Exam 12: Integer Linear Optimization Models

A shipping freighter has space for two more shipping containers, but the combined weight cannot go over 20 tons. Four shipping containers are being considered. The following table provides details on the weight (in tons) and value of the contents of each container. Container 1 2 3 4 Weight of container (tons) 5 6 9 7 Value/Container \ 6000 \ 5500 \ 7500 \ 6000 ​ Develop a binary integer model that will determine the two containers that will maximize the value of the shipment.

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.

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?

The importance of _________ for integer linear programming problems is often intensified by the fact that a small change in one of the coefficients in the constraints can cause a relatively large change in the value of the optimal solution.

Greenbell Software Inc. conducted a study on its smartphone products in the market to determine which phone has the best features in terms of three prominent attributes: operating system of the phone (A or B), RAM (512MB or 1GB), and the rear camera specifications (3MP, 5MP, or 7MP). A sample of eight customers participated in the study and provided the following part-worths for each of the above attributes. ​ Operating System RAM Camera Consumer A B 512 1 3 5 7 1 25 29 20 45 18 18 15 2 35 32 30 35 27 19 13 3 45 35 30 30 15 25 30 4 55 65 25 45 25 20 35 5 40 40 35 40 20 25 30 6 30 47 40 35 15 20 15 7 35 45 30 30 20 20 20 8 25 25 25 30 25 30 30 Suppose the overall utility (sum of part-worths) of the current favorite Greenbell smartphone is 100 for each consumer. What new product design will maximize the share of choice for the eight consumers in the sample?

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. In an integer programming model for this problem, the available sizes of the trousers will be represented as

Which of the following is true about the sensitivity analysis for integer optimization problems?

Andrew is ready to invest $200,000 in stocks and he has been provided nine different alternatives by his financial consultant. The following stocks belong to three different industrial sectors and each sector has three varieties of stocks each with different expected rate of return. The average rate of return taken for the past ten years is provided with each of the nine stocks. Stock Industry Annual Return 1 Airlines 18.24\% 2 Airlines 28.75\% 3 Arrlines 11.08\% 4 Banking 20.12\% 5 Banking 14.00\% 6 Banking 26.17\% 7 Agriculture 23.67\% 8 Agriculture 18.25\% 9 Agriculture 16.50\% ​ The decision will be based on the constraints provided below: o Exactly 5 alternatives should be chosen. o One stock can have a maximum invest of $55,000. o Any stock chosen must have a minimum investment of at least $25,000. o For the Airlines sector, the maximum number of stocks chosen should be two. o The total amount invested in Banking must be at least as much as the amount invested in Agriculture. ​ Formulate a model that will decide Andrew's investment strategy to maximize his expected annual return.

Greenbell Software Inc. conducted a study on its smartphone products in the market to determine which phone has the best features in terms of three prominent attributes: operating system of the phone (A or B), RAM (512MB or 1GB), and the rear camera specifications (3MP, 5MP, or 7MP). A sample of eight customers participated in the study and provided the following part-worths for each of the above attributes. ​ Operating System RAM Camera Consumer A B 512 1 3 5 7 1 25 29 20 45 18 18 15 2 35 32 30 35 27 19 13 3 45 35 30 30 15 25 30 4 55 65 25 45 25 20 35 5 40 40 35 40 20 25 30 6 30 47 40 35 15 20 15 7 35 45 30 30 20 20 20 8 25 25 25 30 25 30 30 Assume the overall utility (sum of part-worths) of the current favorite Greenbell smartphone for customers 1 to 5 is 105 and customers 6 to 8 is 90. What new product design will maximize the share of choice for the eight consumers in the sample?

The worksheet formulation for integer linear programs and linear programming problems is exactly the same except that the _____ for integer linear programs.

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.

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

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 objective function for a linear optimization problem is: Max 3x + 5y, with constraints x ≥ 0, y ≥ 0 and x and y are both integers and they are also the only decisions variables. This is an example of a(n)

Delisshious Toasty Chocolates Company primarily produces two types of chocolate bars, Almond Tasty and Cashew Crunchy. The personnel costs incurred per day to produce the two types of chocolate bars are $100 and $120, respectively. The production cost per chocolate bar is $2 for Almond Tasty and $2.5 for Cashew Crunchy. The daily production capacity of Almond Tasty and Cashew Crunchy chocolate bars are 1100 and 1250, respectively. Only one type of bar can be produced on a given day since only one machine is available. ​ Let C₁ = the number of Almond Tasty chocolate bars produced C₂ = the number of Cashew Crunchy chocolate bars are produced Y₁ = 1 if the machine produces Almond Tasty; 0, otherwise Y₂ = 1 if the machine produces Cashew Crunchy; 0, otherwise a. Write a constraint that sets the next day's maximum production of Almond Tasty to 1100. b. Write a constraint that sets the next day's maximum production of Cashew Crunchy to 1250. c. Write a constraint that requires that production be set up for exactly one of the two chocolates bars. d. Write the cost function to be minimized.

In binary integer linear program, the integer variables take only the values

The ___________ approach to solving integer linear optimization problems breaks the feasible region of the LP Relaxation into subregions until the subregions have integer solutions or it is determined that the solution cannot be in the subregion.

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