Hierarchical Model
Structure of the Hierarchical Model
It is one of the most relevant parts of the process. It consists on defining the hierarchical structure of the problem. During this stage the decision-making group should break down the problem into its most relevant components. The basic hierarchy is defined by: criteria (general objective), subcriteria and alternatives.
To build up a group decision, a Workshop was held on January 29, 2015. The workshop was attended by the following people, who acted as experts: representing Enami, José Moscoso, Custodio Araya, and Yerko Gonzales; Representing the Undersecretary of Mining, Francisco Donoso and Emilio Castillo; and finally, as participants of the research team of the project, Raul Jara, Carlos Marquardt, José Joaquín Jara and David Peters.
The choice of experts tried to blend up the skills and the experiences in all the fields of an exploitation and gold placers project. For this, experts were defined based on the hierarchical criteria of the model.
The participants who contributed with their knowledge in the criterion of “business potential” were the UC researchers, who also participated in the bibliographic review and knew the potential of all prospect to evaluate.
In terms of economic technical feasibility, the participants from PUC and ENAMI were the most experts in the area. The reason is because in both group people worked in gold placers in the decade of the 80s.Therfore they knew how this kind of operation works. In addition, ENAMI participants often work with artisanal and small-scale miners. So, they are aware of the impact of such operations in different areas of the country.
As for the criteria of Other (Exploitation Feasibility), the ones with a high level of knowledge were the participants of ENAMI and COCHILCO. The reason is because they are constantly evaluating mining projects and know which variables are the most relevant.
Finally, for the business impact criteria, COCHILCO experts were the best considered. Since they have a wide knowledge of how mining impacts on the different areas where it’s established. The following table summarizes the basic criteria when choosing the experts based on their knowledge in terms of hierarchical model standards.
It is ideal, that most participants in the hierarchical workshop should be familiar with alluvial gold operations. For example, working directly or indirectly on this type of exploitations.
To generate an AHP, the steps are:
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Problem Identification:
It is the situation to be resolved by prioritizing the alternatives. In this case the prioritization will offer a ranking of the deposits based on their viability to be exploited.
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Main Goal Definition:
One goal is to identify directions to improve an existing situation and the background based on which alternatives must be evaluated. The main goal to be found is the possibility of exploitation of each prospect through the analysis of the alternatives and established criteria, is the possibility of exploitation of each prospect.
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Identification of criteria:
They are the most important dimensions that significantly affect main goals and must express the preferences of those involved in decision making. Quantitative and qualitative aspects must be included. For the analyzed case, the following criteria were defined: business potential, economic feasibility, other viability, exploitation and business impact.
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Identification of alternatives:
They are the proposals by which general goals can be achieved. Each of the alternatives has pros and cons.
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Hierarchical Maps:
It consists in the elaboration of a graphical representation of the problem in terms of general goals, criteria and alternatives.
Evaluation of the Model
The evaluation examines the elements of the problem in isolation through peer comparisons.
After analyzing and categorizing the most important features of alluvial gold prospects which exist within the Chilean territory, it is important to order them based on their capacity to carry out an eventual exploitation. The last one is defined by its technical characteristics, business potential and other relevant variables of each prospect. This can be summarized in the following table.
Hierarchical Model’s Introduction
Hierarchical structure. Focus on dark blue, criteria in light blue, subcriteria in green and alternatives on white. All subcriteria has many different alternatives.
To achieve the task, in which the result is linked to the multiple criteria problem’s resolution, we used the process known as AHP (Analytical Hierarchical Process).
The Hierarchical Analytical Process is a method of decomposing complex structures into their components. It works by ordering the components or variables into a hierarchical structure, after that numerical values are obtained to be judged as it’s preferred. Finally, they are synthesized to find out which variable has the highest priority.
In the following graph, you can see how the AHP methodology works. The focus is separated into several subproblems. Every subproblem has different options for each variable. Finally, all the variables are synthesized and the hierarchical level of each general alternative is obtained.
The main difference of this method compared to another method of prioritization is that it breaks down the problem into several subproblems. Every subproblem has a specific weight associated to them. The previous information is based on comparisons made by experts in the area. Once we have the specific weights of every subproblems, we proceed to synthesize all the information. Then we established which alternative of each variable is more convenient. In this way, this method finds out a solution to a multicriteria prioritization problem.
El AHP is based on:
In other words, the steps are:
• Define variables of the problem.
• Do paired comparisons to find out the specific weights.
• Weighting the specific weights of each alternative.
• Establish a standard scale of preferences.
• Build up the ranking.
AHP Mathematical Base
The AHP deals with ordered pairs of priorities or preferences of elements in pairs based on a common criterion, which is represented in the decision hierarchy. In this case once the hierarchy and valorization of each field are obtained they are combined by the geometric average.
To establish a matrix of priorities, the following steps must be followed:
1. Paired Comparisons
2. Priority setting
3. Synthesis
4. Judgments consistency verification
5. Definition of final priorities of the prioritization model
