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

Quiz Results

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

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 2 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 2 𝑆 𝑥𝑥 Prediction for an individual y value at Xo ± 𝑡 𝛼 2 ,𝑛−2 𝑀𝑆 𝐸 1+ 1 𝑛 + 𝑥 0 − 𝑥 2 𝑆 𝑥𝑥 , where 𝑆 𝑥𝑥 = 𝑖=1 𝑛 𝑥 𝑖 − 𝑥 2 for each of each above Regression equations for confidence and prediction

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

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

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)

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

Seasonal Example

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

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/(0.50+0.25) = .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)

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

The newspaper problem

The newspaper problem