Simulation Exam
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EXAM GUIDELINES:
· PLEASE SAVE YOUR FILE FREQUENTLY!
· Exam is designed for 140 minutes.
· This is an individual exam.
· No cell phone use please.
· You can (Not Required to) use MS Excel, @Risk, and Citrix!
· Please show your work and explain your reasoning in the space provided.
· You need to type your answers in this file, save this file frequently; at the end of your test you need to save it one last time, and submit it via Blackboard.
· No Excel screenshot will be accepted.
· No late submission via email or Blackboard will be accepted.
· No Excel file will be accepted as a solution. You can use Excel and/or @Risk to build and test your model; but eventually, you must submit your typed answers in this MS Word document.
· Formula Sheet is in the next page
1- What is the advantage(s) and disadvantage(s) of using physical methods for generating random numbers? Please elaborate your answer.
In an art festival that lasts 9 days, you sell hand-made artistic posters. The following table shows distribution of demand for different days. You have built this distribution based on historical data. Posters you sell are handmade by Lea, a local artist in Washington D.C. area. Making these posters take a long time and you have to place your order way in-advance. Lea can make up to 50 of these unique posters at a cost of $220 a piece. Regular price of these posters is $320. If number of remaining posters at the beginning of day 9 is more than 6, then you mark down your posters 25% on day 9 to avoid possibility of any left-over poster at the end of day 9. Lea is willing to buy back no more than one unsold poster at the price of $100 at the end of the festival.
Demand (number of posters)
Day 1 demand distribution
Day 2-8 demand distribution
Day 9 demand distribution without 25% price discount
Day 9 demand distribution with 25% price discount
2- Assume that you order 50 posters. Complete the following template that will calculate profit after 9 days. You can use the space in the next page:
$ (per poster)
Purchase cost
Day 1 demand distribution
Regular price
$ 320.00
Day 2-8 demand distribution
Discounted price
$ 240.00
Day 9 demand distribution without 25% price discount
Buy back price
$ 100.00
Day 9 demand distribution with 25% price discount
Festival days
Inventory at the beginning of the day
Units sold
Inventory at the end of the day
Total Revenue
Total Cost Of Goods Sold (COGS)
Total Profit
Average Profit
3- Very elaborately explain how you would construct a 90% confidence interval for the probability of ending up with 0 posters at the end of day 9.
4- Very elaborately explain how you can use RiskOptimizer to maximize average profit. You need to identify your decision variable(s), explain your constraints, and elaborately talk about your solution procedure along with RiskOptimizer settings.
4- Daisy owns a fancy private jet with capacity of 15 passengers. Daisy has promised 14 of her friends that right after the simulation exam, she will fly them to sunny Florida for a nice vacation. Daisy and her friends are lined up to pass the airport security check and board this airplane! Each of these 15 people has a boarding pass with an assigned seat. However, Shakira, the first passenger to board has lost her boarding pass and takes a random seat. After Shakira, each person takes the assigned seat if it is unoccupied, and one of unoccupied seats at random otherwise. What is the probability that , Daisy’s very close friend and the last person to board, gets to sit in her assigned seat? Please put together a simulation model in Excel, calculate the requested probability, and submit your Excel file. For this question, you do NOT have a template.
It will cost $500,000 to develop and launch a new product. For legal reasons, the market for this product will last exactly two years. Price will be $100, variable costs will be $20, and annual fixed expenditures will be $400,000. Unit sales in the first year are uncertain, but are thought to follow a triangular distribution with a minimum of 500 units, a most-likely value of 6,000 units, and a maximum of 24,000 units. Unit sales in year two are judged to be some fraction of the unit sales in the first year. The fraction will be independent of the realized unit sales in the first year; this fraction is thought to follow the normal distribution with a mean of 0.70 and a standard deviation of 0.07. Ignore taxes. Assume that the product is made to order, so that you don’t have to worry about leftover inventory, unsatisfied demand, etc. For simplicity, you can assume that the initial costs and the first year cash flows occur at time zero; discount cash flows (if any) in year two by 10%. The firm has the option of bailing out after the first year (which would allow it to avoid the $400,000 fixed expenditure in year two) without damage to its reputation. It has tentatively decided to bail out if it sells 6,000 or less units in the first year. Assume that none of the $500,000 initial costs are salvageable at the end of the product’s life. Please scroll to the next pages for the questions
5- Construct an @Risk simulation model to decide if the firm should develop and launch this product. Write down formulas and numbers in column B. In column C, identify the output cell(s) you would want to track.
Initial Cost ($)
Price ($/unit)
Variable Costs ($/unit)
Annual Fixed Expenditure ($/year)
First Year Sales (units)
First year Profit ($)
Bail-out Cutoff
After First Year? (Yes = 1, 0 = No)
Second Year Sales (units)
Second Year Profits ($)
Discount Rate
Overall Profits ($)
6- Describe how you would use @Risk and/or Risk-optimizer to decide on the bail-out first year sales cutoff value (it is currently 6000) which maximize expected profit. Be thorough.
7- Many people who are involved in a small auto accident do not file a claim because they are afraid their insurance premiums will be raised. Suppose your insurance company has three rates. How might you use simulation to determine whether you should file a claim?
8- Consider a newsvendor problem with two products with correlated demands (similar to newsvendor with Sweater and Top problem we discussed in the class). After running the simulation for 2000 iterations, we got the following scatter plot for Total profit vs Demand for sweater. What can you say about the correlation between demand for sweater and Top? Explain your answer in detail.
JeansRUs is trying to determine how many pairs of Jeans to order for the winter season. Demand for the Jeans is assumed to follow a normal distribution with mean 4000 pairs and standard deviation of 800 pairs. The contract between APO (manufacturer) and JeansRUs works as follows: At the beginning of the season, JeansRUs reserves C units of capacity. JeansRUs must take delivery for at least 0.8C pairs of jeans and can, if desired, take delivery on up to C pairs of jeans. Each pair sells for $160 and APO charges $50 per pair. If JeansRUs does not take delivery on all C pairs of jeans, it owes APO a $5 penalty for each unit of reserved capacity that is unused.
9- Complete the following template. Please write appropriate formulas in each cell. You would want to build a simulation model in determining how many units of capacity should JeansRUs reserve to maximize its expected profit.
Demand Distribution
Pair Selling Price
Pair Charge
Pair Penalty Cost
Purchase Cost
Penalty Cost
10- How would you set up your simulation optimization model in RiskOptimizer? What is your adjustable cell? What are the possible constraints? How would you set them up in RiskOptimizer?
11- How can you solve this simulation optimization problem just using @Risk capabilities (rather than using RiskOptimizer)? Elaborate your answer.
PLEASE SAVE YOUR FILE FREQUENTLY!
Sweater / Demand
46.6%11.5%
Totals / Profit vs. Sweater / Demand
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