1. Operations Management
Chapter 4 -
Forecasting
PowerPoint presentation to accompany
Heizer/Render
Principles of Operations Management, 6e
Operations Management, 8e
© 2006 Prentice Hall, Inc.

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

3. 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

4. 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

5. Types of Forecasts Economic forecasts Technological forecasts
Address business cycle – inflation rate, money supply, housing starts, etc.
Technological forecasts
Predict rate of technological progress
Impacts development of new products
Demand forecasts
Predict sales of existing product

6. 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

7. 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

8. 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

9. Overview of Qualitative Methods
Jury of executive opinion
Delphi method
Sales force composite
Consumer Market Survey

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

11. 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)

12. 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

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

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

15. Time Series Forecasting
Set of evenly spaced numerical data
Obtained by observing response variable at regular time periods
Forecast based only on past values
Assumes that factors influencing past and present will continue influence in future

16. Time Series Components
Trend
Cyclical
Seasonal
Random

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

18. 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

19. Cyclical Component Repeating up and down movements
Affected by business cycle, political, and economic factors
Multiple years duration

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

21. Naive Approach
Assumes demand in next period is the same as demand in most recent period
e.g., If May sales were 48, then June sales will be 48
Sometimes cost effective and efficient

22. ∑ 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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)

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

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

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

34. 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 =

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

36. 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

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

38. 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

39. Comparison of Forecast Error
MAD =
∑ |deviations| n
Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast Deviation
Tonage with for with for
Quarter Unloaded a = .10 a = .10 a = .50 a = .50
= 84/8 = 10.50
For a = .10
= 100/8 = 12.50
For a = .50

40. 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

41. 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

42. 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

43. 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

44. 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

45. 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

46. 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

47. 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)
Figure 4.3

48. 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 ^

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

50. 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

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

52. 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

53. 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

54. 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

55. Least Squares Requirements
We always plot the data to insure a linear relationship
We do not predict time periods far beyond the database
Deviations around the least squares line are assumed to be random

56. Seasonal Variations In Data
The multiplicative seasonal model can modify trend data to accommodate seasonal variations in demand
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

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

58. 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

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

60. Seasonal Index Example
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
Demand Average Average Seasonal
Month Monthly Index
Forecast for 2006
Expected annual demand = 1,200
Jan x .957 = 96
1,200 12
Feb x .851 = 85
1,200 12

61. Seasonal Index Example
2006 Forecast
2005 Demand
2004 Demand
2003 Demand
140 –
130 –
120 –
110 –
100 –
90 –
80 –
70 –
| | | | | | | | | | | |
J F M A M J J A S O N D
Time
Demand