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# 1. Preface¶

A first version of this volume was born several years ago, in Italian, as the main
reference material for an advanced course on optimization modeling for students
in Management Engineering at my Università degli Studi di Firenze. That
course is no more active and the material remained unused for quite a few
years. I have decided now to reconsider it as I think that, in these days,
modeling skills are fundamental, possibly even more than before. Differently
from when I wrote my Italian book, nowadays data, data science, analytics
are terms we can find everywhere. Every company is moving towards
data-driven approaches, mainly following the giant waves of machine
learning and artificial intelligence. However, some companies are
experiencing difficulties, as the return on investment seems to be
below expectations. I have neither an explanation nor a recipe for
this. I suspect there might be many reasons: from one side the too
high expectation, but, from another side, the fact that managers
forgot that most of modern data science and machine learning is devoted
to *predictive* analytics. Having the
possibility of learning from data so that future trends (demand, production,
yield, interest rates, …) can be reliably and robustly estimated is
absolutely wonderful. However, after a reliable forecast becomes available, managers
still need to *take decisions*. And this is where optimization
(operations research) comes into play.

Optimization is *the* tool for good decision making or, better,
for good decision support. In order to be able to suggest rational and
effective decisions the Operations Research scientific community has
offered courses, developed methods, analyzed theoretical aspects of *optimization*. However I
feel there is still a wide gap which separates academic research from
day to day adoption. And, in my opinion, part of this
is due to the lack of sufficient modeling skills. If we cannot model
a problem, no matter how sophisticated our optimization algorithms are,
we will not be able to solve it nor suggest any decision. We need to communicate our
problem to a solver. And to do this we need a deep knowledge of
models.

Modeling is a creative skill, which is best learned by doing; however, especially for more advanced models involving integer variables or graph theory, modeling practice should be paired with a deep theoretical knowledge, if we wish to be able to solve large scale problems.

My interest in modeling arose by chance, thanks to a very stimulating activity as a book reviewer that I performed in my early years in the academia. Among the many books I received, I got to review, at some time, the fundamental volume of Hans Paul Williams [Williams, 2013] (indeed it was a much earlier edition than the one cited here). That book opened a new world to me: up to that time I had been thinking to the algorithmic aspects of optimization as the most relevant ones. That book made me understand that without suitable formulation no problem can ever be solved, whichever the refined algorithms we have available. This seemingly trivial observation has indeed many consequences. One of these is the fact that we need to be organized and disciplined in formulating an optimization model; formulating a linear optimization model is not something which can be done simply after having learned the details of the simplex algorithm: practice and modeling theory is needed before a robust, reliable, useful model can be produced. Williams’ book opened my eyes on this fascinating subject; more or less at the same time I also had the opportunity of learning and using GAMS - Generalized Algebraic Modeling System. This modeling tool let me understand that even to formulate a “simple” linear optimization problem it is not enough to be able to write the cost vector, the constraint matrix, the right hand side. Or, to be more precise: it would be enough. But the effort in preparing these data can be enormously reduced if a modeling language is used; moreover the readability and the possibility of maintaining large models is enormously enhanced when using a modeling language. This is even more true when dealing with non linear models. GAMS is nowadays not the unique modeling system available. I have been using AMPL - A Mathematical Programming Language, AIMMS, which are commercial products, or JuMP (Julia Mathematical Programming) and Pyomo (Python Optimization Modeling) which are open source. There exist many others, most of which however are limited to specific classes of problems like, e.g., linear models only.

Given the availability of Williams’ book and of several software modeling languages, one may ask why I felt the need to write a book on optimization modeling. First of all, of course, I confess I like writing and teaching and this is something I would do even if proven to be useless… But I also think that it is quite unusual that for such an important topic the most authoritative textbook (if not the only one) is still the excellent book by Williams which although re-published several times, is more or less unchanged since the 80’s, when the first edition appeared. I think there is a space nowadays for a more modern view of that classical textbook, which is and remains a fundamental reference for me as well as for many in the optimization community. But in these years many things happened: advances in software, in modeling environments, in programming languages, in application domains. And, among the many novelties, also the way in which we publish radically changed. I took the decision to publish my book mainly as a web site, with a companion GitHub repo for models and data and, only recently, as a traditional printed book. The idea is that of a dynamic book, which can easily change thanks to the addition of models, data, modeling languages. For many different reasons, I became more familiar with the AMPL language than any other. But I would like to ask my readers to contribute with translations of AMPL models in other modeling environments (and, of course, to suggest modification and corrections to those I wrote). The printed edition of this book is for those who prefer having a book on paper but the on line web edition will in any case be the most up-to-date one.

Most of the applications in this book are quite classical, from blending to production to routing on road networks. They mostly come from many years of teaching to Management Science Engineers. Very recently, however, I have been involved in the world of non-profit organizations and discovered the enormous possibilities that may exist to apply optimization models for improving the quality of life of many people. Thanks to the collaboration with the Analytics for a Better World ABW group I discovered that, as an example, the elementary diet problem which, for many years, I refused to teach as I considered it to be too silly an example, indeed has been enriched and used and contributed to fight hunger for millions of people. And similarly, many other models: locating health care facilities, locating ambulances, planning routes for emergency, organizing the logistics after a disaster, even cleaning the ocean from plastic are relevant social problem which can enormously benefit from optimization. I plan, in the future, to expand this volume with specific chapters on humanitarian logistics.

In writing this book I also decided, for the first time in my long academic life, not to write a book (or a paper) in LaTeX from beginning to end. It was a difficult choice, as I cannot think of any other way to write math. But modern markup languages and systems, like Sphinx, make the effort in writing a web book so light that eventually I decided to use this system. Of course, however, all of the mathematical formulae and the figures have been composed in LaTeX, with the help of the tikz package and the printed book was composed with the help of many packages, one of the most important of which is the memoir LaTeX class.

Finally: in a modern book on modeling, it is impossible to avoid sharing the developed models. Most of modeling, in fact, can be learned not only by studying existing modeling techniques, but also by experimenting with models and real data. Thus I created a github repository devoted to the material presented in this book. I invite readers not only to browse these models and use them, but also to suggest modifications, improvements and, in particular, to add models in all possible modeling languages. At the moment of writing this preface, only AMPL models are fully available, as described in the book. Volunteers are more than welcome to contribute new or existing models implemented in Julia/Jump, Pyomo, GAMS, Aimms, SCIP or any other high level modeling language. This can be easily done through the github repository. I thank in advance any reader who will help to improve and extend this material.

© Fabio Schoen 2024