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# 01 - Industrial Engineering 634 Fall 2011 Integer...

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Unformatted text preview: Industrial Engineering 634 Fall 2011 Integer Programming Lecturer: Nelson Uhan Scribe: Isaac Tetzloff August 22, 2011 Lecture 1. Introduction and Basic Modeling Techniques 1 Introduction What is an integer program? In an integer program (IP) we are given matrices of integer values A ∈ Z m × n and B ∈ Z m × k . Along with the matrices, several vectors of integer values are also given, in particular b ∈ Z m , c ∈ Z n , and d ∈ Z k . Using these given matrices and vectors, an integer program is formulated as: minimize x,y cx + dy subject to Ax + By = b, (1.1) x ∈ Z n ≥ ,y ∈ R k ≥ . Note that the above formulation is general. Inequality constraints can always be represented as equality constraints by using slack / surplus variables (like when we transform linear programs into standard form). Since the decision variables x are integers and the decision variables y are real, the integer program in (1.1) is a mixed integer program (MIP) . When there are no continuous variables y ( k = 0), then (1.1) is an integer program (IP) . Furthermore, if there are no continuous variables and the values of x are restricted to values of 0 or 1 (i.e. x ∈ { , 1 } n ), then (1.1) is a binary integer program (BIP) ....
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01 - Industrial Engineering 634 Fall 2011 Integer...

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