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Fall 2011 — ORIE 3300/5300
OPTIMIZATION I (Linear programming)
Course outline
Planning, scheduling, and design problems in large organizations or engineering systems
can often be modeled mathematically using variables satisfying linear equations and in
equalities. Planners seek good solutions by maximizing or minimizing linear objective
functions in the variables, often corresponding to proﬁts or costs. The study of these
models, their formulation, solution, and interpretation, is called
linear programming
. This
course introduces the theory underlying linear programming (a natural extension of linear
algebra), the process of modeling concrete problems, and solution and analysis using the
AMPL
modeling language.
Core topics
Each lecture topic lasts about one week.
1. Linear programs, graphical solution, optimal solutions, unboundedness, transforming
to standard forms.
2. Building linear programming models.
3. Using
AMPL
to deﬁne linear programming models, and to solve and analyze.
4. Linear algebra review: linear independence, bases, matrices, elementary row opera
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