Describe the simple additive weighting method.
SAW - Simple Additive Method (SAW) is probably more often used method of MADM.
- The method is based on maximal the trade-off of variants.
- The simplification is established only by linear function of trade-off.
- The method requires – нуждается во all maximal criteria, the same scale and existing - существующих weights’ vectors.
Simple Additive Method:
1. Transformation all qualitative criteria to quantitative (qualitative criteria => quantitative)
2. Transformation cost criteria to benefit criteria (cost criteria => benefit criteria)
3. Find -Ideal (H) variant – max in every column
-non-ideal (basal) (D) variant – min in every column
4. Construction of weighted vector (Normalization ???):
• Dj is non-ideal (a column minimum)
• Hj is ideal (a column maximum)
• xij is a value of i-th variant under j-th criterion
• aij is standardized value of xij (aij is an element of A matrix); Aij принадлежит <0;1>
5. Utility (total trade-off) calculation
Madm Advanced methods
What is the principle of the topsis method?
TOPSIS (=Technique for Order of Preference by Similarity to Ideal Solution).
TOPSIS calls for ordinal information on attributes of variants as well as the criteria preference expressed in weight vector. The method is based on measuring distance from the ideal and negative-ideal solution. The main idea is that the best (preferred) variant is the closest to the ideal and in the highest distance from the negative-ideal solution.
Describe the priam method and the role of standard levels.
PRIAM (=Priam – Programme utilisant l’Intelligence Artificiele en Multicritere)
It is a distance from standard level.
It is a method based on standard level information consequential t the Sequence method. The satisfying alternative must meet certain absolute standards i.e. minimal attribute values.
Describe the ahp method. For which cases it is suitable?
AHP - ANALYTICAL HIERARCHY PROCESS
This method can be used in decision making in specially complicated situations. This task could be divided into several layers and the Saaty ́s method is used in each layer.
The highest level can have only one element - the goal of decision making - with the weight equal to 1. Second layer can have several elements ( e.g. criteria or experts) and the weight 1 is divided among them using Saaty ́s method. Each of these elements can have its subordinate layer (e.g. subordinate criteria, subordinate experts, variants) and the weight of the superior element ( not 1! ) is divided among subordinate element using Saaty ́s method. This process is repeated till the lowest layer (usually decision variants )
Input-output analysis
Describe the quadrants in the input-output table.
In the input-output analysis we have 3 quadrants (3 сектора):
1. (Xij) - Sector of semi-finished products (Сектор полуфабрикатов) - книги
2. (Yi) - Sector of final products (Сектор финальной продукции) – лес, веревки и тп (материал, необходимый для изготовления книги)
3. (Zkj) -Sector of costs/outgoings/expenses (Сектор издержек) – издержки на зарплату и тп
3 Conditions / rules:
Sum Xij + Yi = Xi (Sum in row = Xi)
Sum Xij + Sum Zkj = Xj (Sum in column = Xj)
Xi = Xj (it mean that table is symmetrical)