Prescriptive Analytics Optimization and Simulation - IT Computer Science Assignment Help

Assignment Task

Task 

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. 

a) Describe the decision variables, objective function, and constraints.

b) 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 (A feasible solution is given in the R file).
•  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.
•  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. Used the rounded solution to answer the following questions.

c) Based on your final assortment policy: How many products have positive stock quantity?

d) 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 (For example, your table should show the number of furniture products with a positive stock qunatity).

e) Based on your final assortment policy: What is the maximum, minimum, mean, and median of the stock quantities for products with positive stock quantity?

f) Are there any other constraints that could be considered in this 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. 

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 impacts the purchasing cost of products. 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 where the standard deviation is 20% of the mean. 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 20% of the corresponding number in column “Purchasing_cost”. Since cost cannot be negative, you need to pick 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 asthe initial feasible point of optim in the first run. Compare this policy with the optimal assortment policy.

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