有轉(zhuǎn)換成本的生產(chǎn)計(jì)劃

1、案例題目：有轉(zhuǎn)換成本的生產(chǎn)計(jì)劃七葉樹制造廠(BuckeyeManufacturing)是為了卡車生產(chǎn)發(fā)動(dòng)機(jī)頭的制造企業(yè)。生產(chǎn)發(fā)動(dòng)機(jī)頭的生產(chǎn)線非常復(fù)雜，有900英尺長(zhǎng)。這條生產(chǎn)線生產(chǎn)兩種類型的發(fā)動(dòng)機(jī)頭：P型機(jī)頭和H型機(jī)頭。P頭在重型卡車?yán)锸褂?，H頭在小型卡車?yán)锸褂?。因?yàn)樵谝欢〞r(shí)間只能生產(chǎn)一種類型的發(fā)動(dòng)機(jī)頭，生產(chǎn)線啟動(dòng)后只能生產(chǎn)P型機(jī)頭或者生產(chǎn)H型機(jī)頭，不能同時(shí)生產(chǎn)兩種類型的機(jī)頭。轉(zhuǎn)換發(fā)生在每個(gè)周末，從P型機(jī)頭轉(zhuǎn)換變成H型機(jī)頭的成本為500美元，反過(guò)來(lái)也是這樣。當(dāng)生產(chǎn)P型機(jī)頭時(shí)，最大的產(chǎn)出率為每周100單位；當(dāng)生產(chǎn)H型機(jī)頭時(shí)，最大生產(chǎn)率為每周80單位。七葉樹制造廠在使用生產(chǎn)線生產(chǎn)P型發(fā)動(dòng)機(jī)頭后關(guān)閉

2、了一周。公司經(jīng)理想安排未來(lái)8周的生產(chǎn)和生產(chǎn)轉(zhuǎn)換。當(dāng)前，七葉樹的庫(kù)存包括125單位的P型發(fā)動(dòng)機(jī)頭和143單位的H型發(fā)送機(jī)頭。存貨的年庫(kù)存費(fèi)用是存貨價(jià)值的19.5%°P型發(fā)動(dòng)機(jī)頭的生產(chǎn)成本是225美元，H型發(fā)動(dòng)機(jī)頭的生產(chǎn)成本是310美元。安排生產(chǎn)計(jì)劃的目標(biāo)是使制造成本加上庫(kù)存成本和轉(zhuǎn)換成本的總和最小化。七葉樹收到下面來(lái)自客戶(機(jī)頭組裝廠)在未來(lái)9個(gè)星期的需求訂單。安全庫(kù)存的要求是周末庫(kù)存水平必須至少達(dá)到下周需求水平的80%。產(chǎn)品需求周P型發(fā)動(dòng)機(jī)頭H型發(fā)動(dòng)機(jī)頭1553825538344304005454864548736588355793558管理報(bào)告為七葉樹的經(jīng)理準(zhǔn)備一份報(bào)告，闡述關(guān)于未

3、來(lái)8周的生產(chǎn)和生產(chǎn)轉(zhuǎn)換計(jì)劃。一定要注意,按照這樣的生產(chǎn)計(jì)劃，總成本是多少，多少來(lái)源于庫(kù)存成本，多少來(lái)源于生產(chǎn)轉(zhuǎn)換成本。精選范本案例分析：1)建立模型：設(shè)定決策變量Xjk,1=第1,2,3,4,5,6,7,8周;j=P,H代表生產(chǎn)機(jī)頭類型；k=1or0,1代表轉(zhuǎn)換生產(chǎn)，0代表不轉(zhuǎn)換生產(chǎn)；年庫(kù)存費(fèi)用是存貨價(jià)值的19.5%,那么周庫(kù)存費(fèi)用=19.5%/52=0.375%勺存貨價(jià)值;假設(shè)安全庫(kù)存的要求是每周末庫(kù)存水平必須至少達(dá)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(kù)存成本+制造成本+轉(zhuǎn)換成本最小的目標(biāo)函數(shù)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(jì)25951X2H1+25451冷h0+23506.25xbp1+23006.25價(jià)。+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(kù)存的要求是周末庫(kù)存水平必須至少達(dá)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(chǎn)的產(chǎn)品必須與上一周生產(chǎn)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(jì)算結(jié)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(xué)m拈附so7牛上）MeisiLWiVdrmbteSuhiltibHValueUnitCosllm四川前TcallUdft隔UbofiRedbieedCast-15HimXIU23,6/b.OUOOGubasic2X2I.ODOO23jz$.00(n23,17.000023,175.MMa4hound302EJ044

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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(wǎng)Q汴和OD

18、OOQ過(guò)弗3IMJOUAbound32X32024riSS3ODODQN，S93.O0B0aiboundFunctiofl(Miri卜1W.2B7TOO1508:51|20iS-r2-ii1量曦MTV2-111左口8:5flF午201Kl211長(zhǎng)。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(cè)onnV3）驗(yàn)證結(jié)果是否與實(shí)際相符，并作分析:庫(kù)存成本+制造成本+轉(zhuǎn)換成本最小為145,287.9美元。經(jīng)過(guò)驗(yàn)證，計(jì)算結(jié)果與實(shí)際相符。第1,2,3周均不換線生產(chǎn)P；第4周換線生產(chǎn)H;第5,6周不換線生產(chǎn)H,第7,8周停產(chǎn)。由于七葉樹制造廠在使用生產(chǎn)線生產(chǎn)P型發(fā)動(dòng)機(jī)頭后關(guān)閉了一周，所以C1=0和C2=0,假如在生產(chǎn)前可以根據(jù)需求決定換線與

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