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# 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.

Course

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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
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).  It is also helpful if you know Javascript, but not required

Estimated Effort

6 Hours

Level

Beginner

Skills You Will Learn

Decision Optimization, Mathematical Programming, Operational Research, Optimization

Language

English

Course Code

CP0101EN