Question 1

An optimization technique useful for solving problems with more than one objective function is
A) dual programming.
B) sensitivity analysis.
C) multi-objective linear programming.
D) goal programming.

Accepted Answer

Multi-objective linear programming is specifically designed to handle problems with multiple objective functions, optimizing them simultaneously.

Question 2

Goal Programming and Multiple Objective Optimization are not related​

Accepted Answer

Goal Programming and Multiple Objective Optimization are related. Goal Programming is a technique used in Multiple Objective Optimization to find the best solution that satisfies multiple conflicting objectives simultaneously.

Question 3

Exhibit 7.1
The following questions are based on the problem below.
A company wants to advertise on TV and radio. The company wants to produce about 6 TV ads and 12 radio ads. Each TV ad costs $20,000 and is viewed by 10 million people. Radio ads cost $10,000 and are heard by 7 million people. The company wants to reach about 140 million people, and spend about $200,000 for all the ads. The problem has been set up in the following Excel spreadsheet. 
-Refer to Exhibit 7.1. Which of the following is a constraint specified to Analytic Solver Platform for this model?
A) $B$9:$E$9=$B$6:$E$6
B) $B$9:$E$9<$B$10:$E$10
C) $B$9:$E$9=$B$10:$E$10
D) $B$9:$E$9>$B$10:$E$10

Accepted Answer

The constraint $B$9:$E$9=$B$10:$E$10 is specifying that the total number of people reached by the ads (calculated by multiplying the number of TV ads and the number of people each TV ad reaches, plus the number of radio ads and the number of people each radio ad reaches) should be equal to the target number of people the company wants to reach. This is a necessary constraint for the optimization model.

Question 4

​Hard constraints can be violated, if necessary

Accepted Answer

Hard constraints are non-negotiable and cannot be violated under any circumstances.

Question 5

In MOLP, a decision alternative is dominated if ​another alternative produces a better value of at least one objective without worsening the value of other objectives

Accepted Answer

This is an accurate definition of domination in multi-objective linear programming (MOLP). In other words, if one alternative is dominated by another, it means that the other alternative is better in at least one objective and no worse in any other objectives.

Question 6

Exhibit 7.1
The following questions are based on the problem below.
A company wants to advertise on TV and radio. The company wants to produce about 6 TV ads and 12 radio ads. Each TV ad costs $20,000 and is viewed by 10 million people. Radio ads cost $10,000 and are heard by 7 million people. The company wants to reach about 140 million people, and spend about $200,000 for all the ads. The problem has been set up in the following Excel spreadsheet. 
-Refer to Exhibit 7.1. If the company is very concerned about going over the $200,000 budget, which cell value should change and how should it change?
A) D13, increase
B) D13, decrease
C) D14, increase
D) D14, decrease

Accepted Answer

The answer of Exhibit 7.1
The following questions are based on...

Question 7

Deviational variables
A) are added to constraints to indicate acceptable departures from the target values of their corresponding goals
B) are negative
C) are positive for underachievement only
D) are positive for overachievement only

Accepted Answer

Deviational variables are added to constraints to indicate acceptable departures from the target values of their corresponding goals. They can be positive or negative, indicating both overachievement and underachievement.

Question 8

Linear programming problems cannot have multiple objectives​

Accepted Answer

Linear programming problems can have multiple objectives, known as multi-objective linear programming. However, the traditional linear programming approach involves optimizing a single objective function.

Question 9

If no other feasible solution to a multi-objective linear programming (MOLP) problem allows an increase in any objective without decreasing at least one other objective, the solution is said to be
A) dually optimal.
B) Pareto optimal.
C) suboptimal.
D) maximally optimal.

Accepted Answer

This is the definition of Pareto optimality, which means that the solution is efficient in terms of multiple objectives and there is no alternative solution that can improve one objective without worsening at least one other objective.

Question 10

Which of the following is false regarding a goal constraint?
A) A goal constraint allows us to determine how close a given solution comes to achieving a goal.
B) A goal constraint will always contain two deviational variables.
C) Deviation variables are non-negative.
D) If two deviation variables are used in a constraint at least one will have a value of zero.

