1. Forecasting

2. Chapter Objectives Be able to:
Discuss the importance of forecasting and identify the most appropriate type of forecasting approach, given different forecasting situations.
Apply a variety of time series forecasting models, including moving average, exponential smoothing, and linear regression models.
Develop causal forecasting models using linear regression and multiple regression.
Calculate measures of forecasting accuracy and interpret the results.

3. Why Forecast? Assess long-term capacity needs
Develop budgets, hiring plans, etc.
Plan production or order materials
Get agreement within firm and across supply chain partners (CPFR, discussed later)

4. Types of Forecasts Demand Supply Price Firm-level Market-level
Materials
Labor supply
Price
Cost of supplies and services
Cost of money — interest rates, currency rates
Market price for firm’s product or service

5. Forecast Laws Almost always wrong by some amount
More accurate for shorter time periods
More accurate for groups or families
No substitute for calculated values.

6. Qualitative Forecasting
Executive opinions
Sales force composite
Consumer surveys
Outside opinions
Delphi method
Life cycle analogy*
The various phases of the life cycle are discussed in detail in the presentation for Chapter 7. These can be used if needed to expand on this forecasting consideration.
*See accompanying notes

7. Forecasting Approaches
Qualitative Methods
Used when situation is vague and little data exists
New products
New technology
Involves intuition, experience
*****************************
E.g., forecasting sales to a new market
Quantitative Methods
Used when situation is ‘stable’ and historical data exists
Existing products
Current technology
Heavy use of mathematical techniques
*******************************
E.g., forecasting sales of a mature product

8. Quantitative, then qualitative factors to “filter” the answer
“Q2” Forecasting
Quantitative, then qualitative factors to “filter” the answer

9. Demand Forecasting Uses historical data Basic time series models
Linear regression
For time series or causal modeling
Measuring forecast accuracy

10. Time Series Models What assumptions must we make to use this data to
Period Demand
1 12
2 15
3 11
4 9
5 10
6 8
7 14
8 12
What assumptions
must we make to
use this data to
forecast?

11. Time Series Components of Demand . . .
. . . randomness
Time

12. Time Series with . . .
Demand
. . . randomness and trend
Time

13. Time series with . . . . . . randomness, trend, and seasonality Demand
Class discussion: what could account for this? Lawnmower sales? Camping trailer sales? Vacation package sales?
May
May
May
May

14. Idea Behind Time Series Models
Distinguish between random fluctuations and true changes in underlying demand patterns.

15.  Moving Average Models Period Demand 1 12 2 15 3 11 4 9 5 10 6 8 7 14
1 12
2 15
3 11
4 9
5 10
6 8
7 14
8 12 
3-period moving average
forecast for Period 8:
= ( ) / 3
= 10.67

16. Weighted Moving Averages
Forecast for Period 8
= [(0.5  14) + (0.3  8) + (0.2  10)] / ( )
= 11.4
What are the advantages?
What do the weights add up to?
Could we use different weights?
Compare with a simple 3-period moving average.
The heaviest weight is typically applied to the most recent data.
If weights add up to 1.0, the denominator disappears as shown in the text. However, arbitrary weighting values like 4,3, and 1 can be used as long as the weighted demand sum is divided by the sum of the weights.

17. Table of Forecasts and Demand Values . . .
Period
Actual Demand
Two-Period Moving Average Forecast
Three-Period Weighted Moving Average Forecast Weights = 0.5, 0.3, 0.2 1 12 2 15 3 11
13.5 4 9 13
12.4 5 10
10.8 6 8
9.5
9.9 7 14
8.8
11.4
11.8

18. . . . and Resulting Graph
Note how the forecasts smooth out demand variations

19. Exponential Smoothing I
Sophisticated weight averaging model
Needs only three numbers:
Ft = Forecast for the current period t Dt = Actual demand for the current period t a = Weight between 0 and 1

20. Exponential Smoothing II
Formula Ft+1 = Ft + a (Dt – Ft) = a × Dt + (1 – a) × Ft
Where did the current forecast come from?
What happens as a gets closer to 0 or 1?
Where does the very first forecast come from?
Very first forecast is often set equal to the actual demand to start the process.
An alternate approach is to set the first forecast to the moving average of the previous two or three months.
Alpha should be large if the demand data is relatively stable, small if the demand data varies quite a bit.
Otherwise it takes a long time for the forecast to converge on relatively smooth demand (overdamped correction) and the forecast overshoots the variations for fluctuating demand (underdamped correction)

21. Exponential Smoothing Forecast with a = 0.3
Period
Actual Demand
Exponential Smoothing Forecast 1 12
11.00 2 15
11.30 3 11
12.41 4 9
11.99 5 10
11.09 6 8
10.76 7 14
9.93
11.15
11.41
F2 = 0.3× ×11 =
= 11.3
F3 = 0.3× ×11.3 =

22. Resulting Graph

23. Trends
What do you think will happen to a moving average or exponential smoothing model when there is a trend in the data?

