# Decompositions Algorithms Broken Down and Explained

This post explores how to use various decomposition techniques to solve LPs and MIPs. I have written these using Gurobi as a solver and as the mathematical formulation software. This is a reproducible example if you have R Studio just make sure you have installed the correct packages. library(gurobi) ## Warning: package ‘slam’ was built under R version 4.1.2 library(tictoc) library(Matrix) library(ggplot2) ## Warning: package ‘ggplot2’ was built under R version 4.

# Benders Decomposition Algorithm Explained

This post explores how to use Benders Decomposition to solve LPs and MIPs. I have written these using Gurobi as a solver and as the mathematical formulation software. This is a reproducible example if you have R Studio just make sure you have installed the correct packages. library(gurobi) ## Warning: package ‘slam’ was built under R version 4.1.2 library(lpSolveAPI) library(tictoc) library(Matrix) library(ggplot2) ## Warning: package ‘ggplot2’ was built under R version 4.

# Quadratic Programming Examples and Algorithms

Background This post explores how to solve QPs by hand and with Gurobi. I have written these using Gurobi as a solver and as the mathematical formulation software. This is a reproducible example if you have R Studio just make sure you have installed the correct packages. library(gurobi) ## Warning: package ‘slam’ was built under R version 4.1.2 library(tictoc) library(Matrix) library(ggplot2) ## Warning: package ‘ggplot2’ was built under R version 4.

# Gurboi’s R Examples 2

This post explores how to use Gurobi to solve more advanced LPs, MIPs, and QPs. I have written these using Gurobi as a solver and as the mathematical formulation software. This is a reproducible example if you have R Studio just make sure you have installed the correct packages. library(gurobi) ## Warning: package ‘slam’ was built under R version 4.1.2 library(Matrix) This example formulates and solves the following simple QP model:

# Gurobi Basic LP/MIP Examples

This post explores how to use Gurobi to solve LPs and MIPs. I have written these using Gurobi as a solver and as the mathematical formulation software. This is a reproducible example if you have R Studio just make sure you have installed the correct packages. library(gurobi) ## Warning: package ‘slam’ was built under R version 4.1.2 library(Matrix) This example formulates and solves the following simple LP model: (max: x + 2y + 3z)

# Basics of Markov Chains

Background This post explores how to markov chains work and how to visulaize them in R. I use a R package specifically designed to visualize markov chains. I also represent these markov chains using tables. This is a reproducible example if you have R Studio just make sure you have installed the correct packages. library(markovchain) ## Warning: package ‘markovchain’ was built under R version 4.1.2 library(diagram) #Allows the use of exponential operators in matrix library(expm) ## Warning: package ‘expm’ was built under R version 4.

# Linear Programming Examples and Applications

Background This post explores how to use the fundamental algorithms to solve LPs. I have written these using Gurobi as a solver and as the mathematical formulation software. This is a reproducible example if you have R Studio just make sure you have installed the correct packages. library(gurobi) ## Warning: package ‘slam’ was built under R version 4.1.2 library(tictoc) library(Matrix) library(ggplot2) ## Warning: package ‘ggplot2’ was built under R version 4.

# The Basics of Simulation

Background This post explores some of the basic concepts of simulation. I mostly explore these concepts using basic probablity and the built in distribution functions. This is a reproducible example if you have R Studio just make sure you have installed the correct packages. Ideas from Probablity Course https://www.probabilitycourse.com/chapter13/chapter13.php set.seed(123) p <- 0.5 n <- 1000 U <- runif(n) toss <- as.

# Statistic Basics and Linear Regression

Background This post explores some of the basic concepts of statistics. I mostly explore these concepts using linear regression. This is a reproducible example if you have R Studio just make sure you have installed the correct packages. library(DataExplorer) ## Warning: package ‘DataExplorer’ was built under R version 4.1.2 library(tidyverse) ## Warning: package ‘tidyverse’ was built under R version 4.1.2 ## Warning: package ‘ggplot2’ was built under R version 4.