1. Chapter 3 –Forecasting

2. Contents Introduction Overview of forecasting methods
Qualitative Methods
Quantitative Methods
Measure of forecast accuracy

3. What is Forecasting?
Forecasts are predictions, projections or estimates of future events or conditions in the environment in which an enterprise operates. Or
Forecasts are estimates of occurrence, timing or magnitude of uncertain future events

4. ?? What is Forecasting? Process of predicting a future event
Underlying basis of all business decisions
Production
Inventory
Personnel
Facilities ??

5. What is Forecasting? The estimates can be
Occurrence of an event
Timing of happening
Magnitude or volume
The purpose of forecasting is to use the best available information to guide future activities toward organizational goals.

6. Forecasting can be used to determine
Demand of product or service
prices or costs
Change of technology
Competitors
Interest rate
Exchange rate
Good forecasts enables managers to plan and budget for appropriate levels of personnel, raw materials, capitals, inventory and a lot of other variables.
Forecasting is the basis for all planning and budgeting efforts.

7. Forecasting Time Horizons
Short-range forecast
Up to 1 year, generally less than 3 months
Purchasing, job scheduling, workforce levels, job assignments, production levels
Medium-range forecast
3 months to 3 years
Sales and production planning, budgeting
Long-range forecast
3+ years
New product planning, facility location, research and development

8. Distinguishing Differences
Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes
Short-term forecasting usually employs different methodologies than longer-term forecasting
Short-term forecasts tend to be more accurate than longer-term forecasts

9. Influence of Product Life Cycle
Introduction – Growth – Maturity – Decline
Introduction and growth require longer forecasts than maturity and decline
As product passes through life cycle, forecasts are useful in projecting
Staffing levels
Inventory levels
Factory capacity

10. Company Strategy/Issues Drive-through restaurants
Product Life Cycle
Introduction Growth Maturity Decline
Company Strategy/Issues
Best period to increase market share
R&D engineering is critical
Practical to change price or quality image
Strengthen niche
Poor time to change image, price, or quality
Competitive costs become critical
Defend market position
Cost control critical
Internet search engines
Sales
Xbox 360
Drive-through restaurants
CD-ROMs
3 1/2” Floppy disks
LCD & plasma TVs
Analog TVs
iPods
Figure 2.5

11. Product Life Cycle Introduction Growth Maturity Decline
OM Strategy/Issues
Product design and development critical
Frequent product and process design changes
Short production runs
High production costs
Limited models
Attention to quality
Forecasting critical
Product and process reliability
Competitive product improvements and options
Increase capacity
Shift toward product focus
Enhance distribution
Standardization
Less rapid product changes – more minor changes
Optimum capacity
Increasing stability of process
Long production runs
Product improvement and cost cutting
Little product differentiation
Cost minimization
Overcapacity in the industry
Prune line to eliminate items not returning good margin
Reduce capacity
Figure 2.5

12. Types of Forecasts Economic forecasts Technological forecasts
Address business cycle – inflation rate, money supply, etc.
Technological forecasts
Predict rate of technological progress
Impacts development of new products
Demand forecasts
Predict sales of existing products and services

13. Strategic Importance of Forecasting
Human Resources – Hiring, training, laying off workers
Capacity – Capacity shortages can result in undependable delivery, loss of customers, loss of market share
Supply Chain Management – Good supplier relations and price advantages

14. Seven Steps in Forecasting
Determine the use of the forecast
Select the items to be forecasted
Determine the time horizon of the forecast
Select the forecasting model(s)
Gather the data
Make the forecast
Validate and implement results

15. The Realities! Forecasts are seldom perfect
Most techniques assume an underlying stability in the system
Product family and aggregated forecasts are more accurate than individual product forecasts

16. Forecasting Approaches
Qualitative Methods
Used when situation is vague and little data exist
New products
New technology
Involves intuition, experience
e.g., forecasting sales on Internet

17. Forecasting Approaches
Quantitative Methods
Used when situation is ‘stable’ and historical data exist
Existing products
Current technology
Involves mathematical techniques
e.g., forecasting sales of color televisions

18. Overview of Qualitative Methods
Jury of executive opinion
Pool opinions of high-level experts, sometimes augment by statistical models
Delphi method
Panel of experts, queried iteratively

19. Overview of Qualitative Methods
Sales force composite
Estimates from individual salespersons are reviewed for reasonableness, then aggregated
Consumer Market Survey
Ask the customer

