# Operational Research

# Resources

#### The Canon

Name | Author |
---|---|

Principles of Operations Research with applications to managerial decicisions | Harvey M. Wagner |

Operations Research: Applications and Algorithms. | W. L. Winston |

Introduction to Management Science | B. W. Taylor III |

## Others

- Advanced - Search Methodologies >> Search Methodologies. Introductory Tutorials in Optimization and Decision Support Techniques (2005), by E. K. Burke

- Advanced - Scheduling problems >> Scheduling: Theory, Algorithms, and Systems (2016), by M. Pinedo

- Advanced - Integer programming >> Integer Programming (2014), by M. Conforti

- Advanced - Nonlinear Programming >> Nonlinear Programming (2016), by D. P. Bertsekas

- Advanced - Supply Chain >> Management and Advanced Planning: Concepts, Models, Software and Case Studies (2014), by H. Stadtler

- Advanced - Data Analysis >> Guide to Intelligent Data Analysis: How to Intelligently Make Sense of Real Data (2010), By M. R. Berthold

- Advanced - Artificial Intelligence >> Artificial Intelligence a Modern Approach (AIMA) (2010), by S. J. Russell

Here are a few societies that I like (look at their blogs, magazines, and journals):

- The OR Society (The Operational Research Society);

- INFORMS (The Institute For Operations Research and The Management);

- CORMSIS (Centre for Operational Research, Management Science and Information Systems). It is one of the largest groups of OR/MS researchers in the UK.

# What is Operation Research (OR)?

What is O.R. >> http://www.theorsociety.com/Pages/Careers/WhatIsOR.aspx

https://www.youtube.com/watch?v=ILWbaWrjgU4

## What is a system?

# All of my exercises

https://github.com/sanchezcarlosjr/uabc/tree/main/essays/operations research

# Optimization

## Linear programming

Gurobi, Lindo, and Cplex

### Terminology

**Linear programming**. Mathematical technique in which a linear function is maximized or minimized subject to linear constraints.

**Objective function. **Linear function to be maximized or minimized.

**The Standard Maximum Problem. **Find a $x=(x_1,...,x_n)^T$ such that

**Feasible set. **Set of $x=(x_1,...,x_n)$ such that checks the functional constraints and constraints.

**The Standard Maximum Feasible Set. **Set of $x=(x_1,...,x_n)$ such that

## References

[1] “LINEAR PROGRAMMING. A concise introduction” [Online]. Available: https://www.math.ucla.edu/~tom/LP.pdf.

## Lagrange method

https://ebrary.net/134819/mathematics/constrained_optimization_method_lagrange_multipliers

# Markov chains

## Ergodic Markov Chains

Ergodic. Involving or relating to the probability that any state will recur; especially: having zero probability that any state will never recur.

**: **involving or relating to the probability that any state will recur *especially***: **having zero probability that any state will never recur

## Stability

# Waiting Line systems and Queue theory

When you encounter systems displaying characteristics of waiting phenomena, like distributed systems and queues in real life, you often resort to applying queue theory. This approach entails evaluating and enhancing system performance by characterizing these phenomena through mathematical models and simulations.

More concretely, queue theory is used to model systems that exhibit concurrent access to a shared resource such as highway toll station, line at a restaurant, airport check, bandwidth, server, disk, memory,

Discrete-time Markov chains, Continuous-time Markov chains, Multi server and finite capacity queues.

## Simulators

# TODO

- Bayesian statistics: STAN.

- Agent-based modelling: NetLogo.

- Optimisation: GAMS.

- Legacy spreadsheet: Excel VBA.

- System modelling: Vensim and a whole lot of dynamic modelling software.