Combinatorial explosion

Combinatorial optimization is about picking one element of a set of finite objects that optimizes an objective function. Put in this way, the solution may seem straightforward: just enumerate all elements of the set and assess the objective function for each object.

The problem with this naïve approach is that the number of elements of the set can be very large. Let's consider, for instance, the symmetric travelling salesperson problem. For an instance of n nodes, the number of possible solutions is the factorial of (n-1) divided by two. This means that, for a problem of size n=20, and taking one millisecond to assess each solution, it takes around 1,108,606 years to assess all solutions. This effect is called combinatorial explosion.

This video shows an example of an even faster combinatorial explosion. Additionally, helps in learning how to count large numbers in Japanese...

Modeling and Solving Linear Programming with R

Citation

Sallan, Jose M.; Lordan, Oriol; Fernandez, Vicenc (2015). Modeling and Solving Linear Programming with R. Omniascience.

Abstract

Linear programming is one of the most extensively used techniques in the toolbox of quantitative methods of optimization. One of the reasons of the popularity of linear programming is that it allows to model a large variety of situations with a simple framework. Furthermore, a linear program is relatively easy to solve. The simplex method allows to solve most linear programs efficiently, and the Karmarkar interior-point method allows a more efficient solving of some kinds of linear programming. The power of linear programming is greatly enhanced when came the opportunity of solving integer and mixed integer linear programming. In these models all or some of the decision variables are integers, respectively.

In this book we provide a brief introduction to linear programming, together with a set of exercises that introduce some applications of linear programming. We will also provide an introduction to solve linear programming in R. For each problem a possible solution through linear programming is introduced, together with the code to solve it in R and its numerical solution.

Availability

Please see Omniascience website for details, and the repository containing the code used in the book.

Also available through UPCommons in this direction.

Correlation does not mean causation II

Just another example of spurious correlation...

An Examination of the Effects of Self-Regulatory Focus on the Perception of the Media Richness: The Case of E-Mail

Citation

Armengol, Xavier; Fernandez, V.; Simo, P.; Sallan, J. M. (2015). An Examination of the Effects of Self-Regulatory Focus on the Perception of the Media Richness: The Case of E-Mail. International Journal of Business Communication
http://dx.doi.org/10.1177/2329488415572780

Abstract

Communication is a key element in organizations’ business success. The media richness theory and the channel expansion theory are two of the most influential theories regarding the selection and use of communication media in organizations; however, literature has focused little on the effects of self-regulation by managers and employees in these theories. To analyze these topics, this study develops an empirical investigation by gathering data from 600 managers and employees using a questionnaire. The results suggest that the perception of media richness is positively affected when the individual shows a promotion focus or strategy.

Correlation does not mean causation

A variety of images showing that correlation does not imply causation.

A plot showing the relationship between the number of Nobel prizes earned in each country, and chocolate consumption. Both data are adjusted by the population of each country (an indirect source of this graph here).

Phenomena like the shown in the image above usually come from the fact that both variables involved correlate highly with a third (not shown) variable. Many times this third variable is population (source: xkcd)

The fact that a linear association might be easily confounded with a causal relationship may be the reason of the mith that storks deliver babies. This article shows the strong correlation between stork population and human birth rate.

Conclusion, keep in mind that correlation does not mean causation. Although an unexpected correlation may lead to a serendipious discovering (source: xkcd)...

50 shades of grey

The readers of the novel series on unconventional desires may enjoy this little picture showing (literally) 50 shades of grey:

The picture is easily generated using the following R code:

shades <- seq(0, 1, length.out =50)
m.shades <- matrix(rep(shades, 50), 50, 50)
shades.of.grey <- grey(shades)
png("shades.png")
image(m.shades, col=shades.of.grey)
dev.off()

Estudio de un plan de operaciones para una nueva modalidad de handling en la terminal T1 del aeropuerto BCN-El Prat

Student

Àlvar Jaime Hileno

Supervisors

Oriol Lordan / Jose M Sallan

Defense date 

30th June, 2014

Abstract

Carrying the luggage to the airport on your way back home can be an exhausting and stressing task, and some customers of luxury hotels may be interested in a service in which their luggage is dropped directly in the hotel.

This project assesses the operational, legal and financial viability of a business consisting in facilitating the check in directly in the hotel, and carrying customer's luggage directly to the airport handling services in the context of the El-Prat Barcelona (BCN) airport.