儲裝置有XXXXXXi=0.7zi+0.15z2,2=0.2zi+0.25z2,3=0.2zi+0.18

10、z2,7=0.12zi+0.08z2,8=0.2zi+0.i9z2,9=0.i3zi+0.i2z2Xi=Xii+Xi2+Xi3,X2=X2i+X22+X23,X3=X3i+X32+X33,JX7=X7i+X72+X73,X8=X8i+X82+X83,X9=X9i+X92+X93對重整裝置有對裂解裝置有X4=0.6Xi3+0.52X23+0.45X33X4=X4i+X42+X43X5=0.28X73+0.2X83,又X5=X5i+X526=0.68X73+0.75X83,又X6=X6i+X62對渣油處理裝置有y5=0.5x93對發(fā)動機油混合裝置有yi=xii+X2i+X3i+X4i+X5iIy2

11、=Xi2+X22+X32+X42+X52對煤油、燃料油混合裝置有y3=X6l+X7l+X8l+X91y4=X62+X72+X82+X92各裝置能力限制z11+Z2<45000,X113+X23+X33W10000XI73+X83M8000,發(fā)動機油辛烷值限制90X11+80X21+70X31+115X41+105X51=94(x11+X21+X31+X41+X51)90X12+80X22+70X32+115X42+105X52至84(X12+X22+X32+X42+X52)煤油氣壓的限制1.5X61+1.0X71+0.6X81+0.05X91MX61+X71+X81+X91燃料油比例的限

12、制x62_X72_X82_-X924103原油供應限制乙三20000,z2三30000最終產(chǎn)品數(shù)量限制500My5M1000,y1-0.4y2變量非負限制，所有變量均04:根據(jù)約束條件建立表達式Max=700y1+600y2+400丫3+350丫4+150丫5S.T.xi-0.1zi-0.15z2=0X2-0.2zi-0.25z2=0X3-0.2zi-0.18z2=0X7-0.12zi-0.08z2=0X8-0.2zi-0.19z2=0X9-0.13zi-0.12z2=0Xi-X11-X12-X13=0X2X21-X22-X23=0X3-X31-X32-X33=0X7-X71-X72-X73=

13、0X8-X81-X82-X83=0X9-X91-X92-X93=0X4-0.6X13-0.52X23-0.45X33=0X4-X41-X42-X43=0X5-0.28X73-0.2X83=0X5-X51-X52=0X6-0.68X73-0.75X83=0X6-X61-X62=0y5-0.5X93=0yi-X11-X21-X3i-X4i-X51=0y2-X12-X22-X32-X42-X52=0y3-X61-X71-X81-X91=0y4-X62-X72-X82-X92=0zi+Z2<=45000Xl3+X23+X33<=10000X73+X83<=80004xii+14x2i

14、+24x321x411x51V=0-6x12+4X22+14X32-31X42-21X52<=00.5x61-0.4x81-0.95x91V=0X62_4x92=0X72-IOx92=0X82_3x92=0Zi<=20000Z2<=30000y5>=500y5V=1000yi-0.4y2>=0五、模型求解本題使用LINDO解題一、解題數(shù)據(jù)輸入：DO-entitled-：喀琲dEditSolwfieportsJfiSndkwrHdp口|曲。舊|目|_到國修I即川足|司國I網(wǎng)的屈|礴1tl®STk1-611-0B1S2-Ow2-0.2zl-D.25z2=0m

15、3-02z1-D.18e2-0x?-012±l-0.flaz2-0h9-0.2z1-0.19ie2=07-Q13zl-0.12z2-Qk2-z21-x22-m23»0m3-m31-x32-m33-0h7-s71-x72-h73=0k9-k01-kB2-k93-O«9-i91-M92-xA330k4-06zl3-0.52k23-045b33-0x4k41-k42-k43-Qh5-02Bk73-O.2xS3-Dx5-k51-k52»0h6-06Bse73-O.75930k6-h61-e62»OyS-05k93-OymW1-k31-k41-x51*0

16、5t22-k22-x32-言42-s5Z-0娟一齪6l-K7l-j<a1-x.91*0yW-h62-e72-h82-z92=0=1+z2<-45000wl3+i23+M33<=10000m73+zB3<-BOO0im11+14x21+24m1-21m41-11k51<*0-6k12+4e22+14ec32-31x42-21k52<=00Sw61-04kS1-095sl5。乂62-&工92;口«72-10s92-02-3327zl<=2000Dz2<-3Q000y5>-50055<-1000yl04y2>-0EM

