This is the set of slides I have used on the first class of a tutorial on Julia and JuMP for Operations Research. All the course slides and code are available at: https://github.com/pedrocastellucci/athena.

1. Operations research with Julia and JuMP
Pedro Belin Castellucci
February, 2017
Online material at github.com/pedrocastellucci/athena.
Copyright c 2016 Pedro Belin Castellucci.

2. Mathematical programming
Operations
research
Mathematical
programming
Convex
Semi-
definite
Second-
order
conic
Linear
Integer
Nonlinear
Stochastic
Multi-
objective
Figure 1: Information from en.wikipedia.org/wiki/Mathematical_optimization.
Copyright c 2016 Pedro Belin Castellucci.

3. Which can JuMP handle?
Operations
research
Mathematical
programming
Convex
Semi-
definite
Second-
order
conic
Linear
Integer
Nonlinear
Stochastic
Multi-
objective
Figure 2: For JuMP documentation check www.juliaopt.org/JuMP.jl/0.15/.
Copyright c 2016 Pedro Belin Castellucci.

4. Introduction to Julia programming
Copyright c 2016 Pedro Belin Castellucci.

5. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

6. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

7. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

8. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

9. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

10. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

11. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

12. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

13. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

14. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

15. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

16. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

17. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

18. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

19. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

20. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

21. “We want a language that’s open source, with a liberal license. We
want the speed of C with the dynamism of Ruby. We want a
language that’s homoiconic, with true macros like Lisp, but with
obvious, familiar mathematical notation like Matlab. We want
something as usable for general programming as Python, as easy for
statistics as R, as natural for string processing as Perl, as powerful
for linear algebra as Matlab, as good at gluing programs together as
the shell. Something that is dirt simple to learn, yet keeps the most
serious hackers happy. We want it interactive and we want it
compiled.
(Did we mention it should be as fast as C?)”
(Jeff Bezanson, Stefan Karpinski, Viral Shah, Alan Edelman (2012))
julialang. org/ blog/ 2012/ 02/ why-we-created-julia
Copyright c 2016 Pedro Belin Castellucci.

22. How fast is it?
Figure 3: Speed relative to C smaller is better (C performance is 1.0). According to
julialang.org/benchmarks/.
Copyright c 2016 Pedro Belin Castellucci.

23. Who is using Julia?
Stanford University. Introduction to Multidisciplinary Design
Optimization (Prof. Mykel J. Kochenderfer).
MIT. Integer Programming and Combinatorial Optimization (Prof. Juan
Pablo Vielma).
MIT. Optimization Methods (Prof. Dimitris Bertsimas and Dr. Phebe
Vayanos).
University at Buffalo. Linear Programming (Prof. Changhyun Kwon).
“Sapienza” University of Rome. Operations Research (Giampaolo Liuzzi).
University of South Florida. Nonlinear Optimization and Game Theory
(Prof. Changhyun Kwon).
For more check http://julialang.org/teaching/.
Copyright c 2016 Pedro Belin Castellucci.

24. What can we do with Julia?
Simple Audio IO in Julia (AudioIO),
A neural network (BackpropNeuralNet),
Support vector machines (LIBSVM, LIBLINEAR),
Machine learning (MachineLearning),
Bioinformatics and Computational Biology (Bio),
Curve fitting (CurveFit),
Describe and model financial markets (FinancialMarkets),
Black-box optimization (BlackBoxOptim),
Combinatorics (Combinatorics),
Evolutionary and genetic algorithms (Evolutionary),
Gurobi, GLPK, CPLEX, Cbc, Clp CoinOptServices, JuMP.
For more check: http://pkg.julialang.org/
Copyright c 2016 Pedro Belin Castellucci.

25. What will we do?
Basic Julia programming.
Explore JuMP for mixed integer linear problems.
Copyright c 2016 Pedro Belin Castellucci.

26. Lesson one
Arrays are indexed starting at one.
1
www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.
html
Copyright c 2016 Pedro Belin Castellucci.

27. Lesson one
Arrays are indexed starting at one.
Why numbering should start at zero?1
1
www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.
html
Copyright c 2016 Pedro Belin Castellucci.

28. Lesson one
Arrays are indexed starting at one.
Why numbering should start at zero?1 “I don’t know how many of
you have ever met Dijkstra, but you probably know that arrogance
in computer science is measured in nano-Dijkstras.” (Alan Kay)
1
www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.
html
Copyright c 2016 Pedro Belin Castellucci.

29. Installing Julia
On Linux/Ubuntu:
sudo add-apt-repository ppa:staticfloat/juliareleases
sudo apt-get update
sudo apt-get install julia
For other platforms check
julialang.org/downloads/platform.html.
Copyright c 2016 Pedro Belin Castellucci.

30. This work is licensed under Creative Commons Attribution 4.0
International License. For more information check
https://creativecommons.org/licenses/by/4.0/.
Copyright c 2016 Pedro Belin Castellucci.