02_linear_prog1

02_linear_prog1 - LinearProgramming Topics...

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8/14/04 J. Bard and J. W. Barnes Operations Research Models and Methods Copyright 2004 - All rights reserved Linear Programming Topics • General optimization model • LP model and assumptions • Manufacturing example • Characteristics of solutions  • Sensitivity analysis • Excel add-in
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2 Most of the deterministic OR models can be formulated as mathematical  programs. "Program," in this context, has to do with a “plan,” not a computer  program.  Mathematical Program Maximize / Minimize z  =  f ( x 1 x ,…,  x n Subject to {   =   }    b i       i  =1,…, m x j  ≥ 0,    j  = 1,…, n   Deterministic OR Models g i ( x 1 x , …,  x n )
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3     x j  are called  decision variables .  These are things that you  control   {   =   }   b i are called  structural   (or functional or technological) constraints  x j  ≥ 0 are  nonnegativity  constraints  Model Components f ( x 1 x ,…,  x n ) is the  objective function g i ( x 1 x ,…,  x n )
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4 (   x 1 . . n x A feasible solution    x  =   satisfies all the constraints (both structural and nonnegativity)  The objective function ranks the feasible solutions . )   Feasibility and Optimality
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5 Linear Programming A linear program is a special case of a mathematical program where  f   and  g 1   ,…,  g m   are  linear  functions Linear Program : Maximize/Minimize   z =  c 1 x 1  +  c 2 x 2  +  • • •  +  c n x n   Subject to   a i 1 x 1  +  a i 2 x 2  +  • • •  +  a in x n   {   =   }   b i  ,     i  = 1,…, m x j     u j ,    j  = 1,…, n x j   ≥ 0,    j  = 1,…, n  
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6    x j     u j  are called simple bound constraints     x  = decision vector = "activity levels" a ij  c ,   b u j   are all known data  goal is to find  x LP Model Components
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This note was uploaded on 01/26/2011 for the course IEOR 4004 taught by Professor Sethuraman during the Fall '10 term at Columbia.

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02_linear_prog1 - LinearProgramming Topics...

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