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.
+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 it can be a little disconcerting to explore at first, and how to start investigating the topic with 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 an “amateur mathematician and computer scientist” standpoint.
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 Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English). For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject. If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested by the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms. The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to best approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding to get lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems. If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested in the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms. The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding getting lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems. Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below). The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need. Regarding solvers, there is a list of solvers on JuMP’s documentation, with their capabilities and their license. Free solvers include GLPK (linear programming), Ipopt (non-linear programming), and SCIP (mixed-integer linear programming). Commercial solvers often have better performance, and some of them propose a free academic license: MOSEK, Gurobi, and IBM CPLEX in particular all offer free academic licenses and work very well with JuMP. Another awesome resource is the NEOS Server. It offers free computing resources for numerical optimization, including all major free and commercial solvers! You can submit jobs on it in a standard format, or interface your favourite programming language with it. The fact that such an amazing resource exists for free, for everyone is extraordinary. They also have an accompanying book, the NEOS Guide, containing many case studies and description of problem types. The taxonomy may be particularly useful. Operations research is a fascinating topic, and it has an abundant literature that makes it very easy to dive into the subject. If you are interested in algorithms, modelling for practical applications, or just wish to understand more, I hope to have given you the first steps to follow, start reading and experimenting. 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. 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 it can be a little disconcerting to explore at first, and how to start investigating the topic with 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 an “amateur mathematician and computer scientist” standpoint. 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 Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English). For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject. If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested by the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms. The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to best approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding to get lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems. If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested in the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms. The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding getting lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems. Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below). The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need. Regarding solvers, there is a list of solvers on JuMP’s documentation, with their capabilities and their license. Free solvers include GLPK (linear programming), Ipopt (non-linear programming), and SCIP (mixed-integer linear programming). Commercial solvers often have better performance, and some of them propose a free academic license: MOSEK, Gurobi, and IBM CPLEX in particular all offer free academic licenses and work very well with JuMP. Another awesome resource is the NEOS Server. It offers free computing resources for numerical optimization, including all major free and commercial solvers! You can submit jobs on it in a standard format, or interface your favourite programming language with it. The fact that such an amazing resource exists for free, for everyone is extraordinary. They also have an accompanying book, the NEOS Guide, containing many case studies and description of problem types. The taxonomy may be particularly useful. Operations research is a fascinating topic, and it has an abundant literature that makes it very easy to dive into the subject. If you are interested in algorithms, modelling for practical applications, or just wish to understand more, I hope to have given you the first steps to follow, start reading and experimenting. 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. 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 it can be a little disconcerting to explore at first, and how to start investigating the topic with 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 an “amateur mathematician and computer scientist” standpoint. 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 Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English). For an overall introduction, I recommend Wentzel (1988). It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman’s famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject. If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested by the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms. The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to best approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding to get lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems. If you are interested in optimization, the first thing you have to learn is modelling, i.e. transforming your problem (described in natural language, often from a particular industrial application) into a mathematical programme. The mathematical programme is the structure on which you will be able to apply an algorithm to find an optimal solution. Even if (like me) you are initially more interested in the algorithmic side of things, learning to create models will shed a lot of light on the overall process, and will give you more insight in general on the reasoning behind algorithms. The best book I have read on the subject is Williams (2013). It contains a lot of concrete, step-by-step examples on concrete applications, in a multitude of domains, and remains very easy to read and to follow. It covers nearly every type of problem, so it is very useful as a reference. When you encounter a concrete problem in real life afterwards, you will know how to construct an appropriate model, and in the process you will often identify a common type of problem. The book then gives plenty of advice on how to approach each type of problem. Finally, it is also a great resource to build a “mental map” of the field, avoiding getting lost in the jungle of linear, stochastic, mixed integer, quadratic, and other network problems. Another interesting resource is the freely available MOSEK Modeling Cookbook, covering many types of problems, with more mathematical details than in Williams (2013). It is built for people wanting to use the commercial MOSEK solver, so it could be useful if you plan to use a solver package like this one (more details on solvers below). The basic algorithm for optimization is the simplex algorithm, developed by Dantzig in the 1940s to solve linear programming problems. It is the one of the main building blocks for mathematical optimization, and is used and referenced extensively in all kinds of approaches. As such, it is really important to understand it in detail. There are many books on the subject, but I especially liked Chvátal (1983) (out of print, but you can find cheap used versions on Amazon). It covers everything there is to know on the simplex algorithms (step-by-step explanations with simple examples, correctness and complexity analysis, computational and implementation considerations) and to many applications. I think it is overall the best introduction. Vanderbei (2014) follows a very similar outline, but contains more recent computational considerationsFor all the details about practical implementations of the simplex algorithm, Maros (2003) is dedicated to the computational aspects and contains everything you will need. Regarding solvers, there is a list of solvers on JuMP’s documentation, with their capabilities and their license. Free solvers include GLPK (linear programming), Ipopt (non-linear programming), and SCIP (mixed-integer linear programming). Commercial solvers often have better performance, and some of them propose a free academic license: MOSEK, Gurobi, and IBM CPLEX in particular all offer free academic licenses and work very well with JuMP. Another awesome resource is the NEOS Server. It offers free computing resources for numerical optimization, including all major free and commercial solvers! You can submit jobs on it in a standard format, or interface your favourite programming language with it. The fact that such an amazing resource exists for free, for everyone is extraordinary. They also have an accompanying book, the NEOS Guide, containing many case studies and description of problem types. The taxonomy may be particularly useful. Operations research is a fascinating topic, and it has an abundant literature that makes it very easy to dive into the subject. If you are interested in algorithms, modelling for practical applications, or just wish to understand more, I hope to have given you the first steps to follow, start reading and experimenting.
@@ -33,8 +33,8 @@
. It is out of print, but it is available 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.)Theory and algorithms
@@ -63,6 +63,8 @@
Conclusion
+References
Operations Research and Optimisation: where to start?
+ Operations Research and Optimization: where to start?
-
+
@@ -49,8 +49,8 @@
Why is it hard to approach?
@@ -62,8 +62,8 @@
. It is out of print, but it is available 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.)Theory and algorithms
@@ -92,6 +92,8 @@
Conclusion
+References
Why is it hard to approach?
@@ -29,8 +29,8 @@
. It is out of print, but it is available 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.)Theory and algorithms
@@ -59,6 +59,8 @@
Conclusion
+References