1、案例題目：有轉換成本的生產計劃七葉樹制造廠(BuckeyeManufacturing)是為了卡車生產發動機頭的制造企業。生產發動機頭的生產線非常復雜，有900英尺長。這條生產線生產兩種類型的發動機頭：P型機頭和H型機頭。P頭在重型卡車里使用，H頭在小型卡車里使用。因為在一定時間只能生產一種類型的發動機頭，生產線啟動后只能生產P型機頭或者生產H型機頭，不能同時生產兩種類型的機頭。轉換發生在每個周末，從P型機頭轉換變成H型機頭的成本為500美元，反過來也是這樣。當生產P型機頭時，最大的產出率為每周100單位；當生產H型機頭時，最大生產率為每周80單位。七葉樹制造廠在使用生產線生產P型發動機頭后關閉

2、了一周。公司經理想安排未來8周的生產和生產轉換。當前，七葉樹的庫存包括125單位的P型發動機頭和143單位的H型發送機頭。存貨的年庫存費用是存貨價值的19.5%°P型發動機頭的生產成本是225美元，H型發動機頭的生產成本是310美元。安排生產計劃的目標是使制造成本加上庫存成本和轉換成本的總和最小化。七葉樹收到下面來自客戶(機頭組裝廠)在未來9個星期的需求訂單。安全庫存的要求是周末庫存水平必須至少達到下周需求水平的80%。產品需求周P型發動機頭H型發動機頭1553825538344304005454864548736588355793558管理報告為七葉樹的經理準備一份報告，闡述關于未

3、來8周的生產和生產轉換計劃。一定要注意,按照這樣的生產計劃，總成本是多少，多少來源于庫存成本，多少來源于生產轉換成本。精選范本案例分析：1)建立模型：設定決策變量Xjk,1=第1,2,3,4,5,6,7,8周;j=P,H代表生產機頭類型；k=1or0,1代表轉換生產，0代表不轉換生產；年庫存費用是存貨價值的19.5%,那么周庫存費用=19.5%/52=0.375%勺存貨價值;假設安全庫存的要求是每周末庫存水平必須至少達到下周需求水平的80%旨的是P型或者H型車頭均需滿足。庫存成本+制造成本+轉換成本最小的目標函數如下：MinZ=225*100*(Xipi+Xipc+X2P1+X2P0+X3P1

4、+X3P0+X4P1+X4P0+X5P1+X5P0+X6P1+X6P0+X7P1+X7PC+X8P1+X8P0)+310*80*(X1H1+X1H0+X2H1+X2H0+X3H1+X3H0+X4H1+X4H0+X5H1+X5H0+X6H1+X6H0+X7H1+X7H0+X8H1+X8H0)+500*(X1P1+X1H1+X2P1+X2H1+苑P1+X3H1+X4P1+X4H1+X5P1+X5H1+X5P1+X6H1+X7P1+X7H1+X8P1+X8H1)+225*125*0.375%*8+225*100*(xipi+xip0)*0.375%*8-225*55*0.375%*8+310*143

5、*0.375%*8+310*80*(X1H1+X1H0)*0.375%*8-310*38*0.375%*8+225*100*(X2pi+x2P0)*0.375%*7-225*55*0.375%*7+310*80*(x2H1+X2H0)*0.375%*7-310*38*0.375%*7+225*100*(X3Pi+x3P0)*0.375%*6-225*44*0.375%*6+310*80*(x3H1+X3H0)*0.375%*6-310*30*0.375%*6+225*100*(X4P1+X4P0)*0.375%*5+310*80*(X4H1+x4H0)*0.375%*5+225*100*(X5

6、P1+X5P0)*0.375%*4-225*45*0.375%*4+310*80*(x5H1+X5H0)*0.375%*4-310*48*0.375%*4+225*100*(X6P1+X6P0)*0.375%*3-225*45*0.375%*3+310*80*(x6H1+X6H0)*0.375%*3-310*48*0.375%*3+225*100*(X7P1+X7P0)*0.375%*2-225*36*0.375%*2+310*80*(x7H1+X7H0)*0.375%*2-310*58*0.375%*2+225*100*(X8P1+X8P0)*0.375%-225*35*0.375%+310

7、*80*(X8H1+X8H0)*0.375%-310*57*0.375%=23675KP1+23175X1P0+26044X1H1+25544X1H0+23590.625x>P1+23090.625m計25951X2H1+25451冷h0+23506.25xbp1+23006.25價。+25858總5+25358X3H0+23421.875XP1+22921.875xpg+25765X4H1+25265%H0+23337.5X5P1+22837.5腳。+25672為5+25172卻。+23253.125x)P1+22753.125科0+25579X5H1+25079X5H0+23168.