20. Jury of Executive Opinion
Involves small group of high-level experts and managers
Group estimates demand by working together
Combines managerial experience with statistical models
Relatively quick
‘Group-think’ disadvantage

21. Sales Force Composite Each salesperson projects his or her sales
Combined at district and national levels
Sales reps know customers’ wants
Tends to be overly optimistic

22. Delphi Method
Iterative group process, continues until consensus is reached
3 types of participants
Decision makers
Staff
Respondents
Decision Makers
(Evaluate responses and make decisions)
Staff
(Administering survey)
Respondents
(People who can make valuable judgments)

23. Consumer Market Survey
Ask customers about purchasing plans
What consumers say, and what they actually do are often different
Sometimes difficult to answer

24. Overview of Quantitative Approaches
Naive approach
Moving averages
Exponential smoothing
Trend projection
Linear regression
Time-Series Models
Associative Model

25. Time Series Forecasting
Set of evenly spaced numerical data
Obtained by observing response variable at regular time periods
Forecast based only on past values, no other variables important
Assumes that factors influencing past and present will continue influence in future

26. Time Series Components
Trend
Cyclical
Seasonal
Random

27. Components of Demand Trend component Seasonal peaks Actual demand
Demand for product or service
| | | |
Year
Seasonal peaks
Actual demand
Average demand over four years
Random variation
Figure 4.1

28. Trend Component Persistent, overall upward or downward pattern
Changes due to population, technology, age, culture, etc.
Typically several years duration

29. Seasonal Component Regular pattern of up and down fluctuations
Due to weather, customs, etc.
Occurs within a single year
Number of
Period Length Seasons
Week Day 7
Month Week 4-4.5
Month Day 28-31
Year Quarter 4
Year Month 12
Year Week 52

30. Cyclical Component Repeating up and down movements
Affected by business cycle, political, and economic factors
Multiple years duration
Often causal or associative relationships

31. Random Component Erratic, unsystematic, ‘residual’ fluctuations
Due to random variation or unforeseen events
Short duration and nonrepeating
M T W T F

32. Naive Approach
Assumes demand in next period is the same as demand in most recent period
e.g., If January sales were 68, then February sales will be 68
Sometimes cost effective and efficient
Can be good starting point

33. ∑ demand in previous n periods
Moving Average Method
MA is a series of arithmetic means
Used if little or no trend
Used often for smoothing
Provides overall impression of data over time
Moving average =
∑ demand in previous n periods n

34. Moving Average Example
January 10
February 12
March 13
April 16
May 19
June 23
July 26
Actual 3-Month
Month Shed Sales Moving Average 10 12 13
( )/3 = 11 2/3
( )/3 = 13 2/3
( )/3 = 16
( )/3 = 19 1/3

35. Graph of Moving Average
Moving Average Forecast
| | | | | | | | | | | |
J F M A M J J A S O N D
Shed Sales
30 –
28 –
26 –
24 –
22 –
20 –
18 –
16 –
14 –
12 –
10 –
Actual Sales

36. Weighted Moving Average
Used when trend is present
Older data usually less important
Weights based on experience and intuition
Weighted moving average =
∑ (weight for period n) x (demand in period n)
∑ weights

37. Weighted Moving Average
Weights Applied Period
3 Last month
2 Two months ago
1 Three months ago
6 Sum of weights
Weighted Moving Average
January 10
February 12
March 13
April 16
May 19
June 23
July 26
Actual 3-Month Weighted
Month Shed Sales Moving Average
[(3 x 16) + (2 x 13) + (12)]/6 = 141/3
[(3 x 19) + (2 x 16) + (13)]/6 = 17
[(3 x 23) + (2 x 19) + (16)]/6 = 201/2 10 12 13
[(3 x 13) + (2 x 12) + (10)]/6 = 121/6

38. 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

39. Moving Average And Weighted Moving Average
30 –
25 –
20 –
15 –
10 –
5 –
Sales demand
| | | | | | | | | | | |
J F M A M J J A S O N D
Actual sales
Moving average
Figure 4.2

40. 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

41. 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)

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

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

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

45. Effect of Smoothing Constants
Weight Assigned to
Most 2nd Most 3rd Most 4th Most 5th Most
Recent Recent Recent Recent Recent
Smoothing Period Period Period Period Period
Constant (a) a(1 - a) a(1 - a)2 a(1 - a)3 a(1 - a)4
a =
a =

