Integer_Programming - IntegerProgrammingModels Slide1

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
  1              Slide Integer Programming Models
Background image of page 1

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

View Full DocumentRight Arrow Icon
  2              Slide Motivation for Integer Programming q In a linear programming formulation the variables can be set  to any real value. It may often be necessary to restrict some  of the variables to take only  integer  values due to two major  reasons: 1. Variables may represent quantities that are naturally  integral. 1. In order to model special requirements, such as logical  conditions, integer variables (usually 0-1 variables) may
Background image of page 2
  3              Slide Integer Linear Program q A linear program in which all the variables are restricted  to be integers is called an integer linear program  (ILP), or  integer program ( IP ) in short.                                 Max    3 x 1 + 2 x 2                      s.t.       3 x 1 +    x 2  <   9                                        x 1 + 3 x 2  <   7                                      - x 1 +    x 2  <   1
Background image of page 3

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

View Full DocumentRight Arrow Icon
  4              Slide Mixed  Integer Linear Program  q If only a subset of the variables are restricted to be integers,  the problem is called a mixed integer linear program  (MILP),  or  MIP  in short.                                    Max    3 x 1 + 2 x 2                         s.t.      3 x 1 +    x 2  <   9                                          x 1 + 3 x 2  <   7                                        - x 1 +    x 2  <   1
Background image of page 4
  5              Slide Linear Programming Relaxation of  an Integer Program q LP relaxation of an IP  is a LP obtained from the integer  program without enforcing integer requirements. q The objective function value of the optimal solution of LP  relaxation is at least as good as the optimal solution of IP.
Background image of page 5

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

View Full DocumentRight Arrow Icon
             Slide Modeling Integer Programs with 0-1 Variables q Much of the flexibility provided by linear integer  programming is due to the use of  0-1 variables : Ø 0-1 variables provide selections or choices with the value  of the variable equal to 1 if a corresponding activity is  undertaken, and 0 otherwise. Ø
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/14/2009 for the course MGMT 360 taught by Professor Yanjunli during the Spring '09 term at Purdue University-West Lafayette.

Page1 / 33

Integer_Programming - IntegerProgrammingModels Slide1

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online