有轉(zhuǎn)換成本的生產(chǎn)計(jì)劃

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。案例分析：1）建立模型：設(shè)定決策變量Xijk，i=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%的存貨價(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%指的是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*(x1P1+x1P0+x2P1+x2P0+x3P1+x3P0+x4P1+x4P0+x5P1+x5P0+x6P1+x6P0+x7P1+x7P0+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+x3P1+x3H1+x4P1+x4H1+x5P1+x5H1+x6P1+x6H1+x7P1+x7H1+x8P1+x8H1)+225*125*0.375%*8+225*100*(x1P1+x1P0)*0.375%*8-225*55*0.375%*8+310*143*0.375%*8+310*80*(x1H1+x1H0)*0.375%*8-310*38*0.375%*8+225*100*(x2P1+x2P0)*0.375%*7-225*55*0.375%*7+310*80*(x2H1+x2H0)*0.375%*7-310*38*0.375%*7+225*100*(x3P1+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*(x5P1+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*80*(x8H1+x8H0)*0.375%-310*57*0.375%=23675x1P1+23175x1P0+26044x1H1+25544x1H0+23590.625x2P1+23090.625x2P0+25951x2H1+25451x2H0+23506.25x3P1+23006.25x3P0+25858x3H1+25358x3H0+23421.875x4P1+22921.875x4P0+25765x4H1+25265x4H0+23337.5x5P1+22837.5x5P0+25672x5H1+25172x5H0+23253.125x6P1+22753.125x6P0+25579x6H1+25079x6H0+23168.75x7P1+22668.75x7P0+25486x7H1+24986x7H0+23084.375x8P1+22584.375x8P0+25393x8H1+24893x8H0-674.138約束條件見(jiàn)下：x1P1=0x1H0=0x1P1+x1P0+x1H1+x1H0≤1x2P1+x2P0+x2H1+x2H0≤1x3P1+x3P0+x3H1+x3H0≤1x4P1+x4P0+x4H1+x4H0≤1x5P1+x5P0+x5H1+x5H0≤1x6P1+x6P0+x6H1+x6H0≤1x7P1+x7P0+x7H1+x7H0≤1x8P1+x8P0+x8H1+x8H0≤1約束條件：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+x1P0+x2P1+x2P0+x3P1+x3P0+x4P1+x4P0)-55-55-44≥45*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+x2P1+x2P0+x3P1+x3P0+x4P1+x4P0+x5P1+x5P0+x6P1+x6P0)-55-55-44-45-45≥36*80%143+80*(x1H1+x1H0+x2H1+x2H0+x3H1+x3H0+x4H1+x4H0+x5H1+x5H0+x6H1+x6H0)-38-38-30-48-48≥58*80%125+100*(x1P1+x1P0+x2P1+x2P0+x3P1+x3P0+x4P1+x4P0+x5P1+x5P0+x6P1+x6P0+x7P1+x7P0)-55-55-44-45-45-36≥35*80%143+80*(x1H1+x1H0+x2H1+x2H0+x3H1+x3H0+x4H1+x4H0+x5H1+x5H0+x6H1+x6H0+x7H1+x7H0)-38-38-30-48-48-58≥57*80%125+100*(x1P1+x1P0+x2P1+x2P0+x3P1+x3P0+x4P1+x4P0+x5P1+x5P0+x6P1+x6P0+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+x6H0+x7H1+x7H0+x8H1+x8H0)-38-38-30-48-48-58-57≥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≥0x1H1-x2P1-x2H0≥0x2P1+x2P0-x3P0-x3H1≥0x2H1+x2H0-x3P1-x3H0≥0x3P1+x3P0-x4P0-x4H1≥0x3H1+x3H0-x4P1-x4H0≥0x4P1+x4P0-x5P0-x5H1≥0x4H1+x4H0-x5P1-x5H0≥0x5P1+x5P0-x6P0-x6H1≥0x5H1+x5H0-x6P1-x6H0≥0x6P1+x6P0-x7P0-x7H1≥0x6H1+x6H0-x7P1-x7H0≥0x7P1+x7P0-x8P0-x8H1≥0x7H1+x7H0-x8P1-x8H0≥0Xijk=0,12）軟件計(jì)算結(jié)果見(jiàn)下：3）驗(yàn)證結(jié)果是否與實(shí)際相符