17、D:結果如下局穌日哥國魚”|區(qū)旨I|同國LPOPTIMUMFOUNDATSTEP24OBJECTIVEFUNCTIONVALUEVARIABLEVALUEY16817.778809Y217044.447266Y315156.000000Y40.000000Y5500.000000XI6000.000000Z115000.000000Z230000.000000X210500.000000X38400.000000X74200.000000X88700.000000X95550.000000Xll0.000000X126000.000000X130.000000X210.000000X22105

18、00.000000X230.000000X312751.407959X32241.730240X335406.861816X710.000000X720.000000X734200.000000X814900.000000X820.000000X833800.000000X914550.0000001)0.2113651E+0823412351261299X444X55X66XXXXXXXXX0.0000001000.0000002433.0878912130.370850302.7168880.0000001936.0000001936.0000000.0000005706.00000057

19、06.0000000.000000REDUCEDCOST0.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.00000090,4911420.0000000.00000050.0363120.0000000.0000000.00000039.2828450.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.000

20、000958.1417850.0000000.0000000.0000000.0000000.000000323.207123i圜”舊i昌ixi嘲噌兇晝i刈hialMsl釗倒X620.000000323.207123ROWSLACKORSURPLUSDUALPRICES2)0.000000665.3762213)0.000000548.2700204)0.000000431.1638185)0.000000439.2828376)0.000000400.0000007)0.000000400.0000008)0.000000-665.3762219)0.000000-548.27002010)

21、0.000000-431.163818ID0.000000-439.28283712)0.000000-400.00000013)0.000000-400.00000014)0.000000958.14178515)0.000000-958.14178516)0.000000841.03558317)0.000000-841.03558318)0.000000400.00000019)0.000000-400.00000020)0.000000800.00000021)0.000000712.21875022)0.000000595.11248823)0.000000400.00000024)

22、0.000000350.00000025)0.000000447.13833626)4593.1381840.00000027)0.00000068.20711528)0.00000011.71062229)0.00000011.71062230)3429.5000000.00000031)0.000000273.20712332)0.000000-89.28284533)0.000000-50.00000034)5000.0000000.00000035)0.00000026.48772236)0.000000-650.00000037)500.0000000.00000038)0.0000

23、00-12.218727ITERATIONS=24RANGESINWHICHTHEBASISISUNCHANGED:D|諭闈回爭IXl電卮|，|岡晝I同I1川|培|國37)38)500.0000000.0000000.000000-12.218727NO.ITERATIONS：24RANGESINWHICHTHEBASISISUNCHANGED:VARIABLECURRENTOBJCOEFFICIENTALLOWABLERANGESALLOWABLEY1COEF700.000000INCREASE18.067978DECREASE892.088684Y2600.000000INFINITY15

24、.097159Y3400.000000272.82846174.729973Y4350.00000071.823807INFINITYY5150.000000650.000000INFINITYXI0.000000INFINITY529.754456Z10.00000026.487722447.138336Z20.000000INFINITY26.487722X20.000000INFINITY529.754456X30.0000001324.3861082235.691650X70.000000662.1930543726.152832X80.0000002648.7722172235.69

25、1650X90.0000002648.7722173439.525879Xll0.0000000.000000INFINITYX120.000000INFINITY0.000000X130.00000090.491127INFINITYX210.0000000.000000INFINITYX220.000000INFINITY0.000000X230.00000050.036308INFINITYX310.0000000.0001670.000000X320.0000000.0000000.000167X330.00000050.50000068,731750X710.00000039.282

26、837INFINITYX720.000000129.282852INFINITYX730.000000662.19305439.282837X810.00000068.20711539.282837X820.000000430.942841INFINITYX830.00000039.28283768.207115X910.0000002648.772217325.000000X920.0000001292.828491INFINITYX930.000000325.000000INFINITYX40.000000112.2222216894.907715X410.0000000.0000480.

