Question 1

Which of the following is true about generating alternatives in binary optimization?
A)If the second-best solution is very close to optimal, it is always preferred over the true optimal solution because of factors outside the model.
B)If alternative solutions exist, it would not help management because some factors that make one alternative are not preferred over the factors that make another alternative.
C)If the solution is a unique optimal solution, it would be good for management to know how much worse the second-best solution is than the unique optimal solution.
D)If any alternative solution exists, it would only be a second-best next to the optimal solution because there is no third-best or an alternative second-best solution to any binary integer programming problem.

Accepted Answer

If the solution is a unique optimal solution, it is still important for management to know how much worse the second-best solution is than the unique optimal solution. This can provide insight into the sensitivity and robustness of the solution to changes in the problem parameters. Option A is incorrect because it assumes the second-best solution is always preferred, which may not be the case. Option B is incorrect because even if some factors are not preferred in one alternative, it may still be preferred overall due to other benefits. Option D is incorrect because there could be multiple non-optimal solutions that are equally good, and thus no unique second-best solution.

Question 2

In a production application involving a fixed setup cost and a variable cost, the use of ___________ makes including the setup cost possible in a production model.
A)location variables
B)noninteger constraints
C)objective function coefficients
D)binary variables

Accepted Answer

Binary variables, also known as 0-1 variables, can be used to represent whether a specific setup cost is incurred or not. By setting the binary variable to 1, the setup cost is included in the production model. This allows for a more accurate representation of the true cost of production.

Question 3

Which of the following is a likely constraint on the production quantity x associated with a maximum value and a setup variable y in a fixed-cost problem?
A)x ³ My
B)x £ My
C)Mx £ y
D)xy ³ M

Accepted Answer

In a fixed-cost problem with a setup variable, the constraint on the production quantity x is often limited by the setup resource y. This means that the production quantity cannot exceed a certain multiple of the setup variable. Therefore, the likely constraint on the production quantity x would be x ≤ My, where M is a constant representing the multiple of y that limits x.

Question 4

An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. Pink, green, and black will be __________ of the color attribute.
A)levels
B)constraints
C)regression constants
D)utility values

Accepted Answer

The word "levels" in this context refers to the different options or variations of a certain attribute, in this case, the color of the trousers. The company is developing different levels or variations of the color attribute, which are pink, green, and black, to appeal to customers. Therefore, the best choice is A, levels.

Question 5

In a fixed-cost model, each fixed cost is associated with a binary variable and a specification of the
A)upper bound for the corresponding production variable.
B)upper bound for each of the binary variable.
C)integer constraints involving the corresponding production variables.
D)objective function involving these binary variables only.

Accepted Answer

In a fixed-cost model, fixed costs are associated with binary variables, but the binary variables themselves do not have upper bounds. Rather, the binary variable is used to determine whether or not a fixed cost should be incurred, which then affects the upper bound of the corresponding production variable.

Question 6

For a location problem, if the variables are defined as x_i = 1 if an outlet store is established in region i and 0 otherwise, the objective function is best defined by __________ for i = 1, 2, …, n number of outlet stores included in the problem. A)Min(Sx_i) B)Max(Sx_i) C)Min(px_i) D)Max(px_i)

Accepted Answer

The answer of For a location problem, if the variables...

Question 7

The sum of two or more binary variables must be less than or equal to one in a _____ constraint.
A)corequisite
B)conditional
C)multiple-choice
D)mutually exclusive

Accepted Answer

The term "mutually exclusive" refers to variables that cannot take on the same value at the same time. In this case, the constraint is stating that the sum of the binary variables must be less than or equal to one, meaning that only one of them can be equal to 1 at any given time (and all the others must be 0). Therefore, the constraint is expressing mutual exclusivity between the variables.

Question 8

An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. In an integer programming model for this problem, the available sizes of the trousers will be represented as
A)binary variables
B)constraints
C)attributes
D)regression constants

Accepted Answer

The answer of An apparel designing company is planning to...

Question 9

A constraint involving binary variables that does not allow certain variables to equal one unless certain other variables are equal to one is known as a
A)conditional constraint.
B)corequisite constraint.
C)k out of n alternatives constraint.
D)mutually exclusive constraint.

