Preparing for Quiz 1

1. Preparing for Quiz 1 • Review notes, assignments • Take practice quiz • Read Tips on Taking On-line Exams • Get a good night's rest • Quiz 1 coverage: up to and including wrap-up of forecasting

2. Quiz Schedule All lab sections treated the same

3. When you come to the lab • Find your assigned computer • Logon to the course web • You may copy materials to the desktop before the quiz starts • From USB key, CD, or email • You may not use a USB key, CD, email, etc. during the quiz • Listen carefully to instructions • Have OneCard ready.

4. Reminders • Quiz 3 is now on 30 March • HW 3 due Wed • Quiz Review Session, Thu 5 – 6:30 pm, BUS B-24+28 • Optional • Q&A session, no new material

5. MGTSC 352 Lecture 7: Monte Carlo Simulation Bard Outside example

6. Bard Outside • The Bard Outside theatre group puts on plays by Shakespeare 20 times every summer in a 200-seat outdoor theatre. • Data: • Attendance and weather (rain / no rain) for last five seasons (5 x 20 = 100 shows) • Revenue = $10 per customer • Cost = $1,600 per show • Question: how much would profit increase if the number of seats were increased?

7. Profit • Profit = Revenue – Expenses • Revenue = • Expenses = • What do we need to find out? • How can we do this?

8. Data Analysis • What’s the probability of rain? • What is the mean and standard deviation of demand when it rains? • How about when it doesn’t rain? • How can we simulate demand? To Excel …

9. Simulating Profit per show • Simulate weather • Simulate demand • Make sure 0 ≤ demand ≤ capacity • Calculate revenue • Subtract cost • Replicate! • Remember: freeze tables of simulation results

10. Simulating a value from a Normal Distribution:Breaking the formula down • ROUND(NORMINV(RAND(),mean,stdev),0) • Step 1: generate random numberRAND() • Step 2: convert random number to normal distributionNORMINV(RAND(),mean,stdev) • Step 3: round to whole numberROUND(NORMINV(RAND(),mean,stdev),0)

11. =RAND() =NORMINV(…) Converting random number to a normal distribution Simulated Value = 990.3

12. Final results

13. Want to compare 200 seats and 210 seats Approach 1: Simulate demand for 100 days Compute profit for each simulated day, assuming 200 seats Simulate demand for another 100 days Compute profit for each simulated day, assuming 210 seats Compare average profits Approach 2: Simulate demand for 100 days Compute profit for each simulated day, assuming 200 seats Compute profit for each simulated day, assuming 210 seats (reuse the 100 simulated demands) Compare average profits Active learning: which approach is better? 1 min., in pairs List as many pros and cons as you can Comparing Different Capacities

14. Approach 1(simulate 2  100) Approach 2(simulate 1  100) Pros and Cons

15. Bard Outside: Decision: # of seats Uncertain future demand Demand > # of seats  lost revenue Demand < # of seats  empty seats A newsvendor: Decision: # of newspapers to get Uncertain future demand Demand > # of papers  lost revenue Demand < # of papers  disposal costs Bard Outside Example: A “Newsvendor Problem”

16. Active Learning • In pairs, 1 min. • Think of three other examples of newsvendor problems • Examples:

17. Bard Outside Revisited • We estimated the average profit per show with 200 seats to be about $11 per night • Bard Outside’s accountant says they’ve been earning an average of $100 per night • What’s wrong?

18. Another look at the No Rain Attendance Distribution Attendance (up to 199) 200 or more: 51% of the time

19. What we did: Fit a Normal Distribution with Mean = 176, Stdev = 39 Attendance of 200 or more: 51% Demand of 200 or more: 27% Demand Attendance Can we do better?

20. How about this: Normal Distribution with Mean = 200, Stdev = 50 Attendance of 200 or more: 51% Demand of 200 or more: 50% Demand Attendance The attendance distribution is a “censored” version of the demand distribution. We need to “uncensor” it before using it to simulate.

21. How Much Difference Does this Make?