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The IRR is the solution of the equation for r:
Explanation of individual variables in the equation is provided at the NPV equation.
AHP multi-criteria decision model
AHP višekriterijski model odlučivanja
The AHP is a multi-criteria decision-making technique that decomposes a complex problem into a hierarchy of less complex individual problems. The AHP is applied using the following steps (Saaty 1980):
AHP enables decision makers to incorporate both subjective and objective matters into the decision making process. This is done by describing complexity as a hierarchy and ration through a comparison of those alternatives relative to the objective (called pair-wise comparison). However, at each level of the hierarchy, the relative importance of each component attribute is assessed by comparing them in pairs. The rankings obtained by the pair-wise comparisons between the alternatives are converted into normalized rankings using the eigenvalue method. The pair-wise comparison reflects the makers’ estimates made by the decision maker regarding the relative importance of each alternative in terms of a given decision criterion. A typical problem examined by the AHP consists of a set of alternatives and a set of decision objectives. In applications of the AHP to real decision-making problems, the entries in the above reciprocal matrix are taken from the finite set: {1/9, 1/8,…1, 2,…8, 9} (as suggested by Saaty (1980)). The above discrete set is usually used in practice.
The AHP employs three commonly agreed decision making steps:
(1) Given i = 1, …, m objectives, determine their respective weights wi,
The weights determination is based upon pair-wise comparison matrix. The preferences in the matrix are estimated on the 1–9 comparison scale where 1 expresses equal preference for two compared criterions and 9 the strongest preference for one criterion over the other. Weights of criteria were determined in brainstorming (from six experts) through the Means of pair-wise comparisons (Figure 3).
(2) For each objective i, compare the j = 1, …, n alternatives and determine their weights aij with respect to objective i, and
(3) Determine the final (global) alternative weights (priorities) Wj with respect to all the objectives by Wj = a1jw1 + a2jw2 + … + amjwm.
The alternatives are then ordered by the Wj, with the most preferred alternative having the largest Wj. For more precise description of AHP procedure, see Saaty (1980).
Judgment consistency is checked by the consistency ratio (CR) of CI. A consistency index of 0.10 or less is considered acceptable. If the value is higher, the judgments may not be reliable and have to be elicited again. The AHP has been applied too numerous real-life decisions and evaluation problems (Saaty 2008). In AHP model development, the software package "Expert Choice 2000TM" (EC) was used. The final structure of attributes for the assessment of environment regulation (silvopastoral system) around landfill Gajke is shown in Figure 4.
As seen in Figure 4, the decision problem is constructed as a hierarchy. The hierarchy of the model was also established through the brainstorming of six experts involved in model development. The most common structure is a tree, where higher-level attributes depend on the direct followers. Terminal nodes on the right-hand side of the tree represent inputs to the model, and the left side represents the main output: "Appropriate environment regulation around the landfill Gajke." The decision model is constructed from three main criteria at the primary level, nine sub-criteria at the secondary level, and two sub-criteria at the lowest level. Figure 4 also shows calculated priorities.
The "technological criteria" aggregate attribute consists of four basic attributes and two sub-attributes. The "environment criteria" aggregate attribute consists of three basic attributes. The last aggregate attribute describes the economic