Operations Analytics

Assignment #1: Monte-Carlo Simulation

Solve the following Monte-Carlo simulation problem using Excel data tables. You’ll see that there are bunch of questions that you’ll have to answer using the model you build. Include all your answers directly in your Excel file using text boxes or comment boxes. Have separate Excel files for each data table solution file (so you will submit three Excel files). Make it easy for me to find your answers. Write concisely and clearly. Insert textboxes or visible comments to provide explanations to your solutions.

NCAA Sweatshirt Problem

An enterprising OU student is trying to decide how many sweatshirts to print for an upcoming NCAA Basketball Tournament game. The final four teams have emerged from the quarterfinal round, and there is a week left until the semi-finals, which are then followed by the finals a few days later. Each sweatshirt costs $10 to produce and sells for $25. However, in 3 weeks, any leftover sweatshirts will be put on sale for half price, $12.50. The student assumes that the demand for her sweatshirts during the next three weeks has the distribution shown in the file NCAASweatshirts-shell.xlsx in F5:G10. The residual demand, after the sweatshirts have been put on sale, has the distribution also shown in the same file in J5:K10. The student, being a profit maximizer, realizes that every sweatshirt sold, even at the sale price, makes a profit. However, she also realizes that any sweatshirts printed and still unsold (even at the sale price) must be given away, resulting in a loss of $10 per discarded shirt. Your job is:

1) Build an Excel based Monte-Carlo simulation model that will produce a probability distribution of profit for a given number of sweatshirts printed. Your simulation model should do 1000 replications.

For your base model,

2) Set the number of sweatshirts printed in your model to 10000. Run your model and find the mean and standard deviation of profit as well as the 5th and 95th percentiles of profit.

3) Construct a 95% confidence interval on the mean profit.

4) Now use your model to explore different numbers of printing quantities and find the:

a. Quantity that maximizes mean profit

b. Quantity that maximizes 5th percentile of profit

c. Quantity that maximizes 95th percentile of profit

d. Do these quantities differ?

5) Now, pretend that you are this OU student. Based on your analysis, how many sweatshirts would YOU print and why?

Note: You should submit three Excel files, one with repeated experiments, one using one-way data table with a fix order quantity and a final one using a two-way data table where you analyze the profit distribution of alternative order quantitates.

Sweatshirts for NCAA tournament | ||||||||||

Inputs | Distribution of demand at regular price | Distribution of demand at sale price | ||||||||

Unit cost | Cumul. Prob | Demand | Probability | Cumul. Prob | Demand | Probability | ||||

Original price | 7,000 | 0.05 | 2,000 | 0.20 | ||||||

Sale price | 8,000 | 0.10 | 3,000 | 0.30 | ||||||

9,000 | 0.25 | 4,000 | 0.20 | |||||||

10,000 | 0.30 | 5,000 | 0.15 | |||||||

11,000 | 0.20 | 6,000 | 0.10 | |||||||

Decision variable | 12,000 | 0.10 | 7,000 | 0.05 | ||||||

Order quantity (trial value) |