 # Mathematical Optimization for Business Problems

Intended for developers, IT specialists, business managers, and others who are interested in addressing business optimization problems, the Mathematical Optimization for Business Problems will prepare you to construct simple optimization models. This training provides the fundamentals of mathematical programming, as well as tips for good modelling practice.

Mathematical Programming is a powerful technique used to model and solve optimization problems. This training provides the necessary fundamentals of mathematical programming and useful tips for good modeling practice in order to construct simple optimization models.

In this training, you will explore several aspects of mathematical programing to start learning more about constructing optimization models using IBM Decision Optimization technology, including:

• Basic terminology: operations research, mathematical optimization, and mathematical programming
• Basic elements of optimization models: data, decision variables, objective functions, and constraints
• Different types of solution: feasible, optimal, infeasible, and unbounded
• Mathematical programming techniques for optimization: Linear Programming, Integer Programming, Mixed Integer Programming, and Quadratic Programming
• Algorithms used for solving continuous linear programming problems: simplex, dual simplex, and barrier
• Important mathematical programming concepts: sparsity, uncertainty, periodicity, network structure, convexity, piecewise linear and nonlinear

These concepts are illustrated by concrete examples, including a production problem and different network models.

## Syllabus

Module 1 - The Big Picture

• What is Operations Research?
• What is Optimization?
• Optimization models

Module 2 - Linear Programming

• Introduction to Linear programming
• A production problem : Part 1 - Writing the model
• A production problem : Part 2 - Finding a solution
• A production problem : Part 3 - From feasibility to unboundedness
• Algorithms for solving linear programs : Part 1 - The Simplex and Dual Simplex Algorithm
• Algorithms for solving linear programs : Part 2 - The Simplex and Barrier methods

Module 3 - Network Models

• Introduction to Network Models
• The Transportation problem
• The Transshipment problem
• The Assignment problem
• The shortest path problem
• Critical path analysis

Module 4 - Beyond simple LP

• Nonlinearity and Convexity
• Piecewise linear programming
• Integer programming
• The branch and bound method

Module 5 - Modelling Practice

• Modelling the real world
• The importance of Sparsity
• Tips for better models

## GENERAL INFORMATION

• This course is free.
• It is self-paced.
• It can be taken at any time.
• It can be audited as many times as you wish.

• None

• None

## Course Staff Victoria Genin
Victoria Genin is an Information Developer at IBM in France. She works on IBM Decision Optimization products, writing documentation and creating video tutorials. She has a Master in Multimedia Content Creation from Paris Diderot University. Shirley de Jonk
Shirley de Jonk, PhD is a former UK university lecturer in Information Systems and researcher in Mathematical Programming. Today she is an Information Developer at IBM France working on IBM Decision Optimization products.