管理运筹学案例分析

管理运筹学课程设计1目录一、问题描述二、建立模型并分析三、程序设计建立问题，输入数据对数学模型求解（1）按照肉用种鸡公司标准（2）按照肉用种鸡国家标准（3）原材料结构调整（4）求产蛋鸡的最优饲料配方方案（5）价格系数灵敏度分析管理运筹学课程设计2一、问题描述【案例C-2】配料问题某饲料公司生产鸡混合饲料，每千克饲料所需营养质量要求如表C-4所示。表C-4公司计划使用的原料有玉米、小麦、麦麸、米糠、豆饼、菜子饼、鱼粉、槐叶粉、DL-蛋氨酸、骨粉、碳酸钙和食盐等12种原料。各种原料的营养成分含量及价格见表C-5。表C-5公司根据原料来源，还要求1吨混合饲料中原料的含量为:玉米不低于400kg，小麦不低于100kg，麦麸不低于100kg，米糠不低于150kg，豆饼不超过100kg，菜子饼不低于30kg，鱼粉不低于50kg，槐叶粉不低于30kg，DL-蛋氨酸、骨粉、碳酸钙适量。营养成分肉用种鸡国家标准肉用种鸡公司标准产蛋鸡标准代谢能2.7～2.8Mcal/kg≥2.7Mcal/kg≥2.65Mcal/kg粗蛋白135～145g/kg135～145g/kg≥151g/kg粗纤维﹤50g/kg≤45g/kg≤20g/kg赖氨酸≥5.6g/kg≥5.6g/kg≥6.8g/kg蛋氨酸≥2.5g/kg≥2.6g/kg≥6g/kg钙23～40g/kg≥30g/kg≥33g/kg有效磷4.6～6.5g/kg≥5g/kg≥3g/kg食盐3.7g/kg3.7g/kg3g/kg变量原料单价元/kg代谢能Mcal/kg粗蛋白g/kg粗纤维g/kg赖氨酸g/kg蛋氨酸g/kg钙g/kg有机磷g/kg食盐g/kgX1玉米0.683.3578162.31.20.70.3X2小麦0.723.08114223.41.70.60.34X3麦麸0.231.781429562.30.310X4米糠0.222.1117726.52.7113X5豆饼0.372.44024924.15.13.25X6菜子饼0.321.623601138.17.15.38.4X7鱼粉1.542.8450029.111.86327X8槐叶粉0.381.6117010810.62.244X9DL-蛋氨酸23980X10骨粉0.56300140X11碳酸钙1.12400X12食盐0.421000管理运筹学课程设计3（1）按照肉用种鸡公司标准，求1kg配合饲料中每种原料各配多少成本最低，建立数学模型并求解。（2）按照肉用种鸡国家标准，求1kg配合饲料中每种原料各配多少成本最低。（3）公司采购了一批花生饼，单价是0.6元/kg，代谢能到有机磷的含量分别为（2.4,38,120,0,0.92,0.15,0.17），求肉用种鸡成本最低的配料方案。（4）求产蛋鸡的最优饲料配方方案。（5）公司考虑到未来鱼粉、骨粉和碳酸钙将要涨价，米糠将要降价，价格变化率都是原来的r%。试对两种产品配方方案进行分析。说明：以上5个问题独立求解和分析，如在问题（3）中只加花生饼，其他方案则不加花生饼。二、建立模型并分析(1)按照肉用种鸡公司标准，求1kg配合饲料中每种原料各配多少成本最低，建立数学模型并求解。Minz=0.68x1+0.72x2+0.23x3+0.22x4+0.37x5+0.32x6+1.54x7+0.38x8+23x9+0.56x10+0.12x11+0.42x123.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x8≥2.778x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8≥13578x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8≤14516x1+22x2+95x3+72x4+49x5+113x6+108x8≤452.3x1+3.4x2+6.0x3+6.5x4+24.1x5+8.1x6+29.1x7+10.6x8≥5.61.2x1+1.7x2+2.3x3+2.7x4+5.1x5+7.1x6+11.8x7+2.2x8+980x9≥2.60.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11≥300.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x9≥51000x12=3.7X1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12=1X1≥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)按照肉用种鸡国家标准，求1kg配合饲料中每种原料各配多少成本最低。Minz=0.68x1+0.72x2+0.23x3+0.22x4+0.37x5+0.32x6+1.54x7+0.38x8+23x9+0.56x10+0.12x11+0.42x123.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x8≥2.73.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x8≤2.878x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8≥13578x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8≤14516x1+22x2+95x3+72x4+49x5+113x6+108x8﹤502.3x1+3.4x2+6.0x3+6.5x4+24.1x5+8.1x6+29.1x7+10.6x8≥5.61.2x1+1.7x2+2.3x3+2.7x4+5.1x5+7.1x6+11.8x7+2.2x8+980x9≥2.50.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11≥230.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11≤400.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x9≥4.6管理运筹学课程设计40.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x9≤6.51000x12=3.7X1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12=1X1≥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(3)公司采购了一批花生饼，单价是0.6元/kg，代谢能到有机磷的含量分别为（2.4,38,120,0,0.92,0.15,0.17），求肉用种鸡成本最低的配料方案。新增一种原料为x13,约束条件不变。所以两种肉用种鸡的配料方案的问题的数学模型为：①按照肉用种鸡公司标准：Minz=0.68x1+0.72x2+0.23x3+0.22x4+0.37x5+0.32x6+1.54x7+0.38x8+23x9+0.56x10+0.12x11+0.42x12+0.6x133.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x8+2.4x13≥2.778x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8+38x13≥13578x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8+38x13≤14516x1+22x2+95x3+72x4+49x5+113x6+108x8+120x13≤452.3x1+3.4x2+6.0x3+6.5x4+24.1x5+8.1x6+29.1x7+10.6x8≥5.61.2x1+1.7x2+2.3x3+2.7x4+5.1x5+7.1x6+11.8x7+2.2x8+980x9+0.92x13≥2.60.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11+0.15x13≥300.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x90.17x13≥51000x12=3.7X1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12+x13=1X1≥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≥0②按照肉用种鸡国家标准：Minz=0.68x1+0.72x2+0.23x3+0.22x4+0.37x5+0.32x6+1.54x7+0.38x8+23x9+0.56x10+0.12x11+0.42x12+0.6x133.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x8+2.4x13≥2.73.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x8+2.4x13≤2.878x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8+38x13≥13578x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8+38x13≤14516x1+22x2+95x3+72x4+49x5+113x6+108x8+120x13﹤502.3x1+3.4x2+6.0x3+6.5x4+24.1x5+8.1x6+29.1x7+10.6x8≥5.61.2x1+1.7x2+2.3x3+2.7x4+5.1x5+7.1x6+11.8x7+2.2x8+980x9+0.92x13≥2.50.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11+0.15x13≥230.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11+0.15x13≤400.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x9+0.17x13≥4.6管理运筹学课程设计50.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x9+0.17x13≤6.51000x12=3.7X1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12+x13=1X1≥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(4)求产蛋鸡的最优饲料配方方案。Minz=0.68x1+0.72x2+0.23x3+0.22x4+0.37x5+0.32x6+1.54x7+0.38x8+23x9+0.56x10+0.12x11+0.42x123.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x8≥2.6578x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8≥15116x1+22x2+95x3+72x4+49x5+113x6+108x8≤202.3x1+3.4x2+6.0x3+6.5x4+24