{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

02_linear_prog1

# 02_linear_prog1 - LinearProgramming Topics...

This preview shows pages 1–8. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 )
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 )

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
7 Linear Programming Assumptions (i) proportionality (ii) additivity   linearity (iii) divisibility (iv) certainty

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 26

02_linear_prog1 - LinearProgramming Topics...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online