管理运筹学案例分析.doc

管理运筹学课程设计目 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2.72.8Mcal/kg2.7Mcal/kg2.65Mcal/kg粗蛋白135145g/kg135145g/kg151g/kg粗纤维50g/kg45g/kg20g/kg赖氨酸5.6g/kg5.6g/kg6.8g/kg蛋氨酸2.5g/kg2.6g/kg6g/kg钙2340g/kg30g/kg33g/kg有效磷4.66.5g/kg5g/kg3g/kg食盐3.7g/kg3.7g/kg3g/kg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。（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+1.61x82.778x1+114x2+142x3+117x4+402x5+360x6+450x7+170x813578x1+114x2+142x3+117x4+402x5+360x6+450x7+170x814516x1+22x2+95x3+72x4+49x5+113x6+108x8452.3x1+3.4x2+6.0x3+6.5x4+24.1x5+8.1x6+29.1x7+10.6x85.61.2x1+1.7x2+2.3x3+2.7x4+5.1x5+7.1x6+11.8x7+2.2x8+980x92.60.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11300.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x951000x12=3.7X1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12=1X10.4,x20.1,x30.1,x40.15,x50.1,x60.03,x70.05,x80.03,X1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x120(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+1.61x82.73.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x82.878x1+114x2+142x3+117x4+402x5+360x6+450x7+170x813578x1+114x2+142x3+117x4+402x5+360x6+450x7+170x814516x1+22x2+95x3+72x4+49x5+113x6+108x8502.3x1+3.4x2+6.0x3+6.5x4+24.1x5+8.1x6+29.1x7+10.6x85.61.2x1+1.7x2+2.3x3+2.7x4+5.1x5+7.1x6+11.8x7+2.2x8+980x92.50.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11230.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11400.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x94.60.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x96.51000x12=3.7X1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12=1X10.4,x20.1,x30.1,x40.15,x50.1,x60.03,x70.05,x80.03,X1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x120(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：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+2.4x132.778x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8+38x1313578x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8+38x1314516x1+22x2+95x3+72x4+49x5+113x6+108x8+120x13452.3x1+3.4x2+6.0x3+6.5x4+24.1x5+8.1x6+29.1x7+10.6x85.61.2x1+1.7x2+2.3x3+2.7x4+5.1x5+7.1x6+11.8x7+2.2x8+980x9+0.92x132.60.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11+0.15x13300.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x90.17x1351000x12=3.7X1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12+x13=1X10.4,x20.1,x30.1,x40.15,x50.1,x60.03,x70.05,x80.03,X1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x120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+2.4x132.73.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x8+2.4x132.878x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8+38x1313578x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8+38x1314516x1+22x2+95x3+72x4+49x5+113x6+108x8+120x13502.3x1+3.4x2+6.0x3+6.5x4+24.1x5+8.1x6+29.1x7+10.6x85.61.2x1+1.7x2+2.3x3+2.7x4+5.1x5+7.1x6+11.8x7+2.2x8+980x9+0.92x132.50.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11+0.15x13230.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11+0.15x13400.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x9+0.17x134.60.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x9+0.17x136.51000x12=3.7X1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12+x13=1X10.4,x20.1,x30.1,x40.15,x50.1,x60.03,x70.05,x80.03,X1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x120(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+1.61x82.6578x1+114x2+142x3+117x4+402x5+360x6+450x7+170x815116x1+22x2+95x3+72x4+49x5+113x6+108x8202.3x1+3.4x2+6.0x3+6.5x4+24.1x5+8.1x6+29.1x7+10.6x86.81.2x1+1.7x2+2.3x3+2.7x4+5.1x5+7.1x6+11.8x7+2.2x8+980x960.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11330.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x931000x12=3X1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12=1X10.4,x20.1,x30.1,x40.15,x50.1,x60.03,x70.05,x80.03,X1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x120三、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：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。如图C-1： 图 C-1如图C-2显示求解状态： 图 C-2 （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。如图C-3 图C-3如图C-4为显示求解状态：图C-4（3） 原料结构调整（4） 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。 肉用种鸡公司标准在调整后方案，用WinQSB来处理数据如图C-5：图C-5 点击Solve and AnalyzeSolve the problem问题已解决且存在，求解结果如图C-6所示：图C-6 肉用种鸡国家标准在调整后方案，用WinQSB来处理数据如图C-7：图C-7图C-8点击Solve and AnalyzeSolve the problem问题已解决且存在，求解结果如图C-8所示：（