配料問題 運籌學(xué)

配料問題【摘要】【關(guān)鍵詞】1問題描述某飼料公司生產(chǎn)肉用種雞配合飼料，每千克飼料所需營養(yǎng)質(zhì)量要求如表1所示。表1營養(yǎng)成分肉用種雞國家標(biāo)準(zhǔn)肉用種雞公司標(biāo)準(zhǔn)產(chǎn)蛋雞標(biāo)準(zhǔn)代謝能2.7~2.8Mcal/kg≥2.7Mcal/kg≥2.65Mcal/kg粗蛋白135~145g/kg135~145g/kg≥151g/kg粗纖維<50g/kg≤45g/kg≤20g/kg賴氨酸≥5.6g/kg≥5.6g/kg≥6.8g/kg蛋氨酸≥2.5g/kg≥2.6g/kg≥6g/kg鈣23~40g/kg≥30g/kg≥33g/kg有效磷4.6~6.5g/kg≥5g/kg≥3g/kg食鹽3.7g/kg3.7g/kg3g/kg公司計劃使用的原料有玉米，小麥，麥麩，米糠，豆餅，菜子餅，魚粉，槐葉粉，DL-蛋氨酸，骨粉，碳酸鈣和食鹽等12種原料。各原料的營養(yǎng)成分含量及價格見表C－5。公司根據(jù)原料來源，還要求1噸配合飼料中原料的含量為：玉米不低于400kg，小麥不低于100kg，麥麩不低于100kg，米糠不超過150kg，豆餅不超過100kg,菜子餅不低于30kg，魚粉不低于50kg，槐葉粉不低于30kg，DL-蛋氨酸，骨粉，碳酸鈣適量。（1）按照肉用種雞公司標(biāo)準(zhǔn)，求1千克配合飼料中每種原料各配多少成本最低，建立數(shù)學(xué)模型并求解。（2）按照肉用種雞國家標(biāo)準(zhǔn)，求1千克配合飼料中每種原料各配多少成本最低。（3）公司采購了一批花生餅,單價是0.6元/kg，代謝能到有機磷的含量分別為（2.4,38,120,0,0.92,0.15,0.17）,求肉用種雞成本最低的配料方案。（4）求產(chǎn)蛋雞的最優(yōu)飼料配方方案。（5）公司考慮到未來魚粉、骨粉和碳酸鈣將要漲價，米糠將要降價，價格變化率都是原價的r%試對兩種產(chǎn)品配方方案進行分析。說明：以上5個問題獨立求解和分析，如在問題（3）中只加花生餅，其它方案則不加花生餅。表2變量原料單價元/kg代謝能Mcal/kg粗蛋白g/kg粗纖維g/kg賴氨酸g/kg蛋氨酸g/kg鈣g/kg有效磷g/kg食鹽g/kgx1玉米0.683.3578162.31.20.70.3x2小麥0.723.08114223.41.70.60.34x3麥麩0.231.78142956.02.30.310.0x4米糠0.222.10117726.52.71．013.0x5豆餅0.372.404024924.15.13.25.0x6菜餅0.321.623601138.17.15.38.4x7魚粉1.542.80450029.111.86327x8槐葉粉0.381.6117010810.62.24.04.0x9DL-met23.0980x10骨粉0.56300140x11碳酸鈣1.12400x12食鹽0.4210002建模分析（1）按照肉用種雞公司標(biāo)準(zhǔn)，求1千克配合飼料中每種原料各配多少成本最低，建立數(shù)學(xué)模型并求解。有題目要求可知，目標(biāo)是求成本的最小最優(yōu)值，根據(jù)表C-4中每千肉用種雞公司標(biāo)準(zhǔn)飼料所需營養(yǎng)質(zhì)量要求含量數(shù)據(jù)和表C-5中提供的原材料價格數(shù)據(jù)，設(shè)每千飼料所含各種原材料為xj，z表示成本，z=且xj>=0，j=1，2……12。根據(jù)公司對玉米、小麥、麥麩、米糠、豆餅、菜子餅、魚粉、槐葉粉幾種原料的要求，在這個問題中x1>=0.4，x2>=0.1,x3>=0.1，x4<=0.15，x5<=0.1，x6>=0.03，x7>=0.05，x8>=0.03，因此這個問題的數(shù)學(xué)模型可歸納為：minz=0.68*x10.72*x20.23*x30.22*x40.37*x50.32*x61.54*x70.38*x823*x90.56*x101.12*x110.42*x12;約束條件：3.35*x13.08*x21.78*x32.1*x42.4*x51.62*x62.8*x71.61*x8>=2.778*x1114*x2142*x3117*x4402*x5360*x6450*x7170*x8>=13578*x1114*x2142*x3117*x4402*x5360*x6450*x7170*x8<=14516*x122*x295*x372*x449*x5113*x6108*x8<=452.3*x13.4*x26*x36.5*x424.1*x58.1*x629.1*x710.6*x8>=5.61.2*x11.7*x22.3*x32.7*x45.1*x57.1*x611.8*x72.2*x8980*x9>=2.60.7*x10.6*x20.3*x31*x43.2*x55.3*x663*x74*x8300*x10400*x11>=300.3*x10.34*x210*x313*x45*x58.4*x627*x74*x8140*x10>=51000*x12=3.7x1x2x3x4x5x6x7x8x9x10x11x12=1;x1>=0.4;x2>=0.1;x3>=0.1;x4<=0.15;x5<=0.1;x6>=0.03;x7>=0.05;x8>=0.03;x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12>=0;（2）按照肉用種雞國家標(biāo)準(zhǔn)，求1千克配合飼料中每種原料各配多少成本最低。問題用數(shù)學(xué)模型表示，根據(jù)表C-4中每千肉用種雞國家標(biāo)準(zhǔn)飼料所需營養(yǎng)質(zhì)量要求含量數(shù)據(jù)和表C-5中提供的原材料價格數(shù)據(jù)，每千飼料所含各種原材料為xj，z表示成本，z=且xj>=0，j=1，2……12。要求成本最低，即為minz=，根據(jù)公司對玉米、小麥、麥麩、米糠、豆餅、菜子餅、魚粉、槐葉粉幾種原料的要求，在這個問題中x1>=0.4，x2>=0.1,x3>=0.1，x4<=0.15，x5<=0.1，x6>=0.03，x7>=0.05，x8>=0.03，因此這個問題的數(shù)學(xué)模型可歸納為：minz=0.68x10.72x20.23x30.22x40.37x50.32x61.54x70.38x823x90.56x101.12x110.42x123.35x13.08x21.78x32.1x42.4x51.62x62.8x71.61x8>=2.73.35x13.08x21.78x32.1x42.4x51.62x62.8x71.61x8<=2.878x1114x2142x3117x4402x5360x6450x7170x8>=13578x1114x2142x3117x4402x5360x6450x7170x8<=14516x122x295x372x449x5113x6108x8<502.3x13.4x26.0x36.5x424.1x58.1x629.1x710.6x8>=5.61.2x11.7x22.3x32.7x45.1x57.1x611.8x72.2x8980x9>=2.50.7x10.6x20.3x31.0x43.2x55.3x663x74.0x8300x10400x11>=230.7x10.6x20.3x31.0x43.2x55.3x663x74.0x8300x10400x11<=400.3x10.34x210.0x313.0x45.0x58.4x627x74.0x8140x10>=4.60.3x10.34x210.0x313.0x45.0x58.4x627x74.0x8140x10<=6.51000x12=37x1x2x3x4x5x6x7x8x9x10x11x12

