Linear Programming for Eng

Catalog description

Linear programming (LP, also called linear optimization) is an optimization problem seeking to minimize or maximize a linear function subject to a set of linear inequality or equality constraints. There are a wide variety of applications for this approach, including transportation schedules, corporate planning, inventory management, and many others. Students will learn how to build fundamental mathematical models to find the best decisions in real-life decision-making problems in this course. In particular, the students will study how to build abstractions of mathematical models and develop general methods to solve them, rather than a specific algorithm for each problem. From the algorithmic perspective, this course will cover the simplex method, which stems from essential linear algebraic operation while emphasizing mathematical foundations and computational consideration for practical implementations of the students. In addition, the course will discuss theoretical aspects of linear programming such as polyhedral theory, including projections, duality theory, the guarantee of optimality, convexity, degeneracy, and algorithmic convergence. Also, this course will cover sensitivity analysis, network flows, and network simplex as extendable areas and will encourage learning about actual implementation through the use of computer software. SSIE 553-Operations Research or an undergraduate degree in Industrial Engineering (or related discipline) with a background knowledge of operations research and linear algebra (i.e., ISE 320/420-Optimization & Operations Research I/II) will be prerequisites in this course.