纺织厂案例
指导老师：刘云霞
班级：2009级MBA脱产班第五组
组员：池淑娟，陈勇军，肖荆波
，吴威，赵磊唐韵，张先觉，曾飞
案例一
设：织物
1、织物
2、织物
3、织物
4、织物5的外购数量分别为X
1、x
2、x
3、x
4、x5；织物
1、织物
2、织物
3、织物
4、织物5在帝备纺织机上的生产时间分别为x
6、x
7、x
8、x
9、x10；织物
3、织物
4、织物5在常规纺织机上的生产时间分别为x
11、x
12、x13,目标：总利润
max
z=(0.99-0.80)x1+(0.86-0.70)x2+(1.10-0.60)x3+(1.24-0.70)x4+(0.70-0.70)x5+(0.99-0.66)*4.63x6+(0.86-0.55)*4.63x7+(1.10-0.49)*5.23(x8+x11)+(1.24-0.51)*5.23(x9+x
12)+(0.70-0.50)*4.17(x10+x13)
s.t.
x6+x7+x8+x9+x10
x11+x12+x13
x1+4.63x6=16500
x2+4.63x7=22000
x3+5.23x8+5.23x11=62000
x4+5.23x9+5.23x12=7500
x5+4.17x10+4.17x13=62000
变量≥0
Max
z=0.19x1+0.16x2+0.5x3+0.54x4+1.5279x6+1.4353x7+3.1903x8+3.1903x11+3.8179x12+3.8179x12+0.834X13+0.834x13
s.t.
x6+x7+x8+x9+x10
x11+x12+x13
x1+4.63x6=16500
x2+4.63x7=22000
x3+5.23x8+5.23x11=62000
x4+5.23x9+5.23x12=7500
x5+4.17x10+4.17x13=62000
变量≥0
输出结果：
OBJECTIVE FUNCTION VALUE
1)62531.49
VARIABLEVALUEREDUCED COST
X111831.2001950.000000
X20.0000000.010000
X334292.1914060.000000
X40.0000000.080000
X61008.3801270.000000
X74751.6196290.000000
X80.0000000.072900
X95297.8598630.000000
X110.0000000.072900
X121434.0344240.000000
X130.0000000.072900
X1314868.1054690.000000
X50.0000000.062038
ROWSLACK OR SURPLUSDUAL PRICES
2)0.0000000.648200
3)0.0000000.575300
4)0.0000000.190000
5)0.0000000.170000
6)0.0000000.500000
7)0.0000000.620000
8)0.0000000.062038
NO.ITERATIONS=0
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLECURRENTALLOWABLEALLOWABLE
COEFINCREASEDECREASE
X10.1900000.0157450.010000
X20.1600000.010000INFINITY
X30.5000000.1100000.013939
X40.5400000.080000INFINITY
X51.5279000.0463000.072900
X61.435300INFINITY0.046300
X73.1903000.072900INFINITY
X83.1903000.0729000.575300
X93.8179000.072900INFINITY
X113.817900INFINITY0.072900
X120.8340000.072900INFINITY
X130.834000INFINITY0.072900
X50.0000000.062038INFINITY
RIGHTHAND SIDE RANGES
ROWCURRENTALLOWABLEALLOWABLE
RHSINCREASEDECREASE
25760.0000002555.3347171008.380127
321600.0000006556.8242195297.859863
416500.000000INFINITY11831.200195
522000.0000004668.79980511831.200195
662000.000000INFINITY34292.191406
77500.00000027707.8066417500.000000
862000.00000022092.07617227341.957031
2.计划利润62531.49
各部分的比重：织物1外购所获利润2247.928，织物3外购所获利润17146，织物1自产(帝备纺织机)所获利润1540.7，织物2自产(帝备纺织机)所获利润6820，织物3自产(常规纺织机)所获利润16901.76，织物4自产(常规纺织机)所获利润5474.8686，织物5自产(常规纺织机)所获利润12400
3.帝备纺织机生产时间每增加1小时，总利润增加0.6482。添加一台该纺织机，每月增加生产时间720小时，在其允许增加量的范围之内，故其对偶价格不变，总利润将增加0.6482*720，即466.7
5.目标如果是总费用最小化，则目标函数为：
Min
z=0.8X1+0.7X2+0.6y3+0.7X4+0.7X5+0.66*4.63x6+0.55*4.63x7+0.49*5.23x8+0.51*5.23x9+0.5*4.17x10+0.49*5.23x11+0.51*5.23x12+0.5*4.17x13
即min z=0.8X1+0.7X2+0.6X3+0.7X4+0.7X5+3.0558x6+2.5465x7+2.5627x8+2.6673x9+2.085x10+2.5627x11+2.6673x12+2.085x13
输出结果：
OBJECTIVE FUNCTION VALUE
1)93623.51
VARIABLEVALUEREDUCED COST
X111831.2001950.000000
X20.0000000.010000
X334292.1914060.000000
X40.0000000.080000
X50.0000000.062038
X111008.3801270.000000
X124751.6196290.000000
X130.0000000.072900
X140.0000000.072900
X150.0000000.072900
X235297.8598630.000000
X241434.0344240.000000
X2514868.1054690.000000
ROWSLACK OR SURPLUSDUAL PRICES
2)0.0000000.648200
3)0.0000000.575300
4)0.000000-0.800000
5)0.000000-0.690000
6)0.000000-0.600000
7)0.000000-0.620000
8)0.000000-0.637962
NO.ITERATIONS=7
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLECURRENTALLOWABLEALLOWABLE
COEFINCREASEDECREASE
X10.8000000.0100000.015745
X20.700000INFINITY0.010000
X30.6000000.0139390.110000
X40.700000INFINITY0.080000
X50.700000INFINITY0.062038
X63.0558000.0729000.046300
X72.5465000.046300INFINITY
X82.562700INFINITY0.072900
X92.667300INFINITY0.072900
X102.085000INFINITY0.072900
X112.5627000.5753000.072900
X122.6673000.072900INFINITY
X132.0850000.072900INFINITY
RIGHTHAND SIDE RANGES
ROWCURRENTALLOWABLEALLOWABLE
RHSINCREASEDECREASE
25760.0000002555.3347171008.380127
321600.0000006556.8242195297.859863
416500.000000INFINITY11831.200195
522000.0000004668.79980511831.200195
662000.000000INFINITY34292.191406
77500.00000027707.8066417500.000000
862000.00000022092.07617227341.957031
从输出表可知，最优方案是一样的。最小化的目标函数系数允许增加值与最大化的目标函数系数允许减少值是一样的，最小化的目标函数系数允许减少值与最大化的目标函数系数允许增加值是一样的。这是因为单位成本增加多少就意味着单位利润减少多少。最小化的目标函数系数代表：外购的单位成本与自产(每小时)的单位成本。而最大化的目标函数代表：外购的单位利润与自产(每小时)的单位利润。