Accepted Answer

A goal constraint may contain one or more deviational variables, but it is not necessary for it to always contain two.

Question 11

Exhibit 7.2
The following questions are based on the problem below.
An investor has $150,000 to invest in investments A and B. Investment A requires a $10,000 minimum investment, pays a return of 12% and has a risk factor of .50. Investment B requires a $15,000 minimum investment, pays a return of 10% and has a risk factor of .20. The investor wants to maximize the return while minimizing the risk of the portfolio. The following multi-objective linear programming (MOLP) has been solved in Excel. 
-Refer to Exhibit 7.2. What formula goes in cell B10?
A) =SUMPRODUCT(B2:C2,$B$6:$C$6)/$D$7
B) =B2*C2+B3*C3
C) =SUMPRODUCT(B3:C3,$B$6:$C$6)/$D$7
D) =SUMPRODUCT(B2:C2,$B$6:$C$6)

Accepted Answer

The correct formula for cell B10, based on the context of calculating a weighted average or similar operation that involves summing products of corresponding entries in two ranges and then dividing by a constant, is =SUMPRODUCT(B2:C2,$B$6:$C$6)/$D$7. This formula multiplies each element in the range B2:C2 with the corresponding element in the range $B$6:$C$6, sums up these products, and then divides the result by the value in cell $D$7.

Question 12

The decision maker has expressed concern with Goal 1, budget, achievement. He indicated that future candidate solutions should stay under budget. How can you modify your goal programming model to accommodate this change? A) Make budget a hard constraint in the model. B) Give d₁⁺ an extremely large weight in the objective function. C) Remove d₁⁺ from the goal constraint. D) All of these.

Accepted Answer

To ensure the budget is not exceeded, you can make it a hard constraint, give it a large weight to penalize exceeding it, or remove the allowance for exceeding it.

Question 13

In the goal programming problem, the weights, w_i, attached to deviational variables must decay exponentially

Accepted Answer

In goal programming, the weights attached to deviational variables do not have to decay exponentially; they are determined based on the importance of each goal to the decision-maker and can be set according to various criteria, not necessarily following an exponential decay pattern.

Question 14

The d_i⁺, d_i− variables are referred to as A) objective variables. B) goal variables. C) target variables. D) deviational variables.

Accepted Answer

The variables d_i⁺ and d_i− are deviational variables. Deviational variables are used in goal programming to measure the deviation from a desired target for each objective. They are calculated by subtracting the target value from the actual value for each objective. Options A, B, and C are not correct as they are not commonly used terminology in goal programming.

Question 15

One major advantage of goal programming (GP) is that the technique:
A) allows a decision-maker to jointly examine several objectives
B) multiple objectives can be assigned different weights depending on their relative importance
C) can focus on a single objective, if necessary
D) all of the above

Accepted Answer

Goal programming allows a decision-maker to jointly examine several objectives and assign them different weights depending on their relative importance. However, it can also focus on a single objective if necessary, thus making all the options mentioned in A, B, and C possible. Therefore, the correct answer is D, all of the above.

Question 16

The deviational variables ​represent the amount by which the goal's target is underachieved

Accepted Answer

Deviational variables in goal programming represent both the underachievement and overachievement of a goal's target, indicating the deviation from the target in either direction.

Question 17

​The second step in Goal Programming is defining the goals

Accepted Answer

The second step in Goal Programming is indeed defining the goals. This step involves identifying the objectives or goals that the decision maker wants to achieve, and specifying them in a measurable and achievable form.

Question 18

Trade-offs in goal programming can be made by modifying the weights to satisfy the priorities of a decision maker

Accepted Answer

In goal programming, the decision maker assigns weights to the goals based on their priorities. By modifying these weights, the decision maker can make trade-offs between the goals and satisfy their priorities. Therefore, the statement is true.

