02 - Industrial Engineering 634 Fall 2011 Integer...

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Unformatted text preview: Industrial Engineering 634 Fall 2011 Integer Programming Lecturer: Nelson Uhan Scribe: Mahesh Ramaraj August 24, 2011 Lecture 2. Linear Programs and Polyhedra Following our discussion on integer programs from last class, we will focus this lecture on linear programs and polyhedra. What is a linear program? Given a matrix A R m n and vectors b R m and c R n , a linear program is an optimization problem of following form max cx (1) s.t. Ax b (2) Equality constraints can be rewritten as two inequality constraints, and by multiplying by- 1, we can change the direction of the constraints and the objective function. A feasible solution to a linear program of the form (1)-(2) is a vector x such that Ax b . An optimal solution of a linear program of the form (1)-(2) is a feasible solution with maximum value of cx . A linear program of the form (1)-(2) is infeasible if { x R n : Ax b } = and it is unbounded if for all R , there exists a y { x R n : Ax b } with cy > ....
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This note was uploaded on 02/14/2012 for the course IE 530 taught by Professor Ravindran during the Spring '97 term at Purdue University-West Lafayette.

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02 - Industrial Engineering 634 Fall 2011 Integer...

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