Alberto Rojo-Alboreca

The triangle assessment method

We introduce a new method (MTC) for eliciting expert opinion by comparison of trios.We present the axiomatic bases and theorems for the MTC.We compare the MTC and the Analytic Hierarchy Process (AHP).We illustrate an example of application of the MTC to multi-criteria decision-making. The Analytic Hierarchy Process (AHP) is one of the most widely used Multi-Criteria Decision-Making methods worldwide. As such, it is subject to criticisms that highlight some potential weaknesses. In this study, we present a new Multi-Criteria Decision-Making method denominated the Triangular Assessment Method (referred to by its Spanish abbreviation, MTC). The MTC aims to make use of the potential of AHP while avoiding some of its drawbacks. The main characteristics and advantages of the MTC can be summarised as follows: (i) evaluation of criteria, and of the alternative options for each criterion, in trios instead of pairs; (ii) elimination of discrete scales and values involved in judgements; (iii) a substantial reduction in the number of evaluations (trios) relative to the corresponding number of pairs which would have to be considered when applying the AHP method; (iv) consistent decision-making; (v) introduction of closed cyclical series for comparing criteria and alternatives; and (vi) the introduction of opinion vectors and opinion surfaces. This new method is recommended for supporting decision-making with large numbers of subjective criteria and/or alternatives and also for group decisions where the consensus must be evaluated. The MTC provides a different promising perspective in decision-making and could lead to new research lines in the field of information systems.

Recomendaciones en el uso de la optimización matemática en las disciplinas forestal y agraria con CPUs domésticas

La resolucion de problemas de optimizacion basados en programacion lineal por el metodo de Gauss-Jordan ha demostrado ser viable y aconsejable a la hora de resolver problemas de gestion forestal. Sin embargo, cuando se aplica a problemas de gran magnitud, tal como la gestion de cortas en montes grandes que se dividen en multitud de rodales, la funcion objetivo suele contener un elevado numero de variables basicas, existiendo ademas un conjunto numeroso de restricciones. Esto produce que en los modelos se mezclen coeficientes con gran diferencia de escala, con la consecuente aparicion de residuos derivados de las operaciones matematicas, independiente de la precision numerica que se utilice. Dichos residuos pueden desembocar en una solucion no optima o incluso impedir la resolucion del problema. Para evitar esto, el uso de tecnicas de escalado permite homogeneizar el orden de magnitud de los coeficientes en las restricciones. Sin embargo, los procesos de escalado automatico no siempre son eficientes, mientras que el escalado manual no es viable debido al gran volumen de restricciones. En este trabajo se presenta un protocolo para el escalado de las variables en las restricciones de los problemas de programacion lineal con el objetivo de minimizar la aparicion de residuos.