lecture02 - Hidden Linear Programming Management Science...

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MS&E 211 #2 Hidden Linear Programming Management Science and Engineering Yinyu Ye
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The project is optional. Also, you may choose 3-4 units independently of project choice Please use FORUM for all non-personal questions. HW1 is available today Ask your neighbor if they want to meet up for study- group Discussion Section starts this week Attend if you can; don’t worry if you have class conflict since you can watch it later Will review the Math pre-requisites and software use.
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Definition of LP in abstract form Hidden LPs Air traffic landing time control Sparest data fitting Combinatorial auction for information market
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. . 0 0 2 1 3 2 32 1 31 2 2 22 1 21 1 2 12 1 11 2 2 1 1 s.t. max x x b x a x a b x a x a b x a x a x c x c , + + + + Linear Programming Abstraction 0 , 0 , 5 . 1 , 2 2 , 1 s.t. 2 max 2 1 2 1 2 1 2 1 x x x x x x x x . 0 , 0 , 5 . 1 1 1 , 2 2 0 , 1 0 1 s.t. 2 1 max 2 1 2 1 2 1 2 1 2 1 x x x x x x x x x x
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coef. matrix or table side - hand - left constraint : ,..., 1 ; ,..., 1 , coef. side - hand - right constraint : ,..., coef.; objective : ,..., ariables decision v : ,..., . 0 free 0 1 2 1 1 2 1 2 2 1 1 2 2 2 22 1 21 1 1 2 12 1 11 2 2 1 1 s.t. (min) max n j m i a b b c c x x , , , } , , { + + + } , , { + + + } , , { + + + + + + ij m n n m n mn m m n n n n n n x x x b x a x a x a b x a x a x a b x a x a x a x c x c x c Abstract Linear Programming Model
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LP in Compact Matrix Form n n m x x x x c c c c b b b b a a a a a a a a a A ... , ... , ... , ... ... ... ... ... ... ... 2 1 2 1 2 1 mn 2n n 1 m2 22 12 m1 21 11 free. or 0 } , { , } , , { s.t.
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lecture02 - Hidden Linear Programming Management Science...

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