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1、實用標準文案《數(shù)據(jù)、模型與決策案例》分析報告一、背景分析(Cinergy煤分配問題)DukeEnergy公司利用煤炭分配模型的線性規(guī)劃將其煤炭運送至各發(fā)電站,其費用分為購買費用、運費和附加花費,而該模型的目的在確定購買和向發(fā)電單位運送煤炭花費最少的方法。DukeEnergy公司與煤炭供應商的合同分為固定噸位合同與可變噸位合同,對于固定噸位合同,DukeEnergy公司必須以合同規(guī)定數(shù)目購買煤炭,對于可變噸位合同DukeEnergy公司必須購進不超過合同數(shù)的煤炭。相應的表格數(shù)據(jù)見教材P129二、模型建
2、立1、相應未知數(shù)的假設設7個供應商分別運到5個發(fā)電單位的煤炭如下(單位:噸),公司發(fā)電站邁阿密5號邁阿密7號別克杰徳1號東班徳2號茲蒙1號RAGRM5RM7RB1RD2RC1皮伯蒂煤炭銷售公司PM5PM7PB1PD2PC1美國煤炭銷售公司MM5MM7MB1MD2MC1康社公司KM5KM7KB1KD2KC1賽普羅斯-阿馬斯可克公司SM5SM7SB1SD2SC1阿丁頓采礦公司AM5AM7AB1AD2AC1滑鐵盧公司HM5HM7HB1HD2HC1將書上的幾個表格進行整合可以得到如下表格:精彩文檔實用標準文
3、案2、建模:精彩文檔實用標準文案目標函數(shù):MinZ=37RM5+37RM7+36.75RB1+32RD2+32.75RC1+39.75PM5+39.75PM7+40.5PB1+35.75PD2+36.5PC1+38MM5+38MM7+38.75MB1+34MD2+33.75MC1+45.25KM5+45.25KM7+45.85KB1+42.25KD2+41.85KC1+50SM5+50SM7+49.75SB1+45SD2+45.75SC1+38.25AM5+38.25AM7+39AB1+37.25A
4、D2+37AC1+46HM5+46HM7+45.6HB1+42HD2+43.6HC1約束條件:(1)RM5+RM7+RB1+RD2+RC1=350000(2)PM5+PM7+PB1+PD2+PC1=300000(3)MM5+MM7+MB1+MD2+MC1=275000(4)KM5+KM7+KB1+KD2+KC1<=200000(5)SM5+SM7+SB1+SD2+SC1<=175000(6)AM5+AM7+AB1+AD2+AC1<=200000(7)HM5+HM7+HB1+HD2+HC1<=1800
5、001噸=2204.6磅(8)13000RM5+13300PM5+12600MM5+12250KM5+12000SM5+12000AM5+11300HM5>=550000*1000*10500/2204.6(9)13000RM7+13300PM7+12600MM7+12250KM7+12000SM7+12000AM7+11300HM7>=500000*1000*10200/2204.6(10)13000RB1+13300PB1+126000MB1+12250KB1+12000SB1+12000AB1
6、+11300HB1>=650000*1000*10100/2204.6(11)13000RD2+13300PD2+12600MD2+12250KD2+12000SD2+12000AD2+11300HD2>=750000*1000*10000/2204.6精彩文檔實用標準文案(12)13000RC1+13300PC1+12600MC1+12250KC1+12000SC1+12000AC1+11300HC1>=1100000*1000*10000/2204.6化簡之后得到模型:目標函數(shù):MinZ=37R
7、M5+37RM7+36.75RB1+32RD2+32.75RC1+39.75PM5+39.75PM7+40.5PB1+35.75PD2+36.5PC1+38MM5+38MM7+38.75MB1+34MD2+33.75MC1+45.25KM5+45.25KM7+45.85KB1+42.25KD2+41.85KC1+50SM5+50SM7+49.75SB1+45SD2+45.75SC1+38.25AM5+38.25AM7+39AB1+37.25AD2+37AC1+46HM5+46HM7+45.6HB1+
8、42HD2+43.6HC1約束條件:(1)RM5+RM7+RB1+RD2+RC1=350000(2)PM5+PM7+PB1+PD2+PC1=300000(3)MM5+MM7+MB1+MD2+MC1=275000(4)KM5+KM7+KB1+KD2+KC1>=200000(5)SM5+SM7+SB1+SD2+SC1>=175000(6)AM5+AM7+AB1+AD2+AC1>=200000(7)HM5+HM7+HB1+HD2+HC1>=1800001噸=2204.6磅(