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IBM Developer Skills Network

Mathematical Optimization for Business Problems

This course provides the necessary fundamentals of mathematical programming

Course Number

CP0101EN
Classes Start

Any time, Self-paced
Estimated Effort

3 hours

About This Course

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.

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

General Information

This course is free.
It is self-paced.
It can be taken at any time.

RECOMMENDED SKILLS PRIOR TO TAKING THIS COURSE

Basic understanding of Cloud Computing (the concept). It is also helpful if you know Javascript, but not required

Course Staff

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.