Deck 10: Multi-Criteria Models

Question 1

Goal programming differs from linear programming in the nature of constraints and the objective function.

Answer 1

True

Question 2

Constraints in linear programming may be considered as soft constraints, and the constraints in goal programming may be considered as hard constraints.

Answer 2

False

Question 3

In goal programming, hard constraints are satisfied and soft constraints are brought to acceptable levels (satisfying).

Answer 3

True

Question 4

In goal programming, we need to ensure that while solving problems corresponding to lower priority goals, higher priority goals are not diminished.

Question 5

Goal constraints have deviation variables and are expressed as equations.

Question 6

In goal programming problems with unweighted priority, we solve one linear program to simultaneously optimize all goals.

Question 7

There are two distinct ways in which goal programming problems may be formulated and solved.

Question 8

In goal programming problems with weighted priority, we solve one linear program to simultaneously optimize all goals.

Question 9

Goal programming solutions are similar to linear programming solutions in that they answer the question of how much for each decision variable.

Question 10

While solving goal programming problems using graphical method, deviations from the constraints can be found directly from the graph by reading off the $\mathrm{X}$ and $\mathrm{Y}$ axes.

Question 11

The weighted goal programming model has many similarities with the linear programming model.

Question 12

The Analytical Hierarchy Process answers the question of which alternative to select based on multiple criteria.

Question 13

There are two distinct approaches in which Analytical Hierarchy Process problems may be formulated and solved.

Question 14

In Analytical Hierarchy Process, the normalized pairwise comparison matrix has rows adding up to 1.0.

Question 15

In the Analytical Hierarchy Process, one multiplies the pairwise comparison matrix by criteria $\%$ to get weighted sum priority vector.

Question 16

In the Analytical Hierarchy Process, the normalized pairwise comparison matrix has columns adding up to 1.0 .

Question 17

In the Analytical Hierarchy Process, the pairwise comparison matrix is to be generated for each criterion used for evaluation.

Question 18

Consistency ratio below 0.10 will affect the results of the Analytical Hierarchy Process.

Question 19

As the number of pairwise comparisons increases, the possibilities for inconsistencies decrease as one inconsistency may compensate for the other inconsistency in the opposite direction.

Question 20

As the number of items (decision alternatives) increases, random index value used in consistency calculations increases.

Question 21

Consistency ratio above 0.10 indicates that the problem has an acceptable level of inconsistency.

Question 22

In the Analytical Hierarchy Process, evaluation of the objective criterion such as price will not have any subjectivity.

Question 23

In the Analytical Hierarchy Process, the decision maker's subjective judgment is included in the evaluation process and hence the same problem solved by two different decision makers may yield completely different results.

Question 24

In the Analytical Hierarchy Process, preference scales for pairwise comparisons are given by the decision maker, and the numbers 2 or 4 do not have any ranking (meaning 2 is not necessarily less preferable or more preferable to 4 ).

Question 25

In the Analytical Hierarchy Process, the graphical representation of hierarchies diagram has a number of decision alternatives in the second level (that is, if we had 5 choices from which we want to choose one, there will be five entries in the second level).

Question 26

In the Analytical Hierarchy Process, if the rating for Attribute1-Attribute2 is equal to 5 in the eyes of the decision maker, then the rating for Attribute2-Attribute1 will be equal to 1/5.

Question 27

In the Analytical Hierarchy Process, random index values decrease as the number of criterion increases.

Question 28

In the Analytical Hierarchy Process, consistency of a decision maker is perfect if the consistency index is at least 0 .

Question 29

Pairwise comparison is the foundation of the scoring models for choosing among alternatives.

Question 30

Using the weighted priority scores, the largest one is chosen as the "best" decision for the decision maker described in the problem.

Question 31

In scoring models, weights are assigned to each factor, but the weights do not have to add up to any fixed value.

Question 32

In scoring models, score range (possible score values) for each factor is usually the same.

Question 33

In scoring models, weighted factor score is just one of the criteria needed to make a final selection from among the decision alternatives.

Question 34

Scoring models and the Analytical Hierarchy Process (AHP) differ in the form of the final answer in that AHP presents how much for each decision variable, whereas the scoring model gives which alternative is the best.

Question 35

Scoring models are an example of an objective approach to decision making.

Question 36

In scoring models, the best choice has the highest weighted factor score, where weights are provided by the decision maker.

Question 37

Scoring models can be used as an alternative to the Analytic Hierarchy Process to solve problems involving ranking of choices.

Question 38

Scoring models can be used as an alternative to linear programming models.

Question 39

The primary objective of goal programming is to

A) optimize each goal or objective
B) minimize all goal deviations
C) satisfy all constraints (goal and non-goal)
D) satisfy non-goal constraints and satisfy goal constraints

Question 40

In goal programming models

A) deviation variables appear only in goal constraints
B) goal constraints can be expressed as inequalities
C) conflicting goals are not allowed
D) zero one variables are used to represent goal variations

Question 41

Which of the following phrases best describes deviation variables in goal programming?

