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K353 Optimization and Simulation
创建日期：2024-04-18 17:00:24
标签： K353
Optimization and Simulation

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K353 Group Project

Prescriptive Analytics: Optimization and Simulation 

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

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