END 508 - Mathematical Programming

Course Objectives

• Improve their ability to rigorously prove mathematical statements.
• Analyze the structure of and mathematical models of various complex systems occurring in industrial and engineering applications.
• Develop the mathematical structure of the most commonly used deterministic, discrete, linear and integer optimization models.
• Develop an understanding of the algorithms and techniques used to solve and analyze linear, optimization models using their mathematical structure.
• Develop knowledge of existing solvers for linear optimization

Course Description

Introduction to mathematical programming, also known as mathematical optimization, with an emphasis on modeling and linear deterministic models. We will explore solution procedures and algorithms such as simplex method and interior point algorithms. Topics covered include duality, sensitivity analysis, integer programming and decomposition. Applications relate to design and analysis of problems such as production, inventory control, assembly line balancing, routing, scheduling, healthcare, military and transportation. As a supporting theme, the course will also emphasize effective modeling techniques, and the assignments will require the use of state-of-the-art optimization software.