BIT FInal

Consistency Index Formula

CI = (Average - n)/(n-1), where n is number of items compared

Scoring Model Overview

Each decision alternative is graded in terms of how well it satisfies the criterion according to following formula: Si = Sum of gijwj where: wj = a weight between 0 and 1.00 assigned to criterion j; 1.00 important, 0 unimportant; sum of total weights equals one. gij = a grade between 0 and 100 indicating how well alternative i satisfies criteria j; 100 indicates high satisfaction, 0 low satisfaction.

The Analytic Hierarchy Process (AHP) is a method that can be used for ranking several decision alternatives with only one criterion (objective) each and selecting the best one T/F

F

With AHP, perfect consistency will result in a Consistency Index (CI) of 1.0. T/F

F

Multi-criteria Decision Making

Study of problems with several criteria, i.e, multiple criteria, instead of a single objective

AHP: a process for developing a numerical score to rank each decision alternative based on how well the alternative meets the decision maker's criteria T/F

T

The objective function in a goal programming model seeks to minimize the deviation from goals in the order of the goal priorities. T/F

T

AHP: Preference Scale

assigns numerical values to different levels of performance

AHP: Pairwise Comparisons

two alternatives are compared according to a criterion and one is preferred

All of the following are true concerning multicriteria decision making except: -multicriteria problems can have more than one goal or objective when making a decision. -goal programming can be used to solve certain types of multicriteria problems. -all criteria will be met (i.e. all objectives will be satisfied) when solving a multicriteria problem. -All of the above are true concerning multicriteria problems.

all criteria will be met (i.e. all objectives will be satisfied) when solving a multicriteria problem

AHP: row average values represent the?

preference vector

AHP: Pairwise Comparison Matrix

summarized the pairwise comparisons for a criteria

A CI of what indicates perfect consistency?

0

AHP General Mathematical Process

Mathematically determine preferences for sites with respect to each criterion Mathematically determine preferences for criteria (rank order of importance) Combine these two sets of preferences to mathematically derive a composite score for each site. Select the site with the highest score

Goal programming is a form or variation of linear programming that allows for more than one objective or goal in the objective function. T/F

T

Scoring Models

based on a relatively simple weighted scoring technique

AHP: Consistency Index (CI) does what?

checks for consistency and validity of multiple pairwise comparisons

Analytical Hierarchy Process

develops a score for each decision alternative based on comparisons of each under different criteria reflecting decision makers' preferences

Under goal programming, objectives (goals) are added in:

order of importance

Under AHP: which alternative will the decision maker select?

the alternative that best meets the decision maker's criteria

Degree of consistency is satisfactory if CI/RI < what?

0.10

AHP Process Summary of Mathematical Steps

1. Develop a pairwise comparison matrix for each decision alternative for each criteria. 2. Synthesization a. Sum each column value of the pairwise comparison matrices. b. Divide each value in each column by its column sum. c. Average the values in each row of the normalized matrices. d. Combine the vectors of preferences for each criterion. 3. Develop a pairwise comparison matrix for the criteria. 4. Compute the normalized matrix. 5. Develop the preference vector. 6. Compute an overall score for each decision alternative 7. Rank the decision alternatives.

All of the following are characteristics of a goal programming problem or model except: -Goals, or objectives, of the model are added in order of importance. -All goal constraints are inequalities. -A positive deviational variable is the amount by which a goal is exceeded while a negative deviational variable is the amount by which a goal is underachieved. -At least one or both deviational variables in a goal constraint must equal zero.

All goal constraints are inequalities

Goal programming solutions do NOT always achieve all goals and they are NOT optimal; they achieve the best or most satisfactory solution possible T/F

T

Under AHP: the decision maker makes a decision based on how the alternatives compare according to several criteria T/F

T

Under goal programming: A negative deviation variable (d-) is the amount by which a goal level is underachieved T/F

T

Under goal programming: A positive deviational variable (d+) is the amount by which a goal level is exceeded T/F

T

Under goal programming: All goal constraints are equalities that include deviational variables d- and d+ T/F

T

Under goal programming: At least one or both deviational variables in a goal constraint must equal zero T/F

T

Under goal programming: Two or more goals at the same priority level can be assigned weights to indicate their relative importance T/F

T

Under goal programming: the objective function seeks to minimize the deviation from the respective goals in the order of the goal priorities T/F

T

When combining the preference vector and the preference matrix with AHP, the decision alternative with the highest score is the best decision to choose. T/F

T

Analytical Hierarchy Process (AHP)

method for ranking several decision alternatives and selecting the best one when the decision maker has multiple objectives, or criteria, on which to base the decsiion

All of the following are true concerning pairwise comparisons with the Analytical Hierarchy Process (AHP) method except: -pairwise comparisons are completely objective in their preferences. -pairwise preferences that are approximately equally preferred have a lower score or value than pairwise preferences where one item is greatly preferred over another. -pairwise comparisons are used to create both the preference vector and the preference matrix. -pairwise comparisons in one direction result in a reciprocal score in the opposite direction, i.e. if a comparison of A to B results in a score of 7 then the comparison of B to A would result in a score of 1/7.

pairwise comparisons are completely objective in their preferences

With scoring models, all of the following are true concerning the criteria weights except: -more important decision criteria are assigned weights with larger values. -the cumulative scores that are calculated using the decision criteria weights and scores are simply weighted averages for each decision alternative. -the sum of the decision criteria weights will always be greater than 1. -All of the above are true concerning the criteria weights used with scoring models.

the sum of the decision criteria weights will always be greater than 1

Goal programming

a variation of linear programming considering more than one objective (goals) in the objective function

All of the following are true concerning using scoring models for multicriteria decision making except: -the scores for each criteria are divided by the weights in order to determine which alternative is the best. -each criteria is assigned a weight according to its relative importance to the decision. -each criteria is scored or graded according to how well the alternative satisfies the given criteria. -the decision alternative with the highest weighted total score is the one that is chosen.

the scores for each criteria are divided by the weights in order to determine which alternative is the best