46. Impact of Different  Actual demand a = .5 a = .1 225 – 200 – 175 –
225 –
200 –
175 –
150 –
| | | | | | | | |
Quarter
Demand
Actual demand
a = .5
a = .1

47. Impact of Different 
225 –
200 –
175 –
150 –
| | | | | | | | |
Quarter
Demand
Chose high values of  when underlying average is likely to change
Choose low values of  when underlying average is stable
Actual demand
a = .5
a = .1

48. Choosing 
The objective is to obtain the most accurate forecast no matter the technique
We generally do this by selecting the model that gives us the lowest forecast error
Forecast error = Actual demand - Forecast value
= At - Ft

49. Common Measures of Error
Mean Absolute Deviation (MAD)
MAD =
∑ |Actual - Forecast| n
Mean Squared Error (MSE)
MSE =
∑ (Forecast Errors)2 n

50. Common Measures of Error
Mean Absolute Percent Error (MAPE)
MAPE =
∑100|Actuali - Forecasti|/Actuali n
i = 1

51. Comparison of Forecast Error
Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast Deviation
Tonnage with for with for
Quarter Unloaded a = .10 a = .10 a = .50 a = .50

52. Comparison of Forecast Error
MAD =
∑ |deviations| n
Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast Deviation
Tonnage with for with for
Quarter Unloaded a = .10 a = .10 a = .50 a = .50
= 82.45/8 = 10.31
For a = .10
= 98.62/8 = 12.33
For a = .50

53. Comparison of Forecast Error
MSE =
∑ (forecast errors)2 n
Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast Deviation
Tonnage with for with for
Quarter Unloaded a = .10 a = .10 a = .50 a = .50
= 1,526.54/8 =
For a = .10
MAD
= 1,561.91/8 =
For a = .50

54. Comparison of Forecast Error
MAPE =
∑100|deviationi|/actuali n
i = 1
Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast Deviation
Tonnage with for with for
Quarter Unloaded a = .10 a = .10 a = .50 a = .50
= 44.75/8 = 5.59%
For a = .10
MAD
MSE
= 54.05/8 = 6.76%
For a = .50

55. Comparison of Forecast Error
Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast Deviation
Tonnage with for with for
Quarter Unloaded a = .10 a = .10 a = .50 a = .50
MAD
MSE
MAPE 5.59% 6.76%

56. Exponential Smoothing with Trend Adjustment
When a trend is present, exponential smoothing must be modified
Forecast
including (FITt) =
trend
Exponentially Exponentially
smoothed (Ft) + (Tt) smoothed
forecast trend

57. Exponential Smoothing with Trend Adjustment
Ft = a(At - 1) + (1 - a)(Ft Tt - 1)
Tt = b(Ft - Ft - 1) + (1 - b)Tt - 1
Step 1: Compute Ft
Step 2: Compute Tt
Step 3: Calculate the forecast FITt = Ft + Tt

58. Exponential Smoothing with Trend Adjustment Example
Forecast
Actual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
2 17
3 20
4 19
5 24
6 21
7 31
8 28
9 36 10
Table 4.1

59. Exponential Smoothing with Trend Adjustment Example
Forecast
Actual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
2 17
3 20
4 19
5 24
6 21
7 31
8 28
9 36 10
Step 1: Forecast for Month 2
F2 = aA1 + (1 - a)(F1 + T1)
F2 = (.2)(12) + (1 - .2)(11 + 2)
= = 12.8 units
Table 4.1

60. Exponential Smoothing with Trend Adjustment Example
Forecast
Actual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
3 20
4 19
5 24
6 21
7 31
8 28
9 36 10
Step 2: Trend for Month 2
T2 = b(F2 - F1) + (1 - b)T1
T2 = (.4)( ) + (1 - .4)(2)
= = 1.92 units
Table 4.1

61. Exponential Smoothing with Trend Adjustment Example
Forecast
Actual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
3 20
4 19
5 24
6 21
7 31
8 28
9 36 10
Step 3: Calculate FIT for Month 2
FIT2 = F2 + T1
FIT2 =
= units
Table 4.1

62. Exponential Smoothing with Trend Adjustment Example
Forecast
Actual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
3 20
4 19
5 24
6 21
7 31
8 28
9 36 10
Table 4.1

63. Exponential Smoothing with Trend Adjustment Example
| | | | | | | | |
Time (month)
Product demand
35 –
30 –
25 –
20 –
15 –
10 –
5 –
0 –
Actual demand (At)
Forecast including trend (FITt)
with  = .2 and  = .4
Figure 4.3

