Multi-Criteria Decision Analysis MCDA

B. Objectives of the Study:

The objective of this paper is to present a hypothetical example of the integration and to show how the integration between GIS and the multi-criteria methods can support spatial decisions. The authors present a case study that is aimed at selecting the best municipal district of Rio de Janeiro State, Brazil, in relation to the quality of urban life. Five families of criteria are analysed: infrastructure, education, security, health and work. Selection of criteria in each of these families was based on the existence, collecting periodicity and reliability of the information. Each municipal district is seen as an alternative represented by polygons of the vector GIS database, and the best municipal district is the one that exhibits the characteristics of urban life quality closest to those desired by the decision-maker.

III. Multi-Criteria Decision Analysis MCDA and Multiple Objective Linear Programming MOLP Models

A. Multi-Criteria Decision Analysis MCDA

According to Gomes and Lins 2002, Decision-making can be defined as the process of choices among alternatives. Multi-Criteria Decision Analysis MCDA, developed in the environment of Operational Research, aids analysts and decision-makers in situations in which there is a need for identification of priorities according to multiple criteria. This usually happens in situations where conflictive interests coexist. Multi-Criteria Decision Analysis MCDA, or Multi Criteria Decision Making MCDM, is a procedure aimed at supporting decision makers whose problem involves numerous and conflicting evaluations. MCDA aims at highlighting these conflicts and deriving a way to come to a compromise in a transparent process. For example, European Parliament may apply MCDA to arrive on a number of conclusions on whether introducing software patents in Europe would help or destroy European software industry. Since MCDA involves a certain element of subjectiveness, morals and ethics of the researcher implementing MCDA plays a significant part on accuracy and fairness of MCDAs conclusion. The ethical point is very important when one is making a decision that seriously impact on other people as opposed to a personal decision. Some of the MCDA models are: Analytic Hierarchy Process AHP, Multi-Attribute Global Inference of Quality MAGIQ, Goal Programming, ELECTRE Outranking, and Data Envelopment Analysis. Which model is most appropriate depends on the problem at hand and may be to some extent which model decision maker is most comfortable with http:en.wikipedia.orgwikiMulti-criteria_decision_analysis. B. Multiple Objectives Linear Programming MOLP Models According to Briassoulis 2007, there are two main groups of LP models, the single and the multiple objective or, multiobjectives . The first deal with problems in which there is one objective to optimize and the second address the more realistic situation of finding solutions which satisfy more than one objective. In both cases, the structure of the optimization problem includes one or more in the case of multiple objectives objective functions and a set of constraints . The objective functions for land use problems expresses in mathematical form the question: how much land to allocate to each of a number of land use types in order to optimize objective A or, B, C, D. The objectives may be, for example, maximization of household or individual rent-paying ability, minimization of environmental impacts, Universitas Sumatera Utara maximization of population income, minimization of the cost of development or maximization of the benefits of development, etc. The constraints which can be taken into account depend on the case but representative objectives include: lower and upper limits on land use reflecting, for example, zoning or natural constraints such as land suitability, other constraints on development, availability of labour, and so on. According to Briassoulis 2007, multiple objective linear programming models MOLP address the question of land use solutions which meet more than one objective. Of particular importance in this context are environmental objectives and constraints. The role of environmental factors in determining the optimal allocation of land uses in a region has always been of high importance in the context of planning in agricultural regions. In addition, the need for detailed information on spatial data as well as for the spatial representation of the optimal land configurations always figured high on the researchers’ wish lists. Progress on and diffusion of GIS techniques and technology since the 1980s mostly has made possible the use of information of better spatial detail and specificity. Linear programming models for agricultural regions appeared which are sensitive to the distribution of environmental conditions in the study areas and which are linked to GIS to provide for mappings of the optimal solutions produced by the models. According to Briassoulis 2007, the objective function of the multiple objective LP model seeks to minimize the cost of meeting these demands and includes two components: a the cost of local production and b the cost of imports to complement local production to meet local demand. The assumption is that the economic costs of production determine whether local demand will be met by local production or by imports subject, among others, to the natural resources constraints facing the study region. The MOLP problem can be generalized as follows Sakawa, 1993 cited by Tomas, 2006: Minimize k linear objective functions Z 1 x=c 1 x Z 2 x=c 2 x . . . Z k x=c k x Subject to the linear inequality constrains A X b, And the non-negativity conditions X Where : z 1 ,…,z k are the measures of effectiveness profits or costs. i = 1,…, k Ci = c i1 ,…,c in represent the costprofit coefficients. X = x 1 ,…,x n T refer to the decision variables. A = a 11 , …, a 1n . . . A m1 ,…,a mn B = b 1 ,…,b m T are the available resources. Symbolize the production or activity coefficients Universitas Sumatera Utara If the notion of optimality for single-objective LP is directly applied to this MOLP, we arrive at the following notion of a complete optimal solution.

IV. GIS-Multi-criteria integration