Exam Covers everything not covered by the last exam. Starts with simulation If you cant’ get the optimal solution – get a pretty good one. You may run out of time. Don’t spend time looking for an answer you don’t know until you have finished what you DO know. SAVE AND SUBMIT OFTEN The Exams will begin at 5 minutes after the hour. Everyone will be let into the labs on the hour. Please do not attempt to enter earlier.

What if you see an unfamiliar solver message Ask a TA / manager Possible answers: –I’ll fix it for you –We have discussed the meaning of this message in lecture / labs / assignments –There is a problem with your model Always better to ask than not ask

MGTSC 352 Lecture 16: Forecast Errors and Aggregate Planning Air Alberta revisited: using safety staffing to hedge against uncertain turnover Mountain Wear revisited: using safety stock to hedge against uncertain demand

Forecast errors and aggregate planning Forecasts provide input to aggregate planning So far, we have only used point forecasts What about forecast errors? How do they impact aggregate plans? Material under development: not in course pack

Back to Air Alberta “Normal attrition … is 10% per month.” p = 10% is a point forecast Suppose we have n = 100 employees Actual attrition is a random variable: binomial distribution with n = 100, p =.10. Expected value: n  p = 100  0.1 = 10 Standard deviation:

What’s a Binomial Distribution? Toss a die 5 times X = number of tosses with a 1 or a 2 X has a binomial distribution with n = 5, p = 2/6

Active Learning In pairs, 1 min. Think of 3 other situations that can be described by a binomial distribution

Our goal Random values generated by the computer Formula in B9: =ROUND(NORMINV(RAND(),B7,B8),0)

Back to Air Alberta Actual attrition: –n = # of trained attendants, p = 0.10 –Binomial distribution with mean = 0.1*n, standard deviation SQRT(0.09*n) –We’ll approximate this with a normal distribution with the same mean and standard deviation

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)

Q: What’s the impact of random attrition? A: Attendant hour shortages (and surplus) What we’ll do: –Come up with a hiring plan –Evaluate the hiring plan by simulating attrition –Compute shortages –Replication: simulate n future scenarios –Summarize results of the future scenarios

Active Learning Pairs, 1 min. How can we modify a hiring plan to hedge against uncertain attrition? (Hedge = protect / insure)

Safety capacity vs. staffing cost tradeoff Higher safety capacity  higher staffing cost  less shortage Set safety capacity = X% of required hours Try X = 0, 2.5, 5 Generate a hiring plan for each X Use simulation to evaluate each hiring plan Let’s do it …