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Good afternoon, my name is Gianfranco Cossani and I'm one of the authors of this paper.
INTRODUCTION
In recent years, many countries have starting to worry about their educational systems because of increasing demand, declining of finantial resourses and greater competition.
In Chile, a developing country in south america, we have the same concern.
In the "education at a glance" report of 2016, as you can see here, the OCDE states that Chile have one of the biggest expenses on education between all the countries and, at the same time, the OCDE indicates that the quality between institutions is very uneven. On the other hand, the market share of private institutions has grown, but this kind of institutions are seen as inferior than public universities by the citizens.
The government assigns grants to the institutions. The key to make a fair allocation of the resources is to know the efficiency of all of them, for example, the AFD, or Direct Fiscal Contribution, which is the most important funds that the state gives to the universities in Chile. This consist of free-destination money, and is assigned based on historical data and only the 5% is based on performance indicators, like enrollement, number of PhD professors, the number of publications and research projects.
RANKINGS
The most used way to compare universities are rankings, which are the weighted sum of some indicators.
[The weights for each indicator are assigned by the makers of the ranking. This causes us concern about the influence of a researcher in the rank of an institution on the ranking, even if he doesn't pretend it, as some institutions will have a different vision than the researcher about what a university should do.]
By the other hand, rankings are based on output indicators, without considering the limitation of initial resources.
DEA

INDICADORES Y ESTRUCTURA
Through an extensive bibliographical analysis we can find the most used indicators to describe the universities production process. This indicators are the following:
	- Academic Staff without PhD
	- Operational expenses without labor expenses
	- AFD
	- Infrastructure
	- Weighted PSU Scores
	- Undergraduate Students Enrolled
	- Doctorare-level Students Enrolled
	- Professors with doctoral degree
	- Undergraduate Degree
	- Doctorate-level degree
	- Publications
	- Research Grants
	- SJR Indicator
If we use a DEA network model, we need to determine the processes that conform an university, its internal structure and what inputs and outputs has every process.
Based on the work of (Lee, 2016) and (Monfared, 2013), we determined that the best structure to represent a university is this. With a process of teaching that shares resources with research and a grants applying process that feed the research process on the next years.
MODELO
Our work is based on Tone's Dynamic DEA with network structure SBM model, but using (Kao, 2015)'s method to determine the weights, we don't need to determine the weights beforehand.
We use sets to represent the data. The letters used are based on Kao's work, but, we didn't divide the resources in X for inputs and Y for outputs, instead, we use Z to represent the value of the indicator at the DMU at the period, for example, we can represent the number of undergraduate students on the Universidad de Chile at the year 2016.
Using the sets notation allows us to write the models in different programing languages [in an easy way], and to provides a clear vision about the impact of each variable and each constraint. This model includes all the constraints present in Tone's work.
SHARED RESOURCES
A problem with this model is the lack of shared resources. The universities have shared resources between processes, for example, the infrastructure, defined as the built area , is shared between teaching and research {in a certain fraction}, which may not be the same between all universities, thus, the distribution of resources must be chosen by the institutions, due to each one could have different priorities.
If we add the variable alpha to represent the fraction of an indicator that goes to a certain process, this will result in a non-linear formulation of the problem.
Inspired by the radial models that allow the use of shared resources, as the (Du, 2015)'s radial, network model, we derivate the dual formulation, then add the alpha variable and find the new primal formulation.
The new constraints keep their lineal nature and represent the shared resources.
RESULTADOS
We used as study case the chilean universities at the year 2016, and solve the radial model, Tone's Dynamic SBM with network structure and our proposed model and proceed to compare the results.
As we can see on this table, the number of efficient units is [greater|minor] than with the other methods.
Also, the position of, for example, Pontificia U. Católica De Valparaíso, that is on position 4 on the QS Ranking, 5 on the America Economia ranking, and 9 on the Times Higher Education ranking, is on position 19 on the radial model and 30 on the SBM. Our model places it on position . On all the DEA models this university is considered efficient.
This example university is a big university, one of the greatest of the country, so it has a lot of inputs and is expected to have a lot of outputs. The tradicional rankings, that only counts for outputs indicators, place it into the top, but the DEA models, that evaluate performance based on the inputs and outputs, place it below than the traditional rankings.