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