2007-09-17_Presentation - Introduction to Integer...

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IEOR160 © 2007 1 Introduction to Integer Programming z Integer programming models IEOR160 © 2007 2 A 2-Variable Integer program maximize 3x + 4y subject to 5x + 8y 24 x, y 0 and integer z What is the optimal solution? The Feasible Region 0 1 2 3 4 5 0 1 2 3 4 5 Question: What is the optimal integer solution? What is the optimal linear solution? Can one use linear programming to solve the integer program? A rounding technique that sometimes is useful, and sometimes not. 0 1 2 3 4 5 Solve LP (ignore integrality) get x=24/5, y=0 and z =14 2/5. Round, get x=5, y=0, infeasible! Truncate, get x=4, y=0, and z =12 Same solution value at x=0, y=3. Optimal is x=3, y=1 , and z =13 IEOR160 © 2007 5 Why integer programs? z Advantages of restricting variables to take on integer values More realistic More flexibility z Disadvantages More difficult to model Can be much more difficult to solve IEOR160 © 2007 6 On 0-1 variables z Integer programs: linear equalities and inequalities plus constraints that say a variable must be integer valued. z We also permit “x j {0,1}.” This is equivalent to 0 x j 1 and x j integer.
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IEOR160 © 2007 7 The mystery of integer programming z Some integer programs are easy (we can solve problems with millions of variables) z Some integer programs are hard (even 100
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This note was uploaded on 04/02/2008 for the course ECON 100B taught by Professor Wood during the Spring '08 term at University of California, Berkeley.

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2007-09-17_Presentation - Introduction to Integer...

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