Integer_Programming_(F2011)

Integer_Programming_(F2011) - IntegerProgrammingModels...

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  1              Slide Integer Programming Models
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  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. 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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  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                                 x 1,  x 2 >  0  and  integer
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  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                                x 1,  x 2 >  0  and   x 1 integer  
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             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
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This note was uploaded on 12/12/2011 for the course MGMT 306 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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Integer_Programming_(F2011) - IntegerProgrammingModels...

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