Integer Programming H

Integer Programming H - Integer Programming Models Slide 1...

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  1              Slide Integer Programming Models
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  2              Slide Announcements q This unit covers chapter 6 in our textbook.
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  3              Slide Announcements q Read Chapter 6 in book. q Class next Monday in computer labs.   9am A – K, go to ENAD 135 9am L – Z, go to Krannert Lab 2 10:30am A – J, go to ENAD 135 10:30am K – Z, go to Krannert Lab 2 1:30pm, Krannert Labs 1 and 2 3:00pm, Krannert Labs 1 and 2
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  4              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. 2. In order to model special requirements, such as logical  conditions, integer variables (usually 0-1 variables) may  need to be defined.
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  5              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                                 x 1,  x 2 >  0  and  integer
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  6              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                                x 1,  x 2 >  0  and   x 1 integer  
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             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
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Integer Programming H - Integer Programming Models Slide 1...

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