Distribution of Healthcare resources II.Study and Comparison of a Linear Programming Problem and its Dual. Resolution and Evaluation of a Practical Case and its Programming using Excel and Win QSB.

[EN]This research had as primary objective to model different types of problems using linear programming and apply different methods so as to find an adequate solution to them. To achieve this objective, a linear programming problem and its dual were studied and compared. For that, linear programming techniques were provided and an introduction of the duality theory was given, analyzing the dual problem and the duality theorems. Then, a general economic interpretation was given and different optimal dual variables like shadow prices were studied through the next practical case: An aesthetic surgery hospital wanted to organize its monthly waiting list of four types of surgeries to maximize its daily income. To solve this practical case, we modelled the linear programming problem following the relationships between the primal problem and its dual. Additionally, we solved the dual problem graphically, and then we found the optimal solution of the practical case posed through its dual, following the different theorems of the duality theory. Moreover, how Complementary Slackness can help to solve linear programming problems was studied. To facilitate the solution Solver application of Excel and Win QSB programme were used.

Algoritmos multi-objetivos para la optimización de una secuencia de matrices generadoras en computación cuántica topológica

Quantum Computing is a relatively modern field which simulates quantum computation conditions. Moreover, it can be used to estimate which quasiparticles would endure better in a quantum environment. Topological Quantum Computing (TQC) is an approximation for reducing the quantum decoherence problem1, which is responsible for error appearance in the representation of information. This project tackles specific instances of TQC problems using MOEAs (Multi-objective Optimization Evolutionary Algorithms). A MOEA is a type of algorithm which will optimize two or more objectives of a problem simultaneously, using a population based approach. We have implemented MOEAs that use probabilistic procedures found in EDAs (Estimation of Distribution Algorithms), since in general, EDAs have found better solutions than ordinary EAs (Evolutionary Algorithms), even though they are more costly. Both, EDAs and MOEAs are population-based algorithms. The objective of this project was to use a multi-objective approach in order to find good solutions for several instances of a TQC problem. In particular, the objectives considered in the project were the error approximation and the length of a solution. The tool we used to solve the instances of the problem was the multi-objective framework PISA. Because PISA has not too much documentation available, we had to go through a process of reverse-engineering of the framework to understand its modules and the way they communicate with each other. Once its functioning was understood, we began working on a module dedicated to the braid problem. Finally, we submitted this module to an exhaustive experimentation phase and collected results.

Aplicación de la Programación lineal a la asignación de personal en un centro de llamadas

[ES] La necesidad de gestionar y repartir eficazmente los recursos escasos entre las diferentes operaciones de las empresas, hacen que éstas recurran a aplicar técnicas de la Investigación de Operaciones. Éste es el caso de los centros de llamadas, un sector emergente y dinámico que se encuentra en constante desarrollo. En este sector, la administración del trabajo requiere de técnicas predictivas para determinar el número de trabajadores adecuado y así evitar en la medida de lo posible tanto el exceso como la escasez del mismo. Este trabajo se centrará en el estudio del centro de llamadas de emergencias 112 de Andalucía. Partiendo de los datos estadísticos del número medio de llamadas que se realiza en cada franja horaria, facilitados por la Junta de esta Comunidad Autónoma, formularemos y modelizaremos el problema aplicando la Programación Lineal. Posteriormente, lo resolveremos con dos programas de software, con la finalidad de obtener una distribución óptima de agentes que minimice el coste salarial, ya que supone un 65% del gasto de explotación total. Finalmente, mediante la teoría de colas, observaremos los tiempos de espera en cola y calcularemos el número objetivo de agentes que permita no sólo minimizar el coste salarial sino mejorar la calidad de servicio teniendo unos tiempos de espera razonables.

Mateda-2.0: Estimation of Distribution Algorithms in MATLAB

This paper describes Mateda-2.0, a MATLAB package for estimation of distribution algorithms (EDAs). This package can be used to solve single and multi-objective discrete and continuous optimization problems using EDAs based on undirected and directed probabilistic graphical models. The implementation contains several methods commonly employed by EDAs. It is also conceived as an open package to allow users to incorporate different combinations of selection, learning, sampling, and local search procedures. Additionally, it includes methods to extract, process and visualize the structures learned by the probabilistic models. This way, it can unveil previously unknown information about the optimization problem domain. Mateda-2.0 also incorporates a module for creating and validating function models based on the probabilistic models learned by EDAs.

Environmental Concerns in Water Pricing Policy: an Application of Data Envelopment Analysis (DEA)

25 p.