=1x1>=0.4,x2>=0.1,x3>=0.1,x4<=0.15,x5<=0.1,x6>=0.03,x7>=0.05,x8>=0.03（1）公司采購了一批花生餅,單價是0.6元/kg，代謝能到有機磷的含量為（2.4,38,120,0,0.92,0.15,0.17）,求肉用種雞成本最低的配料方案。當(dāng)在新增了一種新的原材料時，要對生產(chǎn)結(jié)構(gòu)進行調(diào)整，變量增加x13，約束條件個數(shù)不變。兩種肉用雞配料方案中的目標(biāo)函數(shù)，仍為minz=，因此兩種肉用雞的配料方案的問題的數(shù)學(xué)模型可為：按照肉用種雞公司標(biāo)準(zhǔn)：minz=0.68x10.72x20.23x30.22x40.37x50.32x61.54x70.38x823x90.56x101.12x110.42x120.6x133.35x13.08x21.78x32.1x42.4x51.62x62.8x71.61x82.4x13>=2.778x1114x2142x3117x4402x5360x6450x7170x838x13>=13578x1114x2142x3117x4402x5360x6450x7170x838x13<=14516x122x295x372x449x5113x6108x8120x13<=452.3x13.4x26.0x36.5x424.1x58.1x629.1x710.6x8>=5.61.2x11.7x22.3x32.7x45.1x57.1x611.8x72.2x8980x90.92x13>=2.60.7x10.6x20.3x31.0x43.2x55.3x663x74.0x8300x10400x110.15x13>=300.3x10.34x210.0x313.0x45.0x58.4x627x74.0x8140x100.17x13>=5

1000x12=3.7x1x2x3x4x5x6x7x8x9x10x11x12x13=1x1>=0.4,x2>=0.1,x3>=0.1,x4<=0.15,x5<=0.1,x6>=0.03,x7>=0.05,x8>=0.03按照肉用種雞國家標(biāo)準(zhǔn)：minz=0.68x10.72x20.23x30.22x40.37x50.32x61.54x70.38x823x90.56x101.12x110.42x