Decision Support Systems and Intelligent Systems PERTEMUAN 13

Decision Support Systems and Intelligent Systems PERTEMUAN 13 PROGRAM STUDI SISTEM INFORMASI FAKULTAS ILMU KOMPUTER

Weighted Product 2

Acknowledgement These slides have been adapted from these online resources: n n Kaliszewski, I. , & Podkopaev, D. (2016). Simple additive weighting—A metamodel for multiple criteria decision analysis methods. Expert Systems with Applications, 54, 155 -161. Melia, Y. (2016). Multi Attribute Decision Making Using Simple Additive Weighting and Weighted Product in Investment. International Academic Journal Of Business Management, 3(7), 1 -15. 3

Outline n Multiple-criteria decision-making n Weighted Product n Case Study: Food Choice 4

Multiple-criteria decision-making n Multiple-criteria decision making or multiple criteria decision analysis is a field in operational research that explicitly use multiple conflicting criteria for evaluating alternatives. n Typically, the unique optimal solution does not exist for such problems and therefore it is important to use decision-makers’ preferences to evaluate solutions. 5

Multiple-criteria decision-making n Multiple-criteria decision making combines several fields including n Economics n Decision Analysis n Mathematics n Software Engineering n Information Systems n Computer Technology 6

Solving Multiple-criteria decision-making n Methods that are available for solving multiple-criteria decision making: n Analytic Hierarchy Process n Weighted Sum Model n Weighted Product Model n Decision Expert n Rough Set n Goal Programming n Simple Multi-Attribute Rating Technique 7

Solving Multiple-criteria decision-making n Multi-Attribute Decision Making refers to screening, prioritizing, ranking, or selecting a set of alternatives usually under independent, incommensurate or conflicting attributes (Melia, 2016), that can be expressed in the matrix below: 8

Solving Multiple-criteria decision-making n Where n A 1, A 2, . . . , Am are feasible alternatives n C 1, C 2, . . . , Cn are criteria n wj is a weight (significance) of j-th criterion. n xij is the performance rating of i-th alternative with respect to j-th criterion 9

Weighted Product n Weighted product is another scoring method similarly to Simple Additive Weighting (SAW). n It was also proposed as a method for solving multiple objective linear programming with the assumption of concave utility function. 10

Weighted Product Algorithm n n Step 1 -2: identical to SAW method (see previous slide) Step 3: Calculate normalized decision matrix Step 4: Construct weighted normalized decision matrix. Step 5: Calculate the score of each alternative 11

Weighted Product n Step 6: Select the best alternative n Where n n BAwp is the best alternative in Weighted Product (WP) method M is matrix score. 12

Case Study: Food Choice (similar to previous slide) https: //en. wikipedia. org/wiki/Staple_food 13

Step 3: Construct normalized decision matrix n Table 10 shows score (Si) on each alternative with process value of decision matrix (dij) on Table 5 squared by weight conversion on Table 4 based on decision makers. 14

Step 4: Construct weight normalized decision matrix. n Table 11 shows value (v ) weight normalized matrix with process is score each of alternative (S ) multiply by sum of all of score. ij i 15

Step 5: Calculate the score of each alternative Table 12 shows score of each alternative on WP method for food alternative in MADM. 16

Step 6: Select the best alternative n Table 13 shows highest value is alternative on v 7, so alternative A 7 (wheat) is chosen as the best alternative. Best alternative is wheat (highest score). 17

Comparison between WP and SAW 18