Question 19

Exhibit 7.2
The following questions are based on the problem below.
An investor has $150,000 to invest in investments A and B. Investment A requires a $10,000 minimum investment, pays a return of 12% and has a risk factor of .50. Investment B requires a $15,000 minimum investment, pays a return of 10% and has a risk factor of .20. The investor wants to maximize the return while minimizing the risk of the portfolio. The following multi-objective linear programming (MOLP) has been solved in Excel. 
-Refer to Exhibit 7.2. Which cells are the changing cells in this model?
A) $B$6:$C$6, $B$10:$B$11
B) $B$6:$C$6
C) $B$6:$D$6
D) $B$10:$B$11

Accepted Answer

The changing cells in a model are typically the cells that are adjusted to achieve a desired outcome. In this context, $B$6:$C$6 are likely the cells being manipulated to affect the results of the model.

Question 20

Exhibit 7.2
The following questions are based on the problem below.
An investor has $150,000 to invest in investments A and B. Investment A requires a $10,000 minimum investment, pays a return of 12% and has a risk factor of .50. Investment B requires a $15,000 minimum investment, pays a return of 10% and has a risk factor of .20. The investor wants to maximize the return while minimizing the risk of the portfolio. The following multi-objective linear programming (MOLP) has been solved in Excel. 
-Refer to Exhibit 7.2. Which cell(s) is(are) the target cells in this model?
A) $B$6:$C$6, $B$10:$B$11
B) $B$6:$C$6
C) $B$6:$D$6
D) $B$10:$B$11

Accepted Answer

The answer of Exhibit 7.2
The following questions are based on...

Quiz 7: Goal Programming and Multiple Objective Optimization

An optimization technique useful for solving problems with more than one objective function is

Goal Programming and Multiple Objective Optimization are not related

Hard constraints can be violated, if necessary

In MOLP, a decision alternative is dominated if another alternative produces a better value of at least one objective without worsening the value of other objectives

Deviational variables

Linear programming problems cannot have multiple objectives

If no other feasible solution to a multi-objective linear programming (MOLP) problem allows an increase in any objective without decreasing at least one other objective, the solution is said to be

Which of the following is false regarding a goal constraint?

The decision maker has expressed concern with Goal 1, budget, achievement. He indicated that future candidate solutions should stay under budget. How can you modify your goal programming model to accommodate this change?

In the goal programming problem, the weights, w_i, attached to deviational variables must decay exponentially

The d_i⁺, d_i− variables are referred to as

One major advantage of goal programming (GP) is that the technique:

The deviational variables represent the amount by which the goal's target is underachieved

The second step in Goal Programming is defining the goals

Trade-offs in goal programming can be made by modifying the weights to satisfy the priorities of a decision maker

Quiz 7: Goal Programming and Multiple Objective Optimization

An optimization technique useful for solving problems with more than one objective function is

Goal Programming and Multiple Objective Optimization are not related​

​Hard constraints can be violated, if necessary

In MOLP, a decision alternative is dominated if ​another alternative produces a better value of at least one objective without worsening the value of other objectives

Deviational variables

Linear programming problems cannot have multiple objectives​

If no other feasible solution to a multi-objective linear programming (MOLP) problem allows an increase in any objective without decreasing at least one other objective, the solution is said to be

Which of the following is false regarding a goal constraint?

The decision maker has expressed concern with Goal 1, budget, achievement. He indicated that future candidate solutions should stay under budget. How can you modify your goal programming model to accommodate this change?

In the goal programming problem, the weights, wi, attached to deviational variables ​must decay exponentially

The di+, di− variables are referred to as

One major advantage of goal programming (GP) is that the technique:

The deviational variables ​represent the amount by which the goal's target is underachieved

​The second step in Goal Programming is defining the goals

Trade-offs in goal programming can be made by modifying the weights to satisfy the priorities of a decision maker

Goal Programming and Multiple Objective Optimization are not related

Hard constraints can be violated, if necessary

In MOLP, a decision alternative is dominated if another alternative produces a better value of at least one objective without worsening the value of other objectives

Linear programming problems cannot have multiple objectives

In the goal programming problem, the weights, w_i, attached to deviational variables must decay exponentially

The d_i⁺, d_i− variables are referred to as

The deviational variables represent the amount by which the goal's target is underachieved

The second step in Goal Programming is defining the goals