OR-lecturenotes - lecturenotes

Discrete Optimization Models

lectures 28-33

LPs are easy to solve. In other workds, efficient algorithms exist to solve LPs. However, many real-world problems are not linear in the sense that their solutions need to…

Network Flows

lectures 26-27

Network flow problems…

Quantitative Sensitivity Analysis

lectures 23-26

The primal model is the main application of interest. ‘’The dual corresponding to a given primal formulation is a closely related LP with decision variables and constraints…

Sensitivity Analysis and Duality

lectures 20-22

In this lecture, we will discuss the sensitivity analysis and duality in linear programming. Sensitivity analysis is the study of how the optimal solution of a linear…

The Simplex (rudimentary) Algorithm

lectures 17-19

The Simplex Algorithm is a method for solving linear programming problems. It was developed by George Dantzig in 1947. The algorithm is based on the concept of a simplex…

Standard Form of Linear Programming Models

lectures 13-14

Referring to Top Brass Tropy example, the LP model is given as follows:

Blending Models and Linearizable Objectives

lecture 13

Exercise 4.3 illustrates and example of blending problems. \(x_j\) is defined to be the fraction of ingredient \(j\) in the blend. Units costs of the ingredients are given along with the daily requirements for protein, fat, and fiber that a serving…

Basic Solutions

lectures 15-16

A basic solution (feasible or not) to a standard LP is obtained by fixing \(n-m\) variables to zero and solving the remaining \(m\) equations for the remaining \(m\) variables. Varibles fixed to zero are called nonbasic variables and the remaining variables are called…

Machine Learning Integration with Optimization Models

lecture 12

The following LP we solved in the class assumed that the…

Linear Programming Models

lecture 11

We will talk about two categories of models: allocation and blending models. Then, we will talk about converting some non-linear objective…

Introduction to AMPL

lectures 8-10

Large Scale Optimization Models

lectures 5-7

‘In real applications optimization models quickly grow to thousands, even millions, of variables and constraints.’ [Reference 1] It is not practical to solve these models by…

Graphic Solutions of Linear Programming Problems

lectures 3-4

There are famous algorithms to solve LP problems. However, before learning those algorithms, we will learn how to solve LP problems graphically. That gives a good intuition…

Introduction to Decision Science (Operations Research)

lectures 1-2

Operations Research (OR) is the discipline of applying advanced analytical methods to help make better decisions. OR is very often…