AD 616: Enterprise Risk Analytics
Assignment 1
What to submit?
Please submit (i) a Word file explaining in detail your answers to each question (you can use screenshots of the Python to explain your answers) AND (ii) an ipynb file with a separation for each question. For each question, make sure you develop the model and present the simulation results – the ipynb file should be self-explanatory. The assessment of your work will include both the accuracy and the clarity of your Word file and the Python Code.
1. Consider a call center that receives its demand over a set of different travel websites. The weekly demand for each website is normally distributed with a mean and standard deviation given in Table 1. Develop an R script. that creates a simulation with 100,000 trials to determine total call center demand.
Table 1: Weekly demand for travel sites (in hours)
|
Travel Site
|
Mean
|
Standard Deviation
|
|
A
|
200
|
20
|
|
B
|
50
|
10
|
|
C
|
100
|
15
|
|
D
|
150
|
30
|
|
E
|
100
|
30
|
|
F
|
100
|
10
|
a) (1pt) What are the mean and standard deviation of total call center demand according to your simulation?
b) (1pt) Develop a histogram that models the risk profile for total call center demand.
2. A cell phone manufacturer is considering offering a refund to its customers whose battery fails before 5 years. The refund starts at $10 and increases by $1.50 for every month the battery falls short of 5 years. For example, a customer whose battery fails after 4 years and 6 months would receive a refund of $19. A customer whose battery fails after 5 years would receive no refund. Previous studies show that a battery’s life is normally distributed with a mean of 7 years and a standard deviation of 2 years. Develop a simulation with 100,000 trials for the amount of a refund.
a) (2 pts) According to your simulation, what is the expected cost per cell phone to the manufacturer of this offer?
b) (1 pt) According to your simulation, what is the probability a refund will be paid?
c) (2 pts) According to your simulation, what is the average cost per refund?
3. A coffee cart opens at 7:00 a.m., and they generally try to prepare a batch large enough to accommodate their customers until 10:00 a.m., when the cart closes. The operator only sells 16 oz. servings and each serving costs $0.50 to prepare, which includes all costs of production, and any dairy/sweetener customers may add. Any coffee that isn’t sold before 10:00 a.m. is considered stale and disposed of for no monetary gain. When purchased, the coffee is poured into a ripple cup, which costs an additional $0.15 per cup. Demand over this period is normally distributed with a mean of 125 and a standard deviation of 35. Each cup retails for $2.75. The cart operator must also purchase a municipal license, which costs a flat $100 for the three hours. Assume there are no other costs associated with the cart. Develop a R model with 100,000 trials that simulates the daily profit resulting from the preparation of 75, 100, 120, 140, 160, and 180 servings of coffee a day (run them one at a time).
a) (2 pts) For each option, what is the expected profit, and which option results in the highest expected profit?
b) (1 pt) Create a histogram that displays the risk profile of profit for the number of servings with the highest expected profit.