1. 4 Forecasting PowerPoint presentation to accompany Heizer and Render
Operations Management, 10e
Principles of Operations Management, 8e
PowerPoint slides by Jeff Heyl
03: CH4 - Forecasting (MGMT3102: Fall13)

2. Outline What Is Forecasting? Forecasting Approaches
Forecasting Time Horizons
Forecasting Approaches
Overview of Qualitative Methods and Quantitative Methods
Time-Series Forecasting
Decomposition of a Time Series
Naive Approach
Time-Series Forecasting (cont.)
Moving Averages
Exponential Smoothing(with trend)
Associative Forecasting Methods: Regression and Correlation
Using Regression Analysis for Forecasting
Correlation Coefficients for Regression Lines
Multiple-Regression Analysis
03: CH4 - Forecasting (MGMT3102: Fall13)

3. Learning Objectives
When you complete this chapter you should be able to :
Understand the three time horizons and which models apply for each use
Explain when to use each of the four qualitative models
Apply the naive, moving average, and exponential smoothing
Compute measures of forecast accuracy
03: CH4 - Forecasting (MGMT3102: Fall13)

4. Forecasting at Disney World
Revenues are derived from people
Forecast used to adjust opening times, rides, shows, staffing levels, and guests admitted
Model includes gross domestic product, cross-exchange rates, arrivals into the USA
Survey 1 million park guests, employees, and travel professionals each year
Inputs are airline specials, Federal Reserve policies, Wall Street trends, vacation/holiday schedules for 3,000 school districts around the world
Revenues are derived from people – how many visitors and how they spend their money
Forecast used to adjust opening times, rides, shows, staffing levels, and guests admitted
Economic model includes gross domestic product, cross-exchange rates, arrivals into the USA
A staff of 35 analysts and 70 field people survey 1 million park guests, employees, and travel professionals each year
Inputs to the forecasting model include airline specials, Federal Reserve policies, Wall Street trends, vacation/holiday schedules for 3,000 school districts around the world
03: CH4 - Forecasting (MGMT3102: Fall13)

5. Why Forecast? What are we trying to Forecast?
A very well known attribute of a forecast is that they are always wrong.
For example, Snackwell Cookies (1993), But . . .
L. L. Bean
Taco Bell
AMR
Characteristics of Forecasts
A forecast is more than a single number
Aggregate forecasts are better
The further in the future, the more inaccuracy
Forecasts only predict from past events
OOPS! Snack well Cookies - misforecasted demand for Fat-free Devil’s Food Cookies
L. L. Bean -> (Time Series Forecasting) - Forecasts to set labor capacity saved $300,000 per year
Taco Bell -> (Six Week Moving Average) – Staffing savings of $16.4 million
American Airline -> (Linear Regression) – Repairable parts – decreased inventory and increased availability saved $1 million/year
03: CH4 - Forecasting (MGMT3102: Fall13)

6. 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
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
03: CH4 - Forecasting (MGMT3102: Fall13)

7. Forecasting Approaches
Qualitative Methods
Used when situation is vague and little data exist
Involves intuition, experience
Quantitative Methods
Used when situation is ‘stable’ - historical data exist
Involves mathematical techniques
Qualitative Methods
Used when situation is vague and little data exist
New products
New technology
Involves intuition, experience
e.g., forecasting sales on Internet
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
03: CH4 - Forecasting (MGMT3102: Fall13)

8. Overview of Qualitative Methods
Jury of executive opinion
Pool opinions of high-level experts
Delphi method
Sales force composite
Aggregated estimates from salespersons
Consumer Market Survey
03: CH4 - Forecasting (MGMT3102: Fall13)

9. 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)
03: CH4 - Forecasting (MGMT3102: Fall13)

10. Overview of Quantitative Approaches
Naive approach
Moving averages
Exponential smoothing
Trend projection
Linear regression
time-series models
associative model
03: CH4 - Forecasting (MGMT3102: Fall13)

11. Time Series Forecasting
Set of evenly spaced numerical data
Forecast based only on past values, no other variables important
Components of a Time Series:
Trend
Seasonal
Cyclical
Random
Forecast based only on past values,
Assumes that factors influencing past and present will continue influence in future
Trend Component
Changes due to population, technology, age, culture, etc.
Seasonal Component
Occurs within a single year
Cyclical Component
Affected by business cycle, political, and economic factors
Multiple years duration - causal or associative relationships
Random Component
Erratic, unsystematic, ‘residual’ fluctuations
03: CH4 - Forecasting (MGMT3102: Fall13)

12. Average demand over 4 years
Components of Demand
Trend component
Demand for product or service
| | | |
Time (years)
Seasonal peaks
Actual demand line
Average demand over 4 years
Random variation
Figure 4.1
03: CH4 - Forecasting (MGMT3102: Fall13)

