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. Outline What Is Forecasting? Types Of Forecasts
Forecasting Time Horizons
Types Of Forecasts
The Strategic Importance Of Forecasting
Seven Steps In The Forecasting System

3. Outline – Continued Forecasting Approaches Time-series Forecasting
Overview of Qualitative Methods
Overview of Quantitative Methods
Time-series Forecasting
Forecasting In The Service Sector

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

5. 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
These ranges for time lines are just a guideline. There are no absolute rules. However, the next slide does give some basic guidelines for distinguishing the differences between them.

6. 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

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. 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 advance

9. 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

10. The Realities! Forecasts are seldom perfect
Most techniques assume an underlying stability in the system
Product family and aggregated forecasts are generally more accurate than individual product forecasts
Why do you think the last bullet is true?

11. Forecasting Approaches
Qualitative Methods
Used when situation is vague and little data exist
New products
New technology
Involves intuition, experience
e.g., forecasting demand for a new product

12. 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

13. 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

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

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

16. 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
Relates the forecast to only one factor – time

17. Time Series Components
Trend
Cyclical
Seasonal
Random

18. 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

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

20. 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

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

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

23. 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

24. ∑ 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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)

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

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

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

36. 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 =

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

38. 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

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

40. Common Measures of Error
Mean Absolute Percent Error (MAPE)
MAPE =
100 ∑ |actuali - forecasti|/actuali n
i = 1
We will not be using this one, but I left this slide in for completeness.

41. 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

42. 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

43. Comparison of Forecast Error
MSE =
∑ (forecast errors)2 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
MAD
= 1,558/8 =
For a = .10
= 1,612/8 =
For a = .50

44. Comparison of Forecast Error
MAPE =
100 ∑ |deviationi|/actuali n
i = 1
Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast Deviation
Tonage with for with for
Quarter Unloaded a = .10 a = .10 a = .50 a = .50
MAD
MSE
= 45.62/8 = 5.70%
For a = .10
= 54.8/8 = 6.85%
For a = .50

45. 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 5.70% 6.85%

46. 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 ^

47. 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

48. 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

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

50. 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

51. 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

52. 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

53. 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

54. Forecasting in the Service Sector
Presents unusual challenges
Special need for short term records
Needs differ greatly as function of industry and product
Holidays and other calendar events
Unusual events

55. Fast Food Restaurant Forecast
20% –
15% –
10% –
5% –
(Lunchtime)
(Dinnertime)
Hour of day
Percentage of sales
Figure 4.12