1. OUTLINE Questions? Quiz Results Quiz on Thursday Continue Forecasting
Newspaper problem
Least unit cost

2. Quiz Results

3. What will we cover? Regression - equations Smoothing
MAV (Moving average) with MAD (mean average deviation of the error)
Average with Std dev (include all with prediction of probabilities)
Exponential (select a smoothing constant)
Seasonal (when substantial seasonal variations exist)
Remove the seasonality
Calculate the trend and forecast
Return the seasonality to the trend line

4. Regression equations for confidence and prediction
Confidence Interval for the regression equation at Xo:
± 𝑡 𝛼 2 ,𝑛−2 𝑀𝑆 𝐸 1 𝑛 + 𝑥 0 − 𝑥 𝑆 𝑥𝑥
Prediction for an average of k y values at Xo
± 𝑡 𝛼 2 ,𝑛−2 𝑀𝑆 𝐸 1 𝑘 + 1 𝑛 + 𝑥 0 − 𝑥 𝑆 𝑥𝑥
Prediction for an individual y value at Xo
± 𝑡 𝛼 2 ,𝑛−2 𝑀𝑆 𝐸 𝑛 + 𝑥 0 − 𝑥 𝑆 𝑥𝑥 ,
where 𝑆 𝑥𝑥 = 𝑖=1 𝑛 𝑥 𝑖 − 𝑥 for each of each above
Regression equations for confidence and prediction

7. MAV – Moving Average
Average the last n periods of demand
Usually n =3 to 4 periods
Used when you don’t want to go too far back in time and you think the last few data points are the most representative

8. MAD
Mean average deviation
Sum of the absolute deviations from the mean
Calculated on the forecast compared to the actual

9. Exponential Smoothing
Use a constant smoothing constant (α), usually between 0.2 and 0.4
Takes all values into account, but gives a higher weight to the more recent values
Forecast = previous forecast (1-α) + previous actual(α)

10. Seasonal
Seasonal (when substantial seasonal variations exist) – works best when several years of data are available
Remove the seasonality
Calculate the trend and forecast
Return the seasonality to the trend line
Seasonal factor – ratio of current demand divided by the average for the year (a high demand will have a seasonal factor greater than 1)
Remove seasonality by dividing each demand by its seasonal factor (each demand will move closer to the average)
Calculate the trend line and extend for the forecast
Multiply each demand by its seasonal factor

11. Seasonal Example

12. Definitions
Newspaper problem – Deciding how many of a perishable item to order, based on loss of profits (under stocking) and cost of unsold goods (over stocking)
Excel Norm functions to calculate normal probabilities:
NORMINV(percentage, mean, standard deviation) = Value
NORMDIST(Value, mean, standard deviation, TRUE) = percentage

13. Newspaper problem Newspaper person’s cost = $0.25, no salvage value
Profit on a paper = $0.50
Estimated average sales = 60
Estimated standard deviation of sales = 5
Percentage (Service level) = 0.50/( ) = .667
NORMINV(0.667, 60, 5) = 63 or Q= average + z(std. dev)
If the overage cost is lower than the shortage cost we order more than the average
Underage cost = lost profit = Selling price – Cost
Overage cost = Excess unsalvageable inventory = Cost – salvage value
Service level = Underage cost/ (Underage + overage cost)

15. The newspaper problem
Expected Profit at Q = 62: $28.64
Expected Profit at Q = 63: $28.62
The formula for expected profit comes from the probability of demand being less or more than the order quantity

16. The newspaper problem

17. The newspaper problem