Linear Programming Duality
When you are given a linear program, in many cases we call it a primal linear program. It...
Matrix Presentation of Simplex Method
When it comes to Operations Research, we are mainly talking about optimization problems, so the theories are mainly...
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Operations Research (2): Optimization AlgorithmsNational Taiwan University You probably have used some solver / optimizer software to solve...
Heuristic Algorithms: A Case Study
The objectives for any research is that we want to build a mathematical model to formulate the given problem. The...
Non-Linear Programming: Gradient Descent and Newton’s Method
Non-Linear Programs When visualizing a linear program, its feasible region looks like a polygon. Because the objective function...
Branch-and-Bound & Heuristic Algorithms
In some cases, variables must take integer values, or binary values. Formulating and solving the models with integer...
The Simplex Method
The simplex method is the most fundamental tool in linear programming, it is a single algorithm that is...
Linear Algebra in Operations Research
There are 2 perspectives to look at linear equation systems, row view and column view. Both are equivalent,...
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Operations Research (1): Models and ApplicationsNational Taiwan University This is an amazing beginner-level course about Operations Research (abbr....
Operations Research: Nonlinear Programming and Linearization
In many cases, we need to deal with nonlinear situations, e.g.: product pricing decision, inventory, portfolio optimization. Above...
Operations Research: Integer Programming
Integer programming is generally from linear programming but allowing you to have integer variables, which means you may...
Operations Research: Linear Programming
Almost all of problems that Linear Programming is able to solve is about resource allocation, for example: product...
Introducing Operations Research
Motivations Management is the attainment of organizational goals in an effective and efficient manners through planning, organizing, leading,...