Mathematical Models Generators of Decision Support Systems for Help in Case of Catastrophes

Abstract

Immediately after the catastrophes that affected Venezuela at the end of 1999, especially the flood of the State of Vargas, a group of investigators of a consultancy company and of a private university of Caracas Venezuela, started working in decisions support systems (DSS) that could be useful in the moment of a catastrophe, helping to minimize the impact of its three principal stages: Pre-catastrophe, Impact and Post-catastrophe. Clearly, for the development of these DSS, it was indispensable to construct mathematical models to support them. The objective of this chapter is to disclose this experience by presenting some of these mathematical models and its conversion in DSS that supports decision making in the case of catastrophes.

Matrixes of Weighing and Catastrophes

“…Models, including mathematical models have been used to explain the catastrophes (Makowski, 2009;Yahaya, Ahmad, & Abdalla, 2010;Zhou et al, 2009) and to give support before, during or after them (Frysinger et al, 2007) and many of these models have been integrated to decision support systems (DSS) Hernández & García, (2010). Even though support systems to decision making could be of great use during a catastrophe (Borysiewicz, Potempski, & Galkowski, 2001;Gadomski et al, 2001;Mendonça, Beroggi, & Wallace, 2001;Sanders & Tabuchi, 2000) there is also a considerable value for them in the pre-catastrophe phase, when no event that caused an important rapture has occurred, but the population is preparing for such event, especially those that had been determined as possible shelter, as in the post-catastrophe phase, when the event has already occurred and the goal is to recover, at least, the life conditions that existed before the catastrophe.…”

“…Multiplicative factors were taken from other multi-criteria model, the Multiattribute Models (MM) with multiplicative factors, as defined previously by Hernández and García (2007) and presented too in Hernández & García, (2010), mainly following Baucells and Sarin (2003), Ben-Mena (2000) and Ehrgott and Gandibleux (2002) and in interest of this investigation it is enough to present the three equations that rule them, the (3) for MM without multiplicative factors and ( 4) and ( 5) with multiplicative factors.…”

“…In the case of MOW, since there are no attributes for the criteria, there will be no sense in speaking of multiplicative factors of the criteria, but there will only be taken into account the general multiplicative factors, there equation ( 6), becomes a combination from ( 1) and ( 4) maintaining the nomenclature of equation ( 1), and where now the fgh represents the general factors of the MOW, varying from h = 1 to H, with H being the number of total general factors, although in the MM, it is not recommended to be more than three (Hernández & García, 2010), in the MOW there is usually a bigger amount of factors.…”