8、75X7P1+22668.75»P0+25486*H1+24986X7H0+23084.37501+22584.375腳。+25393X8H1+24893xhq-674.138約束條件見下：X1P1=0X1H0=0X1P1+X1P0+X1H1+X1H0<1X2P1+X2P0+X2H1+X2H0<1X3P1+X3P0+X3H1+X3H001X4P1+X4P0+X4H1+X4H001X5P1+X5P0+X5H1+X5H0<1X6P1+X6P0+X6H1+X5H0<1X7P1+X7P0+X7H1+X7H001X8P1+X8P0+X8H1+X3H0<1約束條件：

9、安全庫存的要求是周末庫存水平必須至少達到下周需求水平的80%125+100*(X1P1+X1P0)-55>55*80%143+80*(X1H1+X1H0)-38>38*80%125+100*(X1P1+X1P0+X2P1+X2P0)-55-55>44*80%143+80*(X1H1+X1H0+X2H1+X2H0)-38-38>30*80%125+100*(X1P1+X1P0+X2P1+X2P0+X3P1+X3P0)-55-55-44>0143+80*(X1H1+X1H0+X2H1+X2H0+X3H1+X3H0)-38-38-30>0125+100*(X1P1

10、+X1P0+X2P1+X2P0+X3P1+X3P0+X4P1+X4p0)-55-55-44145*80%143+80*(X1H1+X1H0+X2H1+X2H0+X3H1+X3H0+X4H1+X4H0)-38-38-30>48*80%125+100*(X1P1+X1P0+X2P1+X2P0+X3P1+X3P0+X4P1+X4P0+X5P1+X5P0)-55-55-44-45>45*80%143+80*(X1H1+X1H0+X2H1+X2H0+X3H1+X3H0+X4H1+X4H0+X5H1+X5H0)-38-38-30-48>48*80%125+100*(X1P1+X1P0+X

11、2P1+X2P0+X3P1+X3P0+X4P什X4P0+X5P1+X5P0+X6P1+X3P0)-55-55-44-45-45>36*80%143+80*(X1H1+X1H0+X2H1+X2H0+X3H1+X3H0+X4H1+X4H0+X5H1+X5H0+X6H1+XsH0)-38-38-30-484858*80%125+100*(X1P1+X1P0+X2P1+X2P0+X3P1+X3P0+X4P什X4P0+X5P1+X5P0+X6P1+X5P0+X7P1+X7P0)-55-55-44-45-45-36>35*80%143+80*(X1H1+X1H0+X2H1+X2H0+X3H1+

12、X3H0+X4H1+X4H0+X5H1+X5H0+X6H1+X3H0+X7H1+X7H0)-38-38-30-48-48-58>57*80%125+100*(X1P1+X1P0+X2P1+X2P0+X3P什X3P0+X4P什X4P0+X5P什X5P0+X6P1+X5P0+X7P1+X7P0+X8P1+X8P0)-55-55-44-45-45-36-35>35*80%143+80*(X1H1+X1H0+X2H1+X2H0+X3H1+X3H0+X4H1+X4H0+X5H1+X5H0+X6H1+X3H0+X7H1+X7H0+X8H1+XBH0)-38-38-30-48-48-58-57&

13、gt;58*80%約束條件：如果換線，換線生產的產品必須與上一周生產的不同：X1P0-X2P0-X2H1>OX1H1-X2P1-X2H0>OX2P1+X2P0-X3P0-X3H1>0X2H1+X2H0"X3P1-X3H010X3P1+X3P0-X4P0-X4H1>0X3H1+X3H0-X4P1-X4H0>0X4P1+X4P0-X5P0-X5H1?0X4H1+X4H0-X5P1-X5H0>0X5P1+X5P0-X6P0-X6H1>0X5Hl+X5H0"X6P1-X6H0?0X6P1+X6P0-X7P0X7H1>0X6H1+X6H

14、0-X7P1-X7H0>0X7P1+X7PO-X8P0-X8H1>0X7H1+X7H0-X8P1-X8H0>0Xjk=0,12）軟件計算結果見下:1生08312015-12-1115:岷5口下午20ES-I2-I1瓜口由50下牛如i&s-iii出岷期下早加學m拈附so7牛上）MeisiLWiVdrmbteSuhiltibHValueUnitCosllm四川前TcallUdft隔UbofiRedbieedCast-15HimXIU23,6/b.OUOOGubasic2X2I.ODOO23jz$.00(n23,17.000023,175.MMa4hound302EJ044

15、.OCKHd%.044.maoWLwimJ4X40劉244OOOOaflLajxiuP梏utiJiw92JMJOHI*tiGundXSl.UUUU2J,UHUBJOU打陽U1JUU羽WWL&JIMJ1boundfxru02b如JMJIXJIboundh0a25,451.MMartbound9XS023,50625MG23,5t)6_2G00WLuuimJ10XID1onoo23.00C250n2a.OOG.2GnO?XOOG2nMi遍licHjniJ11X11u黑H山IM1IHI92bJ8E)<JINIIMInibound12X120XiJbUUUUUuZb-JUUIMJ金bou