A) The acceptable level of goal achievement
B) The gap between actual achievement and target performance
C) The variability of resource availability
D) The difference between maximum and minimum achievement levels of goal achievement

Question 42

Goal constraints are referred to as "soft" constraints because

A) they are easy to achieve
B) they have no real physical interpretation
C) they are easily satisfied by any solution
D) they are not strict requirements for feasibility

Question 43

In goal programming models, suppose we have solved the linear program corresponding to the first priority by minimizing $10 \mathrm{u}_{1}$ . If the optimal objective function value is 0 , then the linear program corresponding to the second priority will have

A) no new constraints
B) one additional constraint $\mathrm{u}_{1}=0$
C) one additional constraint $\mathrm{u}_{1} \geq 0$
D) one additional constraint $\mathrm{u}_{1} \leq 0$

Question 44

In goal programming models, suppose we have solved the linear program corresponding to the first priority by minimizing $10 \mathrm{u}_{1}$ . If $\mathrm{u}_{1}=5$ in the optimal solution, then the linear program corresponding to the second priority will have

A) no new constraints
B) one additional constraint $\mathrm{u}_{1}=5$
C) one additional constraint $u_{1} \geq 5$
D) one additional constraint $u_{1} \leq 5$

Question 45

In XYZ Inc. the goal for labor utilization is 500 hours per month, and the firm is making two products $\mathrm{X}_{1}$ and $\mathrm{X}_{2}$ , which denote the units of these products produced per month. $\mathrm{X}_{1}$ requires 3 hours per unit for labor, and $\mathrm{X}_{2}$ requires 5 hours per unit for labor. The corresponding goal programming constraint would be

A) $3 X_{1}+5 X_{2}=500$
B) $3 X_{1}+5 X_{2} \leq 500$
C) $3 \mathrm{X}_{1}+5 \mathrm{X}_{2}+\mathrm{u}_{1}-\mathrm{v}_{1} \leq$ 500
D) $3 \mathrm{X}_{1}+5 \mathrm{X}_{2}+\mathrm{u}_{1}-\mathrm{v}_{1}=$ 500

Question 46

If we have several objectives with different priorities, and we want to decide the quantities for each decision variable, we should use

A) any multi-criteria optimization method
B) Analytical Hierarchy Process
C) linear programming model
D) goal programming

Question 47

If we decide the rank order of decision alternatives from among many alternatives, we should use

A) multi-criteria optimization method
B) Analytical Hierarchy Process
C) scoring models
D) goal programming

Question 48

In the Analytical Hierarchy Process, for the pairwise comparisons of attribute preferences of the decision maker to be completely consistent, where A-B is 3 and B-C is 2, A-C should be

A) at least 3
B) at least 5
C) at least 6
D) exactly 6

Question 49

In the Analytical Hierarchy Process, scores for pairwise comparison matrices of different brands for a single criterion are given by

A) the user subjectively
B) the analyst subjectively
C) the analyst at random
D) the analyst, studying the differences, and using subjective judgment

Question 50

In the Analytical Hierarchy Process, if the problem had 4 criteria, then it would have pairwise criteria pair comparisons.

A) 3
B) 4
C) 5
D) 6

Question 51

In the Analytical Hierarchy Process, all except one of the matrices have 1 in their diagonals. Which is the exception?

A) Pairwise comparison matrix for preferences of attributes
B) Weighted priorities for the criteria matrix
C) Pairwise comparison matrix for an attribute
D) Pairwise comparison matrix for all attributes

Question 52

In the Analytical Hierarchy Process, assuming 5 criteria, 4 brands, and a weighted sum priority of 5.2, the consistency index will be:

A) 0.05
B) 0.4
C) 0.04
D) 1.1

Question 53

In the Analytical hierarchy process (AHP), which of the following statements is incorrect?

A) The decision maker provides the weighted preferences for the criteria used
B) The decision maker ranks each alternative using each criterion
C) AHP develops prioritized ranking for decision alternatives
D) AHP provides a method to choose among alternatives.

Question 54

In the Analytical Hierarchy Process (AHP), which of the following statements is incorrect?

A) The decision maker provides the weighted preferences for the criteria used
B) The decision maker ranks each alternative using each criterion
C) AHP develops prioritized ranking for decision alternatives
D) AHP provides a method to choose among alternatives

Question 55

In Analytical hierarchy process (AHP), all other things remaining the same, consistency ratio will

A) increase as the number of items (decision options) increases
B) decrease as consistency index increases
C) stay the same regardless of the changes in random index
D) decrease if number of items increases or consistency index decreases

Question 56

All of the following are similarities between Analytical Hierarchy Process (AHP) and scoring models except

A) the decision maker provides the weightages or preferences for the criteria
B) the decision maker assigns scores (comparative or absolute) for each alternative-criteria combination
C) AHP and scoring models have subjective elements (or steps)
D) both involve several steps and complex calculations to get the final answer

