管理运筹学案例分析
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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。
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。
(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+0.42x12
3.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x8≥2.7
78x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8≥135
78x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8≤145
16x1+22x2+95x3+72x4+49x5+113x6+108x8≤45
2.3x1+
3.4x2+6.0x3+6.5x4+2
4.1x5+8.1x6+29.1x7+10.6x8≥
5.6
1.2x1+1.7x2+
2.3x3+2.7x4+5.1x5+7.1x6+11.8x7+2.2x8+980x9≥2.6
0.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11≥30
0.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x9≥5
1000x12=3.7
X1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12=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+0.42x12
3.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x8≥2.7
3.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x8≤2.8
78x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8≥135
78x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8≤145
16x1+22x2+95x3+72x4+49x5+113x6+108x8﹤50
2.3x1+
3.4x2+6.0x3+6.5x4+2
4.1x5+8.1x6+29.1x7+10.6x8≥
5.6
1.2x1+1.7x2+
2.3x3+2.7x4+5.1x5+7.1x6+11.8x7+2.2x8+980x9≥2.5
0.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11≥23
0.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11≤40
0.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x9≥4.6
0.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x9≤6.5
1000x12=3.7
X1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12=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
(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+0.6x13
3.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x8+2.4x13≥2.7
78x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8+38x13≥135
78x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8+38x13≤145
16x1+22x2+95x3+72x4+49x5+113x6+108x8+120x13≤45
2.3x1+
3.4x2+6.0x3+6.5x4+2
4.1x5+8.1x6+29.1x7+10.6x8≥
5.6
1.2x1+1.7x2+
2.3x3+2.7x4+5.1x5+7.1x6+11.8x7+2.2x8+980x9+0.92x13≥
2.6
0.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11+0.15 x13≥30
0.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x90.17x13≥5
1000x12=3.7
X1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12+x13=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+0.6x13
3.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x8+2.4x13≥2.7
3.35x1+3.08x2+1.78x3+2.10x4+2.40x5+1.62x6+2.80x7+1.61x8+2.4x13≤2.8
78x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8+38x13≥135
78x1+114x2+142x3+117x4+402x5+360x6+450x7+170x8+38x13≤145
16x1+22x2+95x3+72x4+49x5+113x6+108x8+120x13﹤50
2.3x1+
3.4x2+6.0x3+6.5x4+2
4.1x5+8.1x6+29.1x7+10.6x8≥
5.6
1.2x1+1.7x2+
2.3x3+2.7x4+5.1x5+7.1x6+11.8x7+2.2x8+980x9+0.92x13≥
2.5
0.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11+0.15x
13≥23
0.7x1+0.6x2+0.3x3+1.0x4+3.2x5+5.3x6+63x7+4.0x8+300x10+400x11+0.15x
13≤40
0.3x1+0.34x2+10.0x3+13.0x4+5.0x5+8.4x6+27x6+4.0x8+140x9+0.17x13≥
4.6