General description

Linear programming is a widely used field of optimization. Many practical problems in operations research can be expressed as linear programming problems. It has a wide range of practical business, commerce, and industrial applications and simultaneously has received so thorough a theoretical development. Today, this theory is being successfully applied to problems of capital budgeting, design of diets, conservation of resources, games of strategy, economic growth prediction, and transportation systems. The aim of the course is to introduce basic and advanced theory of linear programming, and to show and solve real-life problems that can be described as linear programs.

Material

• prerequisites: simplex algorithm, two-phase simplex method, fundamental theorem of LP, duality, weak and strong duality theorems
• Integer programming, the branch-and-bound method, knapsack problem
• Network problems: shortest path, minimum spanning tree, maximum flow
• Transshipment, transportation and assignment problems
• Introduciton to stochastic programming: portfolio problem, newspaper vendor
• Introduction to nonlinear programming
• Solving problems with AMPL (and in R, Python, Matlab)