13. 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
03: CH4 - Forecasting (MGMT3102: Fall13)

14. ∑ 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
03: CH4 - Forecasting (MGMT3102: Fall13)

15. 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
( )/3 = 13 2/3
( )/3 = 16
( )/3 = 19 1/3 10 12 13
( )/3 = 11 2/3
03: CH4 - Forecasting (MGMT3102: Fall13)

16. 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
03: CH4 - Forecasting (MGMT3102: Fall13)

17. Weighted Moving Average
Used when some trend might be 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
03: CH4 - Forecasting (MGMT3102: Fall13)

18. 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
03: CH4 - Forecasting (MGMT3102: Fall13)

19. 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
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
Figure 4.2
03: CH4 - Forecasting (MGMT3102: Fall13)

20. Exponential Smoothing
Form of weighted moving average
Weights decline exponentially
Most recent data weighted most
Requires smoothing constant ()
Ranges from 0 to 1
Less need for keeping past data
03: CH4 - Forecasting (MGMT3102: Fall13)

21. 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)
03: CH4 - Forecasting (MGMT3102: Fall13)

22. Exponential Smoothing Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20
03: CH4 - Forecasting (MGMT3102: Fall13)

23. Exponential Smoothing Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20
New forecast = (153 – 142)
03: CH4 - Forecasting (MGMT3102: Fall13)

24. Exponential Smoothing Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20
New forecast = (153 – 142) =
= ≈ 144 cars
03: CH4 - Forecasting (MGMT3102: Fall13)

25. Impact of Different  Actual demand a = .5 a = .1 225 – 200 – 175 –
225 –
200 –
175 –
150 –
| | | | | | | | |
Quarter
Demand
Actual demand
a = .5
a = .1
Chose high values of  when underlying average is likely to change
Choose low values of  when underlying average is stable
03: CH4 - Forecasting (MGMT3102: Fall13)

26. 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
03: CH4 - Forecasting (MGMT3102: Fall13)

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
03: CH4 - Forecasting (MGMT3102: Fall13)

28. Common Measures of Error
Mean Absolute Deviation (MAD)
MAD= |Actual−Forecast| n
Mean Squared Error (MSE)
MSE= (Forecast Errors)𝟐 n
Mean Absolute Percent Error (MAPE)
MAPE= 𝒊=𝟏 𝒏 100|Actuali−Forecasti|/Actuali n
03: CH4 - Forecasting (MGMT3102: Fall13)

29. 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
03: CH4 - Forecasting (MGMT3102: Fall13)

30. 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
03: CH4 - Forecasting (MGMT3102: Fall13)

31. 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
03: CH4 - Forecasting (MGMT3102: Fall13)

32. 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
03: CH4 - Forecasting (MGMT3102: Fall13)

33. 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%
03: CH4 - Forecasting (MGMT3102: Fall13)

34. Exponential Smoothing with Trend Adjustment
When a trend is present, exponential smoothing must be modified
Forecast
including (FITt) =
trend
Exponentially Exponentially
smoothed (Ft) + smoothed (Tt)
forecast trend
© 2011 Pearson Education, Inc. publishing as Prentice Hall
03: CH4 - Forecasting (MGMT3102: Fall13)

35. 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
© 2011 Pearson Education, Inc. publishing as Prentice Hall
03: CH4 - Forecasting (MGMT3102: Fall13)

36. 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
© 2011 Pearson Education, Inc. publishing as Prentice Hall
03: CH4 - Forecasting (MGMT3102: Fall13)

37. 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
© 2011 Pearson Education, Inc. publishing as Prentice Hall
03: CH4 - Forecasting (MGMT3102: Fall13)

38. 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
© 2011 Pearson Education, Inc. publishing as Prentice Hall
03: CH4 - Forecasting (MGMT3102: Fall13)

39. 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 + T2
FIT2 =
= units
Table 4.1
© 2011 Pearson Education, Inc. publishing as Prentice Hall
03: CH4 - Forecasting (MGMT3102: Fall13)

40. 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
© 2011 Pearson Education, Inc. publishing as Prentice Hall
03: CH4 - Forecasting (MGMT3102: Fall13)

41. 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
© 2011 Pearson Education, Inc. publishing as Prentice Hall
03: CH4 - Forecasting (MGMT3102: Fall13)

42. 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
03: CH4 - Forecasting (MGMT3102: Fall13)

43. 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 ^
03: CH4 - Forecasting (MGMT3102: Fall13)

44. 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
03: CH4 - Forecasting (MGMT3102: Fall13)

45. Associative Forecasting Example
Sales Area 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
03: CH4 - Forecasting (MGMT3102: Fall13)

46. Associative Forecasting Example
y = x ^
Sales = (payroll)
If payroll next year is estimated to be $6 billion, then:
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |
Nodel’s sales
Area payroll
3.25
Sales = (6)
Sales = $3,250,000
03: CH4 - Forecasting (MGMT3102: Fall13)