Accepted Answer

A conditional constraint involves binary variables and restricts certain variables from taking a value of one unless certain other variables are also one. This type of constraint is commonly used in optimization problems where certain decisions are dependent on the decision taken for other variables. Therefore, option A is the best choice. Option B is not correct as it refers to a constraint that requires certain variables to be equal to one together, whereas in a conditional constraint, certain variables can only be equal to one if others are also one. Option C refers to a constraint that restricts the number of variables that can be equal to one, and option D refers to a constraint that restricts certain variables from taking the value of one together.

Question 10

An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. What category does the above objective fall under?
A)Capital budgeting problem
B)Covering problem
C)Fixed-cost problem
D)Product design and market share optimization problem

Accepted Answer

The objective of developing a product that will appeal most to customers falls under the product design and market share optimization problem where the company is trying to create a product that meets the needs and preferences of the target market and gain a larger share of the market. The other options such as capital budgeting problem, covering problem, and fixed-cost problem are not applicable to this objective.

Question 11

Coming up with a product design that will have the highest utility for a sufficient number of people to ensure sufficient sales to justify making the product is known as the ___________ in marketing literature.
A)capital budgeting problem
B)share of choice problem
C)fixed-cost problem
D)traveling-salesman problem

Accepted Answer

The challenge described in the question is commonly known as the "share of choice problem" in marketing literature, which refers to the need to design a product that will capture a sufficient share of consumer demand to be commercially viable. The other options listed (capital budgeting problem, fixed-cost problem, traveling-salesman problem) do not accurately describe this particular challenge.

Question 12

An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. The part-worths for each of the attribute levels obtained from an initial customer survey and the subsequent regression analysis can be used to determine the
A)customer utility value.
B)optimal solution for the regression analysis.
C)overall profit for the company.
D)overall sales achieved by the company.

Accepted Answer

The part-worths for each attribute level can be used to calculate the customer utility value, which is a measure of how much the customer values each attribute level. This can help the company determine which attributes are most important to customers and which combination of attribute levels will result in the most appealing product. The other options (B, C, D) are not directly related to the use of part-worths or regression analysis in product development.

Question 13

A binary mixed-integer programming problem in which the binary variables represent whether an activity, such as a production run, is undertaken or not is known as the
A)capital budgeting problem.
B)share of choice problem.
C)fixed-cost problem.
D)covering problem.

Accepted Answer

The fixed-cost problem in binary mixed-integer programming involves binary variables that indicate whether an activity, such as a production run, is undertaken. These problems typically involve a fixed cost associated with initiating an activity and variable costs that depend on the level of activity. The binary variables are used to model the decision of whether to incur the fixed cost by undertaking the activity.

Question 14

_____________ is a market research technique that can be used to learn how prospective buyers of a product value the product's attributes.
A)Part-worth analysis
B)Conjoint analysis
C)Regression analysis
D)Sensitivity analysis

Accepted Answer

Conjoint analysis is a market research technique that determines how prospective buyers value the different attributes of a product. It involves presenting participants with different product profiles that vary in attributes and asking them to rate their preferences. This data is then analyzed to determine how much each attribute contributes to the overall value of the product, helping marketers design products that better meet the needs of their target market. Part-worth analysis is a component of conjoint analysis that specifically focuses on determining the value of each attribute. Regression analysis and sensitivity analysis are not specific to identifying customer preferences for product attributes.

Question 15

In a fixed-cost problem, choosing excessively large values for the maximum production quantity will result in
A)all reasonable levels of production.
B)no production.
C)no solution at all.
D)possibly a slow solution procedure.

Accepted Answer

Choosing excessively large values for the maximum production quantity in a fixed-cost problem can lead to a slow solution procedure because the optimization algorithm may need to evaluate a larger solution space, which can significantly increase computation time.

Question 16

An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. The levels - small, medium, and large of the size attribute are modeled using
A)objective function coefficients.
B)slack variables.
C)binary variables.
D)nonlinear coefficients.

