MGMT 306 - IntegerProgrammingModels Slide1 Announcements q

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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 A Bad Day q A police officer in a small town stopped a motorist who was  speeding down Main Street. "But officer," the man began, "I  can explain."  q "Just be quiet," snapped the officer. "I'm going to let you cool  your heels in jail until the chief gets back."  q "But, officer, I just wanted to say,. .."  q "And I said to keep quiet! You're going to jail!" A few hours  later the officer looked in on his prisoner and said, "Lucky  for you that the chief's at his daughter's wedding. He'll be in a  good mood when he gets back."  q "Don't count on it," answered the fellow in the cell. "I'm the 
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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. In order to model special requirements, such as logical  conditions, integer variables (usually 0-1 variables) may
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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
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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
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  7              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.
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This note was uploaded on 01/31/2011 for the course MGMT 306 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

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MGMT 306 - IntegerProgrammingModels Slide1 Announcements q

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