47. Correlation
How strong is the linear relationship between the variables?
Coefficient of correlation r
measures degree of association
Values range from -1 to +1
Coefficient of Determination r2
the % change in y predicted by the change in x
Values range from 0 to 1
For example, when r = .901 r2 = .81
Correlation does not necessarily imply causality!
03: CH4 - Forecasting (MGMT3102: Fall13)

48. Correlation Coefficienty x
(a) Perfect positive correlation: r = +1 y x
(b) Positive correlation: 0 < r < 1 y x
(c) No correlation: r = 0 y x
(d) Perfect negative correlation: r = -1
03: CH4 - Forecasting (MGMT3102: Fall13)

49. Multiple Regression Analysis
If more than one independent variable is to be used in the model, linear regression can be extended to multiple regression to accommodate several independent variables
y = a + b1x1 + b2x2 … ^
Computationally, this is quite complex and generally done on the computer
03: CH4 - Forecasting (MGMT3102: Fall13)

50. Multiple Regression Analysis
In the Nodel example, including interest rates in the model gives the new equation:
y = x x2 ^
An improved correlation coefficient of r = .96 means this model does a better job of predicting the change in construction sales
Sales = (6) - 5.0(.12) = 3.00
Sales = $3,000,000
03: CH4 - Forecasting (MGMT3102: Fall13)

51. 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
03: CH4 - Forecasting (MGMT3102: Fall13)

52. Fast Food Restaurant Forecast
20% –
15% –
10% –
5% –
(Lunchtime)
(Dinnertime)
Hour of day
Percentage of sales
Figure 4.12
03: CH4 - Forecasting (MGMT3102: Fall13)

53. FedEx Call Center Forecast
12% –
10% –
8% –
6% –
4% –
2% –
0% –
Hour of day
A.M.
P.M. 2 4 6 8 10 12
Figure 4.12
03: CH4 - Forecasting (MGMT3102: Fall13)

54. In-Class Problems from the Lecture Guide Practice Problems
Auto sales at Carmen’s Chevrolet are shown below. Develop a 3-week moving average.
Week
Auto Sales 1 8 2 10 3 9 4 11 5 6 13 7 -
Week
Auto Sales
Three-Week Moving Average 1 8 2 10 3 9 4 11
( ) / 3 = 9 5
( ) / 3 = 10 6 13
( ) / 3 = 10 7 -
( ) / 3 = 11 1/3
03: CH4 - Forecasting (MGMT3102: Fall13)

55. In-Class Problems from the Lecture Guide Practice Problems
Carmen’s decides to forecast auto sales by weighting the three weeks as follows:
Weights Applied
Period 3
Last week 2
Two weeks ago 1
Three weeks ago 6
Total
Week
Auto Sales
Three-Week Moving Average 1 8 2 10 3 9 4 11
[(3*9) + (2*10) + (1*8)] / 6 = 9 1/6 5
[(3*11) + (2*9) + (1*10)] / 6 = 10 1/6 6 13
[(3*10) + (2*11) + (1*9)] / 6 = 10 1/6 7 -
[(3*13) + (2*10) + (1*11)] / 6 = 11 2/3
03: CH4 - Forecasting (MGMT3102: Fall13)

56. In-Class Problems from the Lecture Guide Practice Problems
A firm uses simple exponential smoothing with α=0.1 to forecast demand. The forecast for the week of January 1 was 500 units whereas the actual demand turned out to be 450 units. Calculate the demand forecast for the week of January 8.
03: CH4 - Forecasting (MGMT3102: Fall13)

57. In-Class Problems from the Lecture Guide Practice Problems
Exponential smoothing is used to forecast automobile battery sales. Two value of α are examined α = 0.8 and α=0.5. Evaluate the accuracy of each smoothing constant. Which is preferable? (Assume the forecast for January was 22 batteries.) Actual sales are given below:
Month
Actual Battery Sales
Forecast
January 20 22
February 21
March 15
April 14
May 13
June 16
On the basis of this analysis, a smoothing constant of a = 0.8 is preferred to that of a = 0.5 because it has a smaller MAD.
Month
Actual Battery Sales
Rounded Forecast with  =0.8
Absolute Deviation with  =0.8
Rounded Forecast with  =0.5
Absolute Deviation with  =0.5
January 20 22
2.0
February 21
20.4
0.6
0.0
March 15
20.9
5.9
6.0
April 14
16.2
2.2 18
4.0
May 13
14.4
1.4 16
3.0
June
13.3
2.7
14.5
1.5
 = 14.8
 = 16.5
2.46
2.75
MSE
8.84
11.21
03: CH4 - Forecasting (MGMT3102: Fall13)