# Mathematical Optimization for Business Problems

This training provides the necessary fundamentals of mathematical programming and useful tips for good modelling practice in order to construct simple optimization models.

LEARNING OBJECTIVES

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

Quadratic Programming

Module 5 – Modelling Practice

Modelling in the Real World

The Importance of Sparsity

Tips for Better Models