Exam 10: Multi-Criteria Models

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

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

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

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

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

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

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

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.

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.

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

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

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

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

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.

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

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

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.

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

The primary objective of goal programming is to

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