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. 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
Flat-screen monitors
Sales
DVD
CD-ROM
Drive-through restaurants
Fax machines
3 1/2” Floppy disks
Color printers
Figure 2.5

6. 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

7. 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

8. 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

9. 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

10. 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

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

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

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

14. 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

15. Time Series Components
Trend
Cyclical
Seasonal
Random

16. 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

17. ∑ 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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)

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

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

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

27. 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

28. Common Measure of Error
Mean Absolute Deviation (MAD)
MAD =
∑ |actual - forecast| n

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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 ^

38. 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

39. 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

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

41. 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

42. 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

43. 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

44. 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

45. 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

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

47. 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

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

49. 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