1. Quantitative Forecasting Methods (Non-Naive)
Time Series
Associative
Models
Models
Méthodes chronologiques – Projeter dans le futur les expériences passées, avec ou sans ajustements.
Méthodes causales – Développement d’une équation mathématique qui permet aux gestionnaires de prévoir le volume des ventes en fonction d’autres variables.
Exemples:
- Prix du baril de pétrole
- Prévisions météorologiques
- En terme de dollars publicitaires dépensés
- Demande pour un produit complémentaire (ex: clavier pour ordinateur)
- Indices économiques
Moving
Exponential
Trend
Multiple
Average
Smoothing
Projection
Regression

2. Time Series
Assume that what has occurred in the past will continue to occur in the future
Relate the forecast to only one factor  TIME
Include
naive forecast
simple average
moving average
exponential smoothing
linear trend analysis

3. Moving Averages Naive forecast Simple moving average
Demand of the current period is used as next period’s forecast
Simple moving average
stable demand with no pronounced behavioral patterns
Weighted moving average
weights are assigned to most recent data

4. Naive forecast ORDERS MONTH PER MONTH - 120 90 100 75 110 50 130 Nov -
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90

5. n = number of periods in the moving average
Simple Moving Average n
i = 1  Di
MAn = n
where
n = number of periods in the moving average
Di = demand in period i

6. 3-month Simple Moving Average
ORDERS
MONTH PER MONTH
MOVING
AVERAGE
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
Nov - –
103.3
88.3
95.0
78.3
85.0
105.0
110.0
MA3 = 3
i = 1  Di =
= 110 orders
for Nov
Concentrates on most recent data. The more dynamic the environment, the smaller n is used.
If we use n=2 (110+90) / 2 = 100
If we use n=4 ( ) /4 = 101,3
The n is established through trial and error.
Note: April’s forecast was way too high but the low sales corrected May’s forecast.

7. Weighted Moving Average
WMAn =
i = 1 
Wi Di
where
Wi = the weight for period i, between 0 and 100 percent
 Wi = 1.00
Adjusts moving average method to more closely reflect data fluctuations
Copyright 2006 John Wiley & Sons, Inc.

8. Weighted Moving Average Example
MONTH WEIGHT DATA
August 17% 130
September 33% 110
October 50% 90
WMA3 = 3
i = 1 
Wi Di
= (0.50)(90) + (0.33)(110) + (0.17)(130)
= orders
November Forecast
Traditionally, Nov looks more like Oct than Aug.
Weight is also established by trial and error.
Copyright 2006 John Wiley & Sons, Inc.

9. Potential Problems With Moving Average
Increasing n smooths the forecast but makes it less sensitive to changes
Do not forecast trends well
Require extensive historical data

10. Exponential Smoothing
Form of weighted moving average
Weights decline exponentially
Most recent data weighted most
Requires smoothing constant ()
Ranges from 0 to 1
Subjectively chosen
Involves little record keeping of past data

11. Exponential Smoothing
New forecast = last period’s forecast
+ a (last period’s actual demand
– last period’s forecast)
Ft = Ft – 1 + a(At – 1 - Ft – 1)
where Ft = new forecast
Ft – 1 = previous forecast
a = smoothing (or weighting) constant (0  a  1)

12. Exponential Smoothing Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20

13. Exponential Smoothing Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20
New forecast = (153 – 142)

14. Exponential Smoothing Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20
New forecast = (153 – 142) =
= ≈ 144 cars

15. Common Measures of Error
Mean Absolute Deviation (MAD)
MAD =
∑ |actual - forecast| n
Mean Squared Error (MSE)
MSE =
∑ (forecast errors)2 n

16. Trend analysis Many trends are possible: Linear Exponential
Logarithmic
S-growth curve

17. Linear Trend Analysis