Accepted Answer

Binary variables are used in mathematical modeling to represent choices or attributes that can only take on one of two values, such as "yes" or "no", "exists" or "does not exist". In the context of product development for women's trousers, binary variables can effectively model the size attribute (small, medium, large) by assigning a binary variable to each size category. This allows the company to easily incorporate the size attribute into their optimization models, facilitating decisions on product mix, inventory levels, and marketing strategies tailored to customer preferences.

Question 17

__________ is a constraint requiring that two binary variables be equal and that thus are both either in or out of the solution together.
A)Conditional constraint
B)Corequisite constraint
C)k out of n alternatives constraint
D)Mutually exclusive constraint

Accepted Answer

A corequisite constraint requires that two binary variables be equal, meaning they are both either included in or excluded from the solution together.

Question 18

The part-worth for each of the attribute levels in a conjoint analysis is determined by
A)regression analysis.
B)sensitivity analysis.
C)online surveys.
D)word-of-mouth.

Accepted Answer

The part-worth for each attribute level is determined through regression analysis in a conjoint analysis. This involves analyzing the data obtained from the survey to determine how changes in the attributes and their levels affect the overall product or service preference.

Question 19

The results of _____________ can be used in an integer programming model of a product design and market share optimization problem.
A)conjoint analysis
B)product design
C)part-worth
D)variations analysis

Accepted Answer

Conjoint analysis is a research method used to understand how consumers value different features or attributes of a product or service. The results of a conjoint analysis are typically used to build an integer programming model to optimize the product design and market share. Therefore, option A is the best choice. The other options (B, C, D) are also important factors in product design and optimization, but they do not directly provide the necessary inputs for integer programming models.

Question 20

The ___________ is the utility value that a consumer attaches to each level of each attribute in a conjoint analysis model.
A)weightage
B)share of choice
C)part-worth
D)share of market

Accepted Answer

Part-worth is the utility value that a consumer attaches to each level of each attribute in a conjoint analysis model. A represents the importance or weight given to each attribute, B represents the market share that each product or brand will receive based on the preferences of the consumers, and D represents the percentage of the total market that a particular brand or product will capture.

Quiz 12: Integer Linear Optimization Models

Which of the following is true about generating alternatives in binary optimization?

In a production application involving a fixed setup cost and a variable cost, the use of ___________ makes including the setup cost possible in a production model.

Which of the following is a likely constraint on the production quantity x associated with a maximum value and a setup variable y in a fixed-cost problem?

An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. Pink, green, and black will be __________ of the color attribute.

In a fixed-cost model, each fixed cost is associated with a binary variable and a specification of the

For a location problem, if the variables are defined as xi = 1 if an outlet store is established in region i and 0 otherwise, the objective function is best defined by __________ for i = 1, 2, …, n number of outlet stores included in the problem.

The sum of two or more binary variables must be less than or equal to one in a _____ constraint.

An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. In an integer programming model for this problem, the available sizes of the trousers will be represented as

A constraint involving binary variables that does not allow certain variables to equal one unless certain other variables are equal to one is known as a

An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. What category does the above objective fall under?

Coming up with a product design that will have the highest utility for a sufficient number of people to ensure sufficient sales to justify making the product is known as the ___________ in marketing literature.

A binary mixed-integer programming problem in which the binary variables represent whether an activity, such as a production run, is undertaken or not is known as the

_____________ is a market research technique that can be used to learn how prospective buyers of a product value the product's attributes.

In a fixed-cost problem, choosing excessively large values for the maximum production quantity will result in

An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. The levels - small, medium, and large of the size attribute are modeled using

__________ is a constraint requiring that two binary variables be equal and that thus are both either in or out of the solution together.

The part-worth for each of the attribute levels in a conjoint analysis is determined by

The results of _____________ can be used in an integer programming model of a product design and market share optimization problem.

The ___________ is the utility value that a consumer attaches to each level of each attribute in a conjoint analysis model.

For a location problem, if the variables are defined as x_i = 1 if an outlet store is established in region i and 0 otherwise, the objective function is best defined by __________ for i = 1, 2, …, n number of outlet stores included in the problem.