K353 Group Project, Part 1 Prescriptive Analytics: Optimization and
Simulation Due on Monday, Oct 25, at 11:59 pm BestHome is a company that
sells furniture and home-goods. The company has issued a request for a
proposal and would like to choose one consulting team to help them
become a better data-driven organization. BestHome wants to open a
warehouse in a part of the US that this company has never covered. Thus,
the company does not have any sales-related information (including the
demand) in this area. They only have a pull of items/products that they
want to offer in this customer zone. The managers need your help to
determine the best assortment policy to be used in the new warehouse
they plan to open. As you know, the assortment policy specifies how much
of each product should be carried in the warehouse. Please use
BestHomePart1.csv file for this part of the project. Question 1:
Optimization BestHome has a target capacity limit for each product
class. The limit is not a hard constraint. It means that the capacity
assigned to each class can be more or less than its target, but the
managers want to stay as close as possible to the target. In other
words, BestHome wants to minimize the deviation of the capacity assigned
to each class above or below its desired target. Table 1 shows the
target capacity for each class. Class Furniture Decor Bedding and bath
Rug Appliances Target capacity (square feet) 12900 6000 3900 2500 7000
The total capacity of the warehouse is 32300 square feet. BestHome’s
budget to allocate on purchasing the products is $2.3 million. The
managers plan to allocate between 15%-40% of the budget to furniture
items. a. Describe the decision variables, objective function, and
constraints. b. Use the following notation to write the complete
mathematical formulation for the optimization model that should be used
to find the optimal assortment policy. Your model should include both
the objective function and the constraints. : Total number of products
[1, 2, … , ]: Stock quantity for each product [1, 2, … , ]:
Required capacity per unit of each product [1, 2, … , ]: Unit
purchasing cost of each product F: set of furniture items; D: Set of
decorative items; B: set of bedding and bath items; A: Set of
appliances; R: set of rug items [Hint: The deviation of the capacity
assigned to furniture items from its target (above or below) can be
formulated as follows: |∑ 12900| The above formula is the absolute
value of the difference between the capacity assigned to furniture items
from the target capacity limit for this class. You should write a
similar formula for other classes and add them up to be used as the
objective function.] c. Create a function in R that returns the
objective value for feasible solutions and penalizes infeasible
solutions. Validate your function using one feasible and one
infeasible solution. Solve your optimization model in R to obtain
BestHome’s optimal assortment policy for its new warehouse. If the
optimal stock quantity of any product turns out to be zero, that product
is not included in the assortment of the new store. (Hint: When setting
up the initial feasible solution, try to find a solution that assigns a
capacity relatively close to the target capacity for each class.)
Change the optim() setting to improve your solution. After finding the
optimal solution, use round() function to round the stock quantities in
your optimal solution to the nearest integer value. d. Based on your
final assortment policy: How many products have positive stock quantity
e. Based on your final assortment policy: Generate a table that shows
the number of products that are included in the assortment of the new
store grouped by their class. f. Based on your final assortment policy:
What is the maximum, minimum, mean and median of the stock quantities
for products with positive stock quantity g. Are there any other
constraints that could be considered in an assortment problem Write a
short paragraph discussing what other constraints might be added to this
problem. You do not need to implement these, only provide a discussion
on what limitations might be considered when deciding on which products
and how much of each product to include in a store. Parts a, b, and g
need to be answered only in your pdf file. For the rest of parts, you
need to use R and include related discussions in the pdf file. You
should submit both pdf and R files. Question 2: Simulation BestHome
wants you to conduct a Monte Carlo simulation to test your assortment
policy’s robustness to uncertainty. BestHome believes that the COVID-19
will impact the purchasing cost of the products. For example, many
people, unfortunately, lost their jobs during the pandemic, so BestHome
expects that the demand for home goods decreases due to economic issues.
Lower demand results in reduced prices. BestHome believes that column
“Purchasing_cost” of the dataset is a good estimate of the mean cost,
but it is normally distributed with standard deviation of 100. In other
words, the cost of each product should be generated from a normal
distribution whose mean is equal to the corresponding number in column
“Purchasing_cost” and whose standard deviation is 100. Since cost cannot
be negative, you need to take the maximum of the generated random
variable and zero. You should run your simulation 1000 times. Please use
set.seed(0). a. Formulate BestHome’s cost (the cost of purchasing
products) using the notation in problem 1. b. Use R to simulate the cost
of the optimal assortment policy you obtained in problem 1. c. Based on
your simulation results: What is the sample mean of cost values you
simulated d. Based on your simulation results: What is the 95%
confidence interval on the mean cost e. Answer parts b-d for the
assortment policy you used as the initial feasible point of optim in the
first run. Compare this policy with the optimal assortment policy. Part
a of question 2 needs to be answered only in your pdf file. For parts
b-e, you need to use R and include the related discussions in the pdf
file. You should submit both pdf and R files. Data The description of
different variables in the dataset is given as follows. Grading This is a
team submission project. Please submit only one submission per team.
Individual team members may receive a higher or lower score based on the
quality of their participation and contributions to the project. All
members of the group should submit individual project evaluations under
the “project evaluation-Part1” on Canvas and those evaluations inform
grading. The team submission must consist of two parts: your report as a
pdf file and supporting R script. Your submission will be evaluated on a
45 points scale as follows: Column Name Description ProductID Unique
product ID Brand Product brand Class The class of the product including
furniture, bedding and bath, rugs, decor, and appliances Assembly_status
Information on whether the product requires assembly or not and if the
assembly is included Material_type Type of the material used in the
product Required_capacity Per unit required capacity (in square foot)
Purchasing_cost Per unit purchasing cost (in dollars) Selling_price Per
unit selling price to the customers (in dollars) o If 1500 <
objective value <= 2000, then the score is 4 o If cost > 2000,
then the score is 2. 15 points based on your answers to Question 1,
parts a, b, d-g. 15 points based on your answers to Question 2. 5
points based on the organization and style of your files Organization
and style of your files involve whether files are professionally
presented and edited and whether files are well-organized, labeled, and
free of errors. 10 points are based on the objective value obtained by
your final assortment policy. o If objective value <= 500, then the
score is 10 o If 500 < objective value <= 1000, then the score is 8
o If 1000 < objective value <= 1500, then the score is 6