16、rvd13XUu2X421tteUUu23,*2IIWJIMJ&b4undHXH0221.00a22,921«S00atbound15X151ODODODOO25,花工000。25J5OOM.btPUIMl1GX1Gn判jo;mnnn現湖fmonh!IioijimJ17XI?02.33?SAIII023U3S7JDNIniliHUltdWK1U0豌87smMQ2?,®J?.SUW械bound19xiuu2S.fr.WWq1bound20X2O1ODOD25J72ODW29J72.00002SJ720000闔bound21X21023.2531300023>2*

17、i3J300LsimJnX2?f)77.7313IW1q廿hnd23X?3n打3劉III1IWI035JST9OOWrdtinunii24X241oouo25,0?3UUUU2S?D.aU&b#und25XS5QQ加阻兩川浦boumj?£X26022.66S750002Z；66B.75Waflbound27X370K.486OOM025,<®BOOM演bviind?fiK?Bnmon0川丐加naanrrihoijnrlKIX?!lnzi.nfwrnivi0，工新4XIIWrrihrMjnrl和KW0裳弼劉MJ022.5卅制W&hound31網Q汴和OD

18、OOQ過弗3IMJOUAbound32X32024riSS3ODODQN，S93.O0B0aiboundFunctiofl(Miri卜1W.2B7TOO1508:51|20iS-r2-ii1量曦MTV2-111左口8:5flF午201Kl211長。正切下阡2015-12tl15：。決EOF午*LehHcinil竄在(hrKijliijriRigtrtHxiilSiriftSUlL<Sur|i|ij4StkmJuftiPltiJH1Cl0-dU皿小.。刖2C20=0025,544.0000飛C3ionoDt=10000n04口1UIKIU<=1imiMiu05LbLUUUUC-LUU

19、UUuuGC£10000c-100000D7C7IjfiMO<=1.00000DCDinnooC1nooona!1CMu<-1uuuu1LUUU0u1DCIUuLUUUOTLIOOOD11C110>=Q0012C12n>=ana13cnoA10n口C14u>-uuD15Clb0>-GuU1ECIG0>=00D17C170>0nD10cmIB>>0i01DC19U>-uuD20C2D0>=d0021C?10>ann?CJ21nnnn>-nlirwinnDCZJu>-uuD21匚ZM0>-au

20、u25C25100.0000>=-260000iz&oaoo0邪50>7fionfl7Msrwinn27匕？7nnm>=2(17011(179.8000D孤C2Uu>-auuuu4JUIMIUD29UZS3go0002S.QD0U27L0MU030JO0A-37.0000370000031ninonnnn>=65on«nn32CJ?etoooo>-i41111n7fl川mno33CJ33IJ0UHIlligUD.DUOQ190JJ0UI0CM1600000粗*MW110EMQD3SDTiikim>147noon15?200(n3Rm;

21、240nnrtn>=1D540MJmcimnn3CJ7soa.oau1V100UU11MOW)a的匚弼Z4V.UMM)X16£6D0U"4皿口039匚，9300000021B000Q82.000004n7ionoun770400019冊onnV3）驗證結果是否與實際相符，并作分析:庫存成本+制造成本+轉換成本最小為145,287.9美元。經過驗證，計算結果與實際相符。第1,2,3周均不換線生產P；第4周換線生產H;第5,6周不換線生產H,第7,8周停產。由于七葉樹制造廠在使用生產線生產P型發動機頭后關閉了一周，所以C1=0和C2=0,假如在生產前可以根據需求決定換線與

22、不換線和生產P或者H,那么生產P并換線，對應的成本是23,675,;生產H并不換線，對應的成本是25,544美元。C2-C10表明每周如果生產，涉及的決策變量中僅有一個可以是1。C3-C40m在的狀況已經是最優，約束條件的左邊或者右邊數值的變化并不會帶來庫存成本+制造成本+轉換成本最小值的變化。C9和C10是停產。C22表明第4周換線并生產HoC11-C21和C23-C24表明均未換線。C25表明第1周生產100個P,并有結余126個。C26表明第1周不生產H,有累計結余74.6個。C27表明從第1周到第2周累計生產200個P,并有累計結余179.8個C28表明從第1周到第2周均不生產H,有累計結余43個。C29表明從第1周到第3周累計生產300個P,并有累計結余271個。C30表明從第1周到第3周均不生產H,有累計結余37個。C31表明從第1周到第4周累計生產300個P,并有累計結余235個。C32表明從第1周到第4周累計生產80個H,有累計結余78.6個。C33表明從第1周到第5周累計生產300個P,并有累計結余190個。C34表明從第1周到第5周累計生產160個H,有累計結余110.6個。C35表明從第1周到第6周累計生