运筹学建模炼油厂生产计划安排

1、炼油厂生产计划安排摘要本文主要论述了炼油厂生产计划的优化问题，在该厂的生产能力和市场条件的限制下，通过对炼油厂生产流程的分析，得到了总利润与成品油产量的函数关系，以及成品油产量所需满足的约束条件，从而将问题转化为线性规划问题，然后转换建立了一个模型。模型将总利润作为目标函数，将炼油厂生产所受到的生产能力、原料供应和市场需求方面的限制条件转化为目标函数的约束条件，最后利用lindo软件编程实现求解。一、问题的提出炼油厂通过不同渠道购买原油1和原油2,原油经过分储、重整、裂解和调和处理，所得到油和煤油可以直接用于销售。(1)分储分储是将每一种原油根据沸点不同分解为轻石脑油、中石脑油、重石脑油、轻油

2、、重油和残油。每桶原油可以产生的各种油分储见表1。表1原油分储得到的油分(桶/桶)轻石脑油中石脑油重石脑油轻油重油残油原油10.100.200.200.120.200.13原油20.150.250.180.080.190.12(2)重整石脑油进入重整过程产生辛烷值为115的重整汽油，经过重整得到的重整汽油见表2。表2石脑油经过重整后提到的重整汽油(桶/桶)轻石脑油中石脑油重石脑油重整汽油0.60.520.45(3)裂解轻油和重油经过催化裂解过程而产生裂化油和裂化汽油，轻油和重油裂解产生的产品见表3。表3轻油重油裂解产生的产品(桶/桶)裂解油裂解汽油轻油0.680.28重油0.750.20(4)

3、调合汽油、航空煤油和煤油都可以利用石脑油、轻油、重油和裂解油等调合而成，而航空煤油的蒸汽压必须不超过每平方厘米1公斤，而轻油、重油、裂解油和残油的蒸汽压见表4。表4各种油品的蒸汽压(公斤/平方厘米)裂解渣油蒸汽1.00.61.50.05压煤油的相关数据如下：假定煤油由轻油、裂解油、重油和渣油按10:4:3:1调合而成。每天原油1的可供应量为20,000桶；每天原油2的可供应量为30,000桶；每天最多可分储45,000桶原油；每天最多可重整10,000桶石脑油；每天最多可裂解处理8,000桶；每天生产的润滑油必须在500桶至IJ1,000桶之间；高档发动机油的产量必须是普通发动机油产量的40%

4、。各种产品的利润见表5所示。表5各种最终产品的利润(元/桶)高档发动机油普通发动机油燃料油煤油润滑油利润0.70.60.40.350.15提出问题：应如何制定炼油厂的生产计划，以得到最大利润。假定所有变量之间相互关系均为线形关系。二、模型假设(1)该炼油厂的所有原材料和产品在运输和加工过程中的损耗忽略不计；(2)由原料加工成产品时，产品的体积是原料体积之和；(3)生产普通发动机油和高档发动机油时，只要辛烷值达到要求即可，5种原材料不需要都用到；(4)生产飞机燃料时，只要蒸发压达到要求即可，4种原材料不需要都用到；(5)该炼油厂生产的所有产品品质都是一样的，不生产不同品质的产品；(6)该炼油厂所

5、生产的最终产品都能够卖得出去；(7)该炼油厂所生产的最终产品的利润是稳定的。三、符号说明变量名物品名变量名物品名变量名物品名Z1原油1Z2原油2X1轻石脑油X2中石脑油X3重石脑油X7轻油X8重油X9渣油X11用于生产高档发动机油的轻石脑油X12用于生产普通发动机油的轻石脑油X13用于生产重整汽油的轻石脑油X21用于生产高档发动机油的中石脑油X22用于生产普通发动机油的中石脑油X23用于生产重整汽油的中石脑油X31用于生产高档发动机油的重石脑油X32用于生产普通发动机重石脑油X33用于生产重整汽油的重石脑油X71用于裂解生产的轻油X72用于生产燃料油的轻油X73用于生产煤油的轻油X81用于裂解

6、生产的重油X82用于生产燃料油的重油X83用于生产煤油的重油X91用于生产煤油的渣油X92用于生产燃料油的渣油X93用于生产润滑油的渣油X4重整汽油X5裂解汽油X6裂解油X41用于生产普通发动机油的重整汽油X41用于生产高档发动机油重整汽油X51用于生产普通发动机油的裂解汽油X51用于生产高档发动机油的裂解汽油X61用于生产煤油的裂解油X62用于生产燃料油的裂解油Y1高档发动机油Y2普通发动机油y3煤油丫4燃料油丫5润滑油四、模型建立1:问题整合原料油和中间产品到最终成品油的过程流程图如下:原油轻石油精中石油精重石油精轻油重油残渣V重整汽油裂化汽油裂化油V普通汽油燃料油V飞机燃料润滑油炼油厂通

