## Offered By: IBM

# 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.

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# At a Glance

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

**General Information**

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

**RECOMMENDED SKILLS PRIOR TO TAKING THIS COURSE**

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