An application of mathematical models to select the optimal alternative for an integral plan to desertification and erosion control (Chaco Area – Salta Province – Argentina)

Abstract. Multi-criteria Decision Analysis (MCDA) is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision. These decisions are difficult because the complexity of the system or because of determining the optimal situation or behaviour. This work will illustrate how MCDA is applied in practice to a complex problem to resolve such us soil erosion and degradation. Desertification is a global problem and recently it has been studied in several forums as ONU that literally says: "Desertification has a very high incidence in the environmental and food security, socioeconomic stability and world sustained development". Desertification is the soil quality loss and one of FAO's most important preoccupations as hunger in the world is increasing. Multiple factors are involved of diverse nature related to: natural phenomena (water and wind erosion), human activities linked to soil and water management, and others not related to the former. In the whole world this problem exists, but its effects and solutions are different. It is necessary to take into account economical, environmental, cultural and sociological criteria. A multi-criteria model to select among different alternatives to prepare an integral plan to ameliorate or/and solve this problem in each area has been elaborated taking in account eight criteria and five alternatives. Six sub zones have been established following previous studies and in each one the initial matrix and weights have been defined to apply on different criteria. Three multicriteria decision methods have been used for the different sub zones: ELECTRE, PROMETHEE and AHP. The results show a high level of consistency among the three different multicriteria methods despite the complexity of the system studied. The methods are fully described for La Estrella sub zone, indicating election of weights, Initial Matrixes, algorithms used for PROMETHEE, and the Graph of Expert Choice showing the AHP results. A brief schema of the actions recommended for each of the six different sub zones is discussed.