Question 57

Jim Smith, a senior in Chemistry, is planning the use of his time in college. The planning horizon is the last 15 weeks before he graduates. For planning purposes, it may be assumed that he has a maximum of 350 hours of time that could be spent. He also has $2,000 left for all discretionary expenses. He wants to exceed the budget as little as possible. He has to prepare for the 3 courses (thesis, biochemistry, and molecular biology) he is currently registered for. He has to apply for graduate school, which involves a decision on how many schools to apply to. He would like to have two kinds of recreation - movies and sports. An hour spent on his thesis, biochemistry, and molecular biology classes will earn 1 point, 1.2, and 0.9 points, respectively. He needs a minimum of 90 points for his thesis, which is a hard constraint. He cannot get more than 100 points in any course. He wants to get as many points as possible, noting that he can not exceed a total of 300 points. Each graduate school application costs $\$ 200$ , takes 20 hours, and has a 0.2 chance of admission. If he applies to 10 schools, his expected number of admissions is $10 *(0.2)=2$ . His goal is to make the expected number of admissions as close to 1.5 as possible without exceeding it. Every movie costs $\$ 20.00$ , gives 5 units of pleasure, and requires 5 hours. Every unit of sports costs $\$ 80$ , gives 12 units of pleasure, and takes 8 hours. He wants to have as close to 60 units of pleasure as possible. The first priority is points for the 3 courses; the second is graduate school; the third is to minimize deviation below the 60 units of pleasure; and the fourth priority is to minimize the pleasure beyond 60 units. Formulate a goal programming model.

Question 58

Jim Smith, a senior in Chemistry, is planning the use of his time in college. The planning horizon is the last 15 weeks before he graduates. For planning purposes, it may be assumed that he has a maximum of 350 hours of time that could be spent. He also has $2,000 left for all discretionary expenses. He wants to exceed the budget as little as possible. He has to prepare for the 3 courses (thesis, biochemistry, and molecular biology) he is currently registered for. He has to apply for graduate school, which involves a decision on how many schools to apply to. He would like to have two kinds of recreation-movies and sports. An hour spent on his thesis, biochemistry, and molecular biology classes will earn 1 point, 1.2, and 0.9 points, respectively. He needs a minimum of 90 points for his thesis, which is a hard constraint. He cannot get more than 100 points in any course. He wants to get as many points as possible, noting that he can not exceed a total of 300 points. Each graduate school application costs $\$ 200$ , takes 20 hours, and has a 0.2 chance of admission. If he applies to 10 schools, his expected number of admissions is $10 *(0.2)$ $=2$ . His goal is to make the expected number of admissions as close to 1.5 as possible without exceeding it. Every movie costs $\$ 20.00$ , gives 5 units of pleasure, and requires 5 hours. Every unit of sports costs $\$ 80$ , gives 12 units of pleasure, and takes 8 hours. He wants to have as close to 60 units of pleasure as possible. Use a weight of $1,0.5,1.0$ , and 1.0 for the four goal-related variables $\mathrm{u}_{1}, \mathrm{u}_{2}, \mathrm{u}_{3}$ , and $\mathrm{v}_{3}$ and solve a weighted goal programming model.

Question 59

Solve the following decision problem using the Analytical Hierarchy Process. Joe Greyhair is planning his relocation after retirement. He is currently working in Toledo, Ohio, which is one of the contending retirement cities. The other two competing locations are New Greyland, Mexico-a special region created by Mexican Government to attract American retirees-and Madras (now known as Chennai), India, where Joe has spent sometime before. There are three important criteria for Joe: cost of living on an annualized basis, availability of medical care, and overall quality of life. Cost of living is $\$ 50,000$ in Toledo, $30,000 in New Greyland, and $20,000 in Madras. For availability of medical care, the cities rank (from best to worst): Toledo, New Greyland, and Madras. For the overall quality of life, they rank (from best to worst): Madras, followed by New Greyland, and, a close third, Toledo. Preference scale for pairwise comparisons is given in the Table 1.

Question 60

Using a scoring model, evaluate the following retirement options. Joe Greyhair is deciding between three cities to spend his golden (maybe silver) years in retirement. The factors used by Joe are cost of living, availability of medical care, physical security, and quality of life. He would like to rate them on a 5-point scale, with 5 as most important to 1 as least important. His expected level of satisfaction for any criterion/ city combination is to be rated on a 9-point scale, 9 being extremely favorable to 1 being extremely unfavorable. (Note that high and low may not convey the right meaning: for example cost of living being high will result in a high score, since the other factors like physical security being high may be desirable, resulting in addition of wrong types of scores. Note also that desirability in each scale goes as a higher number.) The scores for the factors under consideration are given in Table 13, and the scores obtained by the three cities under consideration, namely, Toledo, Ohio, New Greyland, Mexico, and Madras, India, are given below in Table 14. The weighted score for each city is given in Table 15.