Mathematical Optimization for Business Problems


This course provides the necessary fundamentals of mathematical programming

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.


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.


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.


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