24. Same Exponential Smoothing Model as Before:
Period
Actual Demand
Exponential Smoothing Forecast 1 11
11.00 2 12 3 13
11.30 4 14
11.81 5 15
12.47 6 16
13.23 7 17
14.06 8 18
14.94 9
15.86
Since the model
is based on
historical demand,
it always lags
the obvious
upward trend

25. Adjusting Exponential Smoothing for Trend
Add trend factor and adjust using exponential smoothing
Needs only two more numbers: Tt = Trend factor for the current period t  = Weight between 0 and 1
Then: Tt+1 =  × (Ft+1 – Ft) + (1 – ) × Tt
And the Ft+1 adjusted for trend is = Ft+1 + Tt+1

26. Simple Linear Regression
Time series OR causal model
Assumes a linear relationship: y = a + b(x) y x

27. Definitions
Y = a + b(X)
Y = predicted variable (i.e., demand) X = predictor variable
“X” can be the time period or some other type of variable (examples?)

28. The Trick is Determining a and b:

29. Example: Regression Used for Time Series
Period (X)
Demand (Y) X2 XY 1
110 2
190 4
380 3
320 9
960
410 16
1640 5
490 25
2450 15
1520 55
5540
Column Sums

30. Resulting Regression Model: Forecast = 10 + 98×Period

31. Example: Simplified Regression I
If we redefine the X values so that their sum adds up to zero, regression becomes much simpler
a now equals the average of the y values
b simplifies to the sum of the xy products divided by the sum of the x2 values

32. Example: Simplified Regression II
Period (X)
Period (X)'
Demand (Y) X2 XY 1 -2
110 4
-220 2 -1
190
-190 3
320
410 5
490
980
1520 10

33. Dealing with Seasonality
Quarter Period Demand
Winter
Spring
Summer
Fall
Winter
Spring
Summer
Fall

34. What Do You Notice? Forecasted Demand = –18.57 + 108.57 x Period
Actual Demand
Regression Forecast
Forecast Error
Winter 02 1 80 90
-10
Spring 2
240
198.6
41.4
Summer 3
300
307.1
-7.1
Fall 4
440
415.7
24.3
Winter 03 5
400
524.3
-124.3 6
720
632.9
87.2 7
700
741.4
-41.4 8
880
850 30

35. Regression picks up trend, but not seasonality effect

36. Calculating Seasonal Index: Winter Quarter
(Actual / Forecast) for Winter Quarters: Winter ‘02: (80 / 90) = Winter ‘03: (400 / 524.3) = 0.76
Average of these two = 0.83
Interpret!
The normal trend line prediction needs to be adjusted downward for Winter quarters.

37. Seasonally adjusted forecast model
For Winter Quarter [ – ×Period ] × 0.83
Or more generally: [ – × Period ] × Seasonal Index

38. Seasonally adjusted forecasts
Forecasted Demand = – x Period
Period
Actual Demand
Regression Forecast
Demand/Forecast
Seasonal Index
Seasonally Adjusted Forecast
Forecast Error
Winter 02 1 80 90
0.89
0.83
74.33
5.67
Spring 2
240
198.6
1.21
1.17
232.97
7.03
Summer 3
300
307.1
0.98
0.96
294.98
5.02
Fall 4
440
415.7
1.06
1.05
435.19
4.81
Winter 03 5
400
524.3
0.76
433.02
-33.02 6
720
632.9
1.14
742.42
-22.42 7
700
741.4
0.94
712.13
-12.13 8
880
850
1.04
889.84
-9.84

39. Would You Expect the Forecast Model to Perform This Well With Future Data?

40. More Regression Models I
Non-linear models
Example: y = a + b × ln(x)

41. More Regression Models II
Multiple regression
More than one independent variable y
y = a + b1 × x + b2 × z x z

42. Causal Models
Time series models assume that demand is a function of time. This is not always true. 1. Pounds of BBQ eaten at party.
2. Dollars spent on drought relief.
3. Lumber sales.
Linear regression can be used in these situations as well.

43. Measuring Forecast Accuracy
How do we know:
If a forecast model is “best”?
If a forecast model is still working?
What types of errors a particular forecasting model is prone to make?
Need measures of forecast accuracy

44. Measures of Forecast Accuracy
Error = Actual demand – Forecast or
Et = Dt – Ft

45. Mean Forecast Error (MFE)
For n time periods where we have actual demand and forecast values:

46. Mean Absolute Deviation (MAD)
For n time periods where we have actual demand and forecast values:
Comments about how negative errors cancel positive errors in MFE, showing bias.
MAD, on the other hand shows the average offset of the error.
What does this tell us that MFE doesn’t?

47. Example What is the MFE? The MAD? Interpret! MFE = – 2/6 = – 0.33

48. MFE and MAD: A Dartboard Analogy
Low MFE and MAD:
The forecast errors
are small and unbiased

49. An Analogy (continued)
Low MFE, but high
MAD:
On average, the
darts hit the
bulls eye (so much
for averages!)

50. An Analogy (concluded)
High MFE and MAD:
The forecasts
are inaccurate and
biased

51. Collaborative Planning, Forecasting, and Replenishment (CPFR)
Supply chain partners, supported by information technology, working together

52. CPFR Elements Mutual business objectives & measures
Joint sales and operations plans
Collaboration on sales forecasts & replenishment plans
Electronic interchange of information

53. Case Study in Forecasting
Top-Slice Drivers