Solving Linear Programs: SIMPLEX Method

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Introduction to Optimization and Operations Research

Covers fundamental concepts of optimization and operations research, exploring real-world examples and key topics over a semester.

Linear Programming Basics

Introduces linear programming basics, including optimization problems, cost functions, simplex algorithm, geometry of linear programs, extreme points, and degeneracy.

Simplex Algorithm: Solution on a Vertex

Explores the simplex algorithm and how optimal solutions can be found on vertices of constraint polyhedra.

Simplex Algorithm: Exercises & Interpretation

Covers exercises on the Simplex Algorithm, optimizing solutions subject to linear constraints.

Linear Optimization: Finding Initial BFS

Explains the process of finding an initial Basic Feasible Solution for linear optimization problems using the Simplex Algorithm.

Optimal Decision Making: Sensitivity Analysis

Covers sensitivity analysis in linear programming, focusing on optimal solutions and their sensitivities to changes.

The Simplex Algorithm: Efficiency and Degeneracy

Covers the Simplex Algorithm, focusing on efficiency and degeneracy in linear optimization problems.

Optimization Programs: Piecewise Linear Cost Functions

Covers the formulation of optimization programs for minimizing piecewise linear cost functions.

Network Flows and LP Formulations

Explains network flows, LP formulations, simplex method, duality, and practical applications.

Relations Between Events

Explores relations between events, disjunctive constraints, and modeling with binary variables in optimization problems.