7、过不同渠道购买原油1和原油2,原油经过蒸储、重整、裂解、调和处理，所得到的产物可直接用于销售。（1）蒸储原油先进入蒸储装置，每桶原油经蒸储后的产品及份额见表1轻石脑油中石脑油重石脑油轻油重油渣油原油10.100.200.200.120.200.13原油20.150.250.180.080.190.12（2）重整石脑油部分直接用于发动机油混合，部分输入重整装置，可得辛烷值为115的重整汽油。经过重整的重整汽油见表2。轻石脑油（桶）中石脑油（桶）重石脑油（桶）重整汽油（桶）0.60.520.45（3）裂解蒸储所得的轻油和重油，一部分直接用于煤油和燃料油的混合，一部分经过裂解装置，可得裂解油和裂解汽

8、油，轻油和重油裂解所得产品见表3。裂解油（桶）裂解汽油（桶）轻油（桶）0.680.28重油（桶）0.750.20（4）调和发动机油，煤油，燃料油等可以利用石脑油、轻油、重油、裂解油等调和而成，而煤油的蒸汽压必须不超过1kg/cm2.。轻油，重油，裂解油、渣油及煤油的蒸汽压表见表4。轻油重油裂解油渣油煤油气压/,，2、(kg/cm)1.00.61.50.051.0轻石脑油、中石脑油等辛烷值轻石脑油中石脑油重石脑油重整汽油裂解汽油高档发动机油普通发动机油908070115105>=94>=84其他相关数据如下燃料油中，轻油、重油、裂解油和渣油的比例应为10:3:4:1每天原油1可供应量

9、为20000桶。每天原油1可供应量为30000桶。蒸储装置能力每天最大为45000桶。重整装置每天最多重整10000桶石脑油。裂化装置能力最大为8000桶。润滑油每天产量为500-1000桶之间。高档发动机油产量不低于普通发动机油产量的40%。各种产品的利润见表6高档动机油（桶）普通发动机油（桶）煤油（桶）燃料油（桶）润滑油（桶）利润（元）7006004003501502:目标函数的建立Max=700yi+600y2+400丫3+350丫4+150丫5；3：约束条件分析各装置投入产出关系如蒸储装置有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对重整装置有对裂解装置有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对渣油处理装置有y5=0.5x93对发动机油混合装置有yi=xii+X2i+X3i+X4i+X5iIy2

11、=Xi2+X22+X32+X42+X52对煤油、燃料油混合装置有y3=X6l+X7l+X8l+X91y4=X62+X72+X82+X92各装置能力限制z11+Z2<45000,X113+X23+X33W10000XI73+X83M8000,发动机油辛烷值限制90X11+80X21+70X31+115X41+105X51=94(x11+X21+X31+X41+X51)90X12+80X22+70X32+115X42+105X52至84(X12+X22+X32+X42+X52)煤油气压的限制1.5X61+1.0X71+0.6X81+0.05X91MX61+X71+X81+X91燃料油比例的限

12、制x62_X72_X82_-X924103原油供应限制乙三20000,z2三30000最终产品数量限制500My5M1000,y1-0.4y2变量非负限制，所有变量均04:根据约束条件建立表达式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、模型求解本题使用LINDO解题一、解题数据输入：DO-entitled-：喀琲dEditSolwfieportsJfiSndkwrHdp口|曲。旧|目|_到国修I即川足|司国I网的屈|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娟一龊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:结果如下局稣日哥国鱼”|区旨I|同国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”旧i昌ixi嘲噌凶昼i刈hialMsl钊倒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|谕闱回争IXl电卮|，|冈昼I同I1川|培|国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稣旧居1,|一隐|>|三|国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国ll曾解1TDADTTMTTMmTTMnATQTT7PFileEditSolveReportsWindowHelpI团危旧I昌Ixl船馆|多|区昼匡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区向第WindowHelp%|凶|野|主IBl©同周国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鸵,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。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电727NOITERATIONS-24三、结果分析1 .根据第一部分（Objectivefunctionvalue目标函数值）结果的第一列可知，最优生产计划是：每日使用的原油1和原油2的桶数分别为150