Question 1

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

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 2

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

Accepted Answer

If the solution is unique, it is still helpful for management to know how much worse the second-best option is. This can provide insight into the sensitivity of the optimal solution to changes in the problem. Options A, B, and D are all incorrect statements.

Question 3

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.

Accepted Answer

Binary variables can be used to represent whether or not the setup cost is incurred for a particular time period or production batch. By multiplying the binary variable with the setup cost coefficient and adding it to the objective function, the setup cost can be included in the model.

Question 4

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

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 5

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?

Accepted Answer

The objective of developing a product that will appeal most to customers falls under the product design and market share optimization problem. This involves identifying customer needs and preferences, developing a product that meets those needs, and optimizing market share through effective marketing and promotion strategies.

Question 6

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

Accepted Answer

Conjoint analysis is a market research technique that can be used to learn how prospective buyers of a product value the product's attributes. The analysis involves presenting respondents with different combinations of attributes and asking them to choose their preferred option. This helps companies determine which attributes are most important to their potential customers and what trade-offs they are willing to make. Part-worth analysis and regression analysis can be used within conjoint analysis to further analyze the results. Sensitivity analysis is a different type of analysis that evaluates how changes in certain variables can impact the outcome of a decision or model.

Question 7

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

Accepted Answer

Conjoint analysis is a market research technique used to determine how people value different features that make up a product. The results of this analysis can be used to create an integer programming model of a product design and market share optimization problem. This method helps in identifying the optimal combination of product features that will maximize market share and customer satisfaction. Therefore, option A is the best choice. Options B, C, and D are not appropriate for creating a mathematical model for product design and market optimization.

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. Pink, green, and black will be __________ of the color attribute.

Accepted Answer

Levels are different variations of a particular attribute. In this case, pink, green, and black are different levels of the color attribute for women's trousers that the company is considering. Constraints are limitations or restrictions, regression constants are statistical measures, and utility values are numerical scores assigned to different attributes by customers to indicate their preference.

Question 9

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

Accepted Answer

In a fixed-cost model, each fixed cost is associated with a binary variable and an upper bound for the corresponding production variable. This is because the fixed cost is incurred regardless of the level of production, and the binary variable indicates whether or not the cost will be incurred. The upper bound on the production variable limits how much the company can produce, and therefore how much of the fixed cost will be incurred. The other options (B, C, D) are not directly related to fixed-cost models.

Question 10

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

Accepted Answer

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

Question 11

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?

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 12

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

Accepted Answer

In a mutually exclusive constraint, only one of the binary variables can be equal to one. Therefore, the sum of two or more binary variables must be less than or equal to one, which fits the given condition.

Question 13

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.

Accepted Answer

The objective function is to minimize the total cost of establishing outlet stores, which is given by the sum of the costs of establishing each store. The cost of establishing a store in region i is given by c_i, and the variable x_i is 1 if a store is established in region i and 0 otherwise. Therefore, the objective function is Min(Sx_i).

Question 14

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

Accepted Answer

Part-worth values are determined through regression analysis in conjoint analysis.

Question 15

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

Accepted Answer

A conditional constraint is a constraint involving binary variables that does not allow certain variables to equal one unless certain other variables are equal to one. Therefore, option A is the correct choice. Corequisite constraint refers to a constraint that requires two or more variables to be equal to one simultaneously. K out of n alternatives constraint requires a certain number of binary variables to be equal to one out of a group of n variables. Mutually exclusive constraint specifies that only one binary variable can be equal to one out of a group of two or more variables.

Question 16

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 ___________ problem in marketing literature.

Accepted Answer

The problem described matches the concept of "share of choice," which refers to the challenge of designing a product that will be the preferred choice for a significant number of consumers over other available options. This requires careful market research, product positioning, and differentiation strategies to create a unique value proposition that attracts and retains customers. Capital budgeting relates to the financial evaluation of investment projects, fixed costs refer to expenses that do not vary with production levels, and the traveling-salesman problem involves finding the shortest route for a salesperson to visit multiple locations.

Question 17

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

Accepted Answer

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

Question 18

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-worth for each of the attribute levels obtained from an initial customer survey and the subsequent regression analysis can be used to determine the

Accepted Answer

The part-worth for each attribute level helps in determining the customer utility value, which is the measure of the customer's satisfaction level for a given product or service. By understanding the customer utility value for each attribute level, the company can develop a product that is most appealing to the customers in the women's trousers market.

Question 19

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

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 20

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

Accepted Answer

Part-worth is the utility value that a consumer attaches to each level of each attribute in a conjoint analysis model. Weightage pertains to the importance of each attribute, share of choice refers to the proportion of respondents choosing a particular product, and share of market pertains to the market share of a particular product or brand.

Quiz 13: Integer Linear Optimization Models