模型求解 软件实现 LINGO model: Global optimal solution found max=72*x1+64*x2; Objective value 3360.000 Imilk xl+ x2<50; Total solver iterations: 2 time Variable value Reduced Cost 12*x1+8*x2<480 X120.00000 0.000000 cpc]3*x1<100: X230.00000 0.000000 end Row Slack or Surplus Dual Price 3360.000 1.000000 MLLK0.000000 48.00000 TIME0.000000 2.000000 CPCT40.00000 0.000000 20桶牛奶生产A1,30桶生产A2,利润3360元 c
模型求解 软件实现 LINGO model: max = 72*x1+64*x2; [milk] x1 + x2<50; [time] 12*x1+8*x2<480; [cpct] 3*x1<100; end Global optimal solution found. Objective value: 3360.000 Total solver iterations: 2 Variable Value Reduced Cost X1 20.00000 0.000000 X2 30.00000 0.000000 Row Slack or Surplus Dual Price 1 3360.000 1.000000 MILK 0.000000 48.00000 TIME 0.000000 2.000000 CPCT 40.00000 0.000000 20桶牛奶生产A1 , 30桶生产A2，利润3360元
结果解释 model: Global optimal solution found max=72*x1+64x2; Obiective value: 3360.000 miIk」x1+x2<50; Total solver iterations: 2 time Ⅴ ariableⅤalue Reduced cost 12*x1+8*x2<480 X120.00000 0.000000 cpct3*x1<100; X2 30.00000 0.000000 end Row Slack or Surplus dual Price 13360.000 1000000 原料无剩余←MILK0.0000 48.00000 种时间无剩余←TME 0.000000 2.000000 资加工能力剩余40←CPCT 40.00000 0.000000 源 “资源”剩余为零的约束为紧约束(有效约束)
结果解释 Global optimal solution found. Objective value: 3360.000 Total solver iterations: 2 Variable Value Reduced Cost X1 20.00000 0.000000 X2 30.00000 0.000000 Row Slack or Surplus Dual Price 1 3360.000 1.000000 MILK 0.000000 48.00000 TIME 0.000000 2.000000 CPCT 40.00000 0.000000 model: max = 72*x1+64*x2; [milk] x1 + x2<50; [time] 12*x1+8*x2<480; [cpct] 3*x1<100; end 三 种 资 源 “资源” 剩余为零的约束为紧约束（有效约束） 原料无剩余 时间无剩余 加工能力剩余40
Global optimal solution found 结果解释 Objective value: 3360.000 Total solver iterations: 2最优解下“资源”增加 Variable value Reduced cost1单位时“效益”的增 X120.00000 0.000000 量 X230.00000 0.000000 Row Slack or Surplus Dual Price 影子价格 13360.000 1.000000 MILK0048.00原料增加1单位,利润增长48 TIME0.0002.00000时间增加1单位,利润增长2 CPCT40.000000加能力增长不影响利润 35元可买到1桶牛奶,要买吗?35<48,应该买! 聘用临时工人付出的工资最多每小时几元?2元!
Global optimal solution found. 结果解释 Objective value: 3360.000 Total solver iterations: 2 Variable Value Reduced Cost X1 20.00000 0.000000 X2 30.00000 0.000000 Row Slack or Surplus Dual Price 1 3360.000 1.000000 MILK 0.000000 48.00000 TIME 0.000000 2.000000 CPCT 40.00000 0.000000 最优解下“资源”增加 1单位时“效益”的增 量 影子价格 • 35元可买到1桶牛奶，要买吗? 35 <48, 应该买！ • 聘用临时工人付出的工资最多每小时几元? 2元！ 原料增加1单位, 利润增长48 时间增加1单位, 利润增长2 加工能力增长不影响利润
敏感性分析(“ LINGORanges”) 最优解不变时目标函 Ranges in which the basis is unchanged: 数系数允许变化范围 Objective Coefficient Ranges(约束条件不变) Current Allowable Allowable Variable Coefficient Increase Decrease X172.0000024.000008.000000 x1系数范围(64,96) X264.000900001.00002系数范围(48,72) Righthand side ranges Row Current Allowable Allowable RHS Increase Decrease MLLK50.0000010.000006666667 x1系数由24×3=72 TIVE480.000053.3333380.00000 增加为30×3=90, CPCT 100.0000 INFINITY 40.00000 在允许范围内 A获利增加到30元/kg,应否改变生产计划?不变
Ranges in which the basis is unchanged: Objective Coefficient Ranges Current Allowable Allowable Variable Coefficient Increase Decrease X1 72.00000 24.00000 8.000000 X2 64.00000 8.000000 16.00000 Righthand Side Ranges Row Current Allowable Allowable RHS Increase Decrease MILK 50.00000 10.00000 6.666667 TIME 480.0000 53.33333 80.00000 CPCT 100.0000 INFINITY 40.00000 最优解不变时目标函 数系数允许变化范围 敏感性分析 (“LINGO|Ranges” ) x1系数范围(64,96) x2系数范围(48,72) • A1获利增加到 30元/kg，应否改变生产计划? x1系数由24 3=72 增加为303=90， 在允许范围内 不变！ (约束条件不变)
结果解释影子价格有意义时约束右端的允许变化范围 Ranges in which the basis is unchanged (目标函数不变) Obiective Coefficient Ranges Current Allowable Allowable Variable Coefficient Increase Decrease X172.0000024.000008.000000 X2 64.00000800000016.00000 Righthand side ranges Row Current Allowable Allowable RHS Increase Decrease MLLK50.0000010.000006.666667 原料最多增加10 TIME480.00053338000时间最多增加53 CPCT 100.0000 INFINITY 40.00000 充分条件! 35元可买到1桶牛奶每天最多买多少?最多买10桶! c
结果解释 Ranges in which the basis is unchanged: Objective Coefficient Ranges Current Allowable Allowable Variable Coefficient Increase Decrease X1 72.00000 24.00000 8.000000 X2 64.00000 8.000000 16.00000 Righthand Side Ranges Row Current Allowable Allowable RHS Increase Decrease MILK 50.00000 10.00000 6.666667 TIME 480.0000 53.33333 80.00000 CPCT 100.0000 INFINITY 40.00000 影子价格有意义时约束右端的允许变化范围 原料最多增加10 时间最多增加53 • 35元可买到1桶牛奶, 每天最多买多少? 最多买10桶! (目标函数不变) 充分条件 !