---
title: "Operations Research and Optimisation: where to start?"
date: 2020-05-26
---

[[https://en.wikipedia.org/wiki/Operations_research][Operations research]] (OR) is a vast area comprising a lot of theory,
different branches of mathematics, and too many applications to
count. In this post, I will try to explain why I find it so
fascinating, but also why it can be a little disconcerting to explore
at first. Then I will try to ease the newcomer's path in this rich
area, by suggesting a very rough "map" of the field and a few
references to get started.

Keep in mind that although I studied it during my graduate studies,
this is not my primary area of expertise (I'm a data scientist by
trade), and I definitely don't pretend to know everything in OR. This
is a field too vast for any single person to understand in its
entirety, and I talk mostly from a "amateur mathematician and computer
scientist" standpoint.

* Why is it hard to approach?

Operations research can be difficult to approach, since there are many
references and subfields. Compared to machine learning for instance,
OR has a slightly longer history (going back to the 17th century, for
example with [[https://en.wikipedia.org/wiki/Gaspard_Monge][Monge]] and the [[https://en.wikipedia.org/wiki/Transportation_theory_(mathematics)][optimal transport
problem]])[fn:optimaltransport]. This means that good textbooks and such
have existed for a long time, but also that there will be plenty of
material to choose from.

[fn:optimaltransport] {-} For a very nice introduction (in French) to
optimal transport, see these blog posts by [[https://twitter.com/gabrielpeyre][Gabriel Peyré]], on the CNRS
maths blog: [[https://images.math.cnrs.fr/Le-transport-optimal-numerique-et-ses-applications-Partie-1.html][Part 1]] and [[https://images.math.cnrs.fr/Le-transport-optimal-numerique-et-ses-applications-Partie-2.html][Part 2]]. See also the resources on
[[https://optimaltransport.github.io/][optimaltransport.github.io]] (in English).


Moreover, OR is very close to applications. Sometimes methods may vary
a lot in their presentation depending on whether they're applied to
train tracks, sudoku, or travelling salesmen. In practice, the
terminology and notations are not the same everywhere. This is
disconcerting if you are used to "pure" mathematics, where notations
evolved over a long time and is pretty much standardised for many
areas. In contrast, if you're used to the statistics literature with
its [[https://lingpipe-blog.com/2009/10/13/whats-wrong-with-probability-notation/][strange notations]], you will find that OR is actually very well
formalized.

There are many subfields of operations research, including all kinds
of optimization (constrained and unconstrained), game theory, dynamic
programming, stochastic processes, etc.

* Where to start

For an overall introduction, I recommend cite:wentzel1988_operat. It
is an old book, published by Mir Publications, a Soviet publisher
which published many excellent scientific textbooks[fn:mir]. It is out
of print, but it is available [[https://archive.org/details/WentzelOperationsResearchMir1983][on Archive.org]]. The book is quite old,
but everything presented is still extremely relevant today. It
requires absolutely no background, and covers everything: a general
introduction to the field, linear programming, dynamic programming,
Markov processes and queues, Monte Carlo methods, and game
theory. Even if you already know some of these topics, the
presentations is so clear that it is a pleasure to read!  (In
particular, it is one of the best presentations of dynamic programming
that I have ever read. The explanation of the simplex algorithm is
also excellent.)

[fn:mir] {-} Mir also published [[https://mirtitles.org/2011/06/03/physics-for-everyone/][/Physics for Everyone/]] by Lev Landau
and Alexander Kitaigorodsky, a three-volume introduction to physics
that is really accessible. Together with Feynman's famous [[https://www.feynmanlectures.caltech.edu/][lectures]], I
read them (in French) when I was a kid, and it was the best
introduction I could possibly have to the subject.


- why it may be more difficult to approach than other, more recent
  areas like ML and DL
  - slightly longer history
  - always very close to applications: somehow more "messy" in its
    notations, vocabulary, standard references, etc, as other "purer"
    fields of maths (similar to stats in this regard)
  - often approached from a applied point of view means that many very
    different concepts are often mixed together
- why it is interesting and you should pursue it anyway
  - history of the field
  - examples of applications
  - theory perspective, rigorous field
- different subfields
  - optimisation: constrained and unconstrained
  - game theory
  - dynamic programming
  - stochastic processes
  - simulation
- how to learn and practice
  - references
  - courses
  - computational assets

* References