64. Trend Projections
Fitting a trend line to historical data points to project into the medium to long-range
Linear trends can be found using the least squares technique
y = a + bx ^
where y = computed value of the variable to be predicted (dependent variable)
a = y-axis intercept
b = slope of the regression line
x = the independent variable ^

65. Actual observation (y value)
Least Squares Method
Time period
Values of Dependent Variable
Deviation1
(error)
Deviation5
Deviation7
Deviation2
Deviation6
Deviation4
Deviation3
Actual observation (y value)
Trend line, y = a + bx ^
Figure 4.4

66. Actual observation (y value)
Least Squares Method
Time period
Values of Dependent Variable
Actual observation (y value)
Deviation7
Deviation5
Deviation6
Deviation3
Least squares method minimizes the sum of the squared errors (deviations)
Deviation4
Trend line, y = a + bx ^
Deviation1
Deviation2
Figure 4.4

67. Least Squares Method Equations to calculate the regression variables
y = a + bx ^
b =
Sxy - nxy
Sx2 - nx2
a = y - bx

68. Least Squares Example Time Electrical Power
Year Period (x) Demand x2 xy
∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063
x = 4 y = 98.86
b = = = 10.54
∑xy - nxy
∑x2 - nx2
3,063 - (7)(4)(98.86)
140 - (7)(42)
a = y - bx = (4) = 56.70

69. Least Squares Example The trend line is y = 56.70 + 10.54x ^
Time Electrical Power
Year Period (x) Demand x2 xy
Sx = 28 Sy = 692 Sx2 = 140 Sxy = 3,063
x = 4 y = 98.86
The trend line is
y = x ^
b = = = 10.54
Sxy - nxy
Sx2 - nx2
3,063 - (7)(4)(98.86)
140 - (7)(42)
a = y - bx = (4) = 56.70

70. Least Squares Example Trend line, y = 56.70 + 10.54x ^ 160 – 150 –
| | | | | | | | |
160 –
150 –
140 –
130 –
120 –
110 –
100 –
90 –
80 –
70 –
60 –
50 –
Year
Power demand

71. Seasonal Variations In Data
The multiplicative seasonal model can adjust trend data for seasonal variations in demand

72. Seasonal Variations In Data
Steps in the process:
Find average historical demand for each season
Compute the average demand over all seasons
Compute a seasonal index for each season
Estimate next year’s total demand
Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season

73. Seasonal Index Example
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
Demand Average Average Seasonal
Month Monthly Index

74. Seasonal Index Example
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
Demand Average Average Seasonal
Month Monthly Index
0.957
Seasonal index =
average monthly demand
average monthly demand
= 90/94 = .957

75. Seasonal Index Example
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
Demand Average Average Seasonal
Month Monthly Index

76. Seasonal Index Example
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
Demand Average Average Seasonal
Month Monthly Index
Forecast for 2008
Expected annual demand = 1,200
Jan x .957 = 96
1,200 12
Feb x .851 = 85
1,200 12

77. Seasonal Index Example
2008 Forecast
2007 Demand
2006 Demand
2005 Demand
140 –
130 –
120 –
110 –
100 –
90 –
80 –
70 –
| | | | | | | | | | | |
J F M A M J J A S O N D
Time
Demand

78. Associative Forecasting
Used when changes in one or more independent variables can be used to predict the changes in the dependent variable
Most common technique is linear regression analysis
We apply this technique just as we did in the time series example

79. Associative Forecasting
Forecasting an outcome based on predictor variables using the least squares technique
y = a + bx ^
where y = computed value of the variable to be predicted (dependent variable)
a = y-axis intercept
b = slope of the regression line
x = the independent variable though to predict the value of the dependent variable ^

80. Associative Forecasting Example
Sales Local Payroll
($ millions), y ($ billions), x
2.0 1
3.0 3
2.5 4
2.0 2
3.5 7
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |
Sales
Area payroll

81. Associative Forecasting Example
Sales, y Payroll, x x2 xy
∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5
b = = = .25
∑xy - nxy
∑x2 - nx2
(6)(3)(2.5)
80 - (6)(32)
x = ∑x/6 = 18/6 = 3
y = ∑y/6 = 15/6 = 2.5
a = y - bx = (.25)(3) = 1.75

82. Associative Forecasting Example
y = x ^
Sales = (payroll)
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |
Sales
Area payroll
If payroll next year is estimated to be $6 billion, then:
3.25
Sales = (6)
Sales = $3,250,000