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

Quiz Schedule Lab section Enter lab Quiz begins Quiz ends 8 am7:558:008:40 9 am8:559:009:40 11 am10:5511:0011:40 12 pm11:5512:0012:40 All lab sections treated the same

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 You may not use a USB key, CD, , etc. during the quiz Listen carefully to instructions Have OneCard ready.

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

MGTSC 352 Lecture 7: Monte Carlo Simulation Bard Outside example

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?

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

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 …

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

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

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

Final results

Comparing Different Capacities 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

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

Bard Outside Example: A “Newsvendor Problem” 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

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

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?

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

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

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

How Much Difference Does this Make? Avg. profit ($/show) 200 seats 210 seats 220 seats Extra profit per seat Take 1$11$24$33$1.10 Take 2$113$146$173$3.00