27、000000X420.0000000.0000000.000048X430.000000958.141785INFINITYX50.0000008277.413086341.035583X510.0000008277.4130860.000037X520.0000000.000037INFINITY阻UNDO-ReportsWindowr-tul1FileEditSolveReportsWindowHelp口1窿1穌舊居1,|一隱|>|三|國1E|心X520.0000000.000037INFINITYX60.000000561.18341190.942818X610.000000S61

28、.18341190.942818X620.000000323.207123INFINITYRIGHTHANDSIDERANGESROWCURRENTALLOWABLEALLOWABLERHSINCREASEDECREASE20.0000001446.9493416000.00000030.000000693.47833310500.00000040.0000008043.830078716.17999350.0000003800.0000004200.00000060.000000INFINITY4900.00000070.000000INFINITY3610.00000080.0000006

29、000.0000001146.94934190.00000010500.000000693.478333100.000000716.1799938043.830078110.0000004200.0000003800.000000120.0000004900.000000INFINITY130.0000003610.000000INFINITY140.0000005671.715820322.280975150.000000322.2809755671.715820160.0000003712.156250367.155579170.000000367.1555793712.156250180

30、.0000006859.0000005706.000000190.0000005706.0000006859.000000200.000000SOO.0000001805.000000210.0000005906.633789433.561890220.0000001083.90466314766.584961230.000000INFINITY15156.000000240.000000INFINITY0.0000002545000.0000005000.00000013412.2021482610000.000000INFINITY4593.138184278000.0000004425.

31、1616211835.777832280.000000109907.63281226368.445312290.00000016741.2441417700.958984300.000000INFINITY3429.500000310.0000000.0000001507.692261320.0000004200.0000000.000000330.0000004900.0000000.0000003420000.000000INFINITY5000.000000asnnnnnnnnnnaqk994141Rnnnnnnnnn36500.000000500.000000500.000000371

32、000.000000INFINITY500.000000380.000000433.5618905906.633789的1國ll曾解1TDADTTMTTMmTTMnATQTT7PFileEditSolveReportsWindowHelpI團危舊I昌Ixl船館|多|區(qū)晝匡Ini盾IMLPOPTIMUMFOUNDATSTEP24OBJECTIVEFUNCTIONVALUE1)0.2113651E+08VARIABLEVALUEREDUCEDCOSTY16817.7788090.000000Y217044.4472660.000000Y315156.0000000.000000Y40.000000

33、0.000000Y5500.0000000.000000XI6000.0000000.000000Z115000.0000000.000000Z230000.0000000.000000X210500.0000000.000000X38400.0000000.000000X74200.0000000.000000X88700.0000000.000000X95550.0000000.000000Xll0.0000000.000000X126000.0000000.000000X130.00000090.491142X210.0000000.000000X2210500.0000000.0000

34、00X230.00000050.036312X312751.4079590.000000X32241.7302400.000000X335406.8618160.000000X710.00000039.282845X720.0000000.000000X734200.0000000.000000X814900.0000000.000000X820.0000000.000000X833800.0000000.000000X914550.0000000.000000X920.0000000.000000X931000.0000000.000000X42433.0878910.000000X4121

35、30.3708500.000000X42302.7168880.000000X430.000000958.141785X51936.0000000.000000X511936.0000000.000000X520.0000000.000000X65706.0000000.000000X615706.0000000.000000EditSolveReportsHI同回昌1區(qū)向第WindowHelp%|兇|野|主IBl©同周國1X615706.000000c,0000000.000000323.207123ROWSLACKOK!SURPLUSDUALPRICES2、0.00000066S

36、,372210.OOOGOOE48.27C0204)0.000000431.163318S)0.000000439,2823376)0.0000004(JO.0000007)0.000000400OOOOOOG)0.oooooo665,3762219)0.0000006鴕,27002010)0.oooooo-431i&3aie11)0.000000-43928283712)0.000000-400.oooooo13)0.oooooc-400.oooooc14)0.OQOOOO95日.1417950.ooooocT58,14178516)0oooooc84103559317)0.oooo

37、oo-641.035583IC)0.oooooo400,000001910.oooooo4DOOOOOOO2C)0.ooooooeoo.oooooc21)0.oooooo712.21875022)0.oooooo59S.11249823)0.oooooo400.00000024)0.oooooo350.0000000.。口?？?。447,1363364593,130104QOOOOOO27)0.oodoqose.2071150.ooooooii.71062229)0.ooooooii.71062230)3429.5000000.OOCOOO31)0.oooooo273.20712332)0.oooooc-09.28284533)0.oooooo-50.oooooo34)&G00.oooooo0oooooo35)0.oooooo26.48772236)Q.oooooo-650.oooaoo27)500.ooooocGoooooo36)0.oooooo-12.21電727NOITERATIONS-24三、結果分析1 .根據(jù)第一部分（Objectivefunctionvalue目標函數(shù)值）結果的第一列可知，最優(yōu)生產(chǎn)計劃是：每日使用的原油1和原油2的桶數(shù)分別為150