1. Forecasting
Chapter 13 1

2. Designing the Forecast System
Deciding what to forecast
Level of aggregation.
Units of measure.
Choosing the type of forecasting method:
Qualitative methods
Judgment
Quantitative methods
Causal
Time-series

3. Deciding What To Forecast
Few companies err by more than 5 percent when forecasting total demand for all their services or products. Errors in forecasts for individual items may be much higher.
Level of Aggregation: The act of clustering several similar services or products so that companies can obtain more accurate forecasts.
Units of measurement: Forecasts of sales revenue are not helpful because prices fluctuate.
Forecast the number of units of demand then translate into sales revenue estimates
Stock-keeping unit (SKU): An individual item or product that has an identifying code and is held in inventory somewhere along the value chain.

4. Choosing the Type of Forecasting Technique
Judgment methods: A type of qualitative method that translates the opinions of managers, expert opinions, consumer surveys, and sales force estimates into quantitative estimates.
Causal methods: A type of quantitative method that uses historical data on independent variables, such as promotional campaigns, economic conditions, and competitors’ actions, to predict demand.
Time-series analysis: A statistical approach that relies heavily on historical demand data to project the future size of demand and recognizes trends and seasonal patterns.

5. Demand Forecast Applications
© 2007 Pearson Education
Demand Forecast Applications
• Causal
• Judgment
• Time series • Causal
Forecasting Technique
• Facility location
• Capacity planning
• Process management
• Staff planning
• Production planning
• Master production scheduling
• Purchasing
• Distribution
• Inventory management
• Final assembly scheduling
• Workforce scheduling
• Master production scheduling
Decision
Area
• Total sales
• Groups or families of products or services
• Individual products or services
Forecast Quality
Long Term
(more than 2 years)
Medium Term
(3 months– 2 years)
Short Term
(0–3 months)
Application
Time Horizon 2

6. Judgment Methods
Sales force estimates: The forecasts that are compiled from estimates of future demands made periodically by members of a company’s sales force.
Executive opinion: A forecasting method in which the opinions, experience, and technical knowledge of one or more managers are summarized to arrive at a single forecast.
Executive opinion can also be used for technological forecasting to keep abreast of the latest advances in technology.
Market research: A systematic approach to determine external consumer interest in a service or product by creating and testing hypotheses through data-gathering surveys.
Delphi method: A process of gaining consensus from a group of experts while maintaining their anonymity.

7. Guidelines for Using Judgment Forecasts
Judgment forecasting is clearly needed when no quantitative data are available to use quantitative forecasting approaches.
Guidelines for the use of judgment to adjust quantitative forecasts to improve forecast quality are as follows:
Adjust quantitative forecasts when they tend to be inaccurate and the decision maker has important contextual knowledge.
Make adjustments to quantitative forecasts to compensate for specific events, such as advertising campaigns, the actions of competitors, or international developments.

8. Forecasting Error
For any forecasting method, it is important to measure the accuracy of its forecasts.
Forecast error is the difference found by subtracting the forecast from actual demand for a given period.
Et = Dt - Ft where
Et = forecast error for period t
Dt = actual demand for period t
Ft = forecast for period t

9. Measures of Forecast Error
Cumulative sum of forecast errors (CFE): A measurement of the total forecast error that assesses the bias in a forecast.
Mean squared error (MSE): A measurement of the dispersion of forecast errors.
Mean absolute deviation (MAD): A measurement of the dispersion of forecast errors.
CFE = Et
Et2 n
MSE =
MAD =
|Et | n

10. Measures of Forecast Error
Mean absolute percent error (MAPE): A measurement that relates the forecast error to the level of demand and is useful for putting forecast performance in the proper perspective.
MAPE =
[ |Et | / Dt ](100) n 74

11. Calculating Forecast Error Example 13.6
The following table shows the actual sales of upholstered chairs for a furniture manufacturer and the forecasts made for each of the last eight months. Calculate CFE, MSE, MAD, and MAPE for this product.
Absolute
Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error,
t Dt Ft Et Et |Et| (|Et|/Dt)(100) % – – –
Total – % 75

12. Example 13.6 Forecast Error Measures
© 2007 Pearson Education
Example 13.6 Forecast Error Measures
CFE = – 15
Cumulative forecast error (bias):
E = = – 1.875
– 15 8
Average forecast error (mean bias):
MSE = = 659.4
5275 8
Mean squared error:
s = 27.4
Standard deviation:
MAD = = 24.4
195 8
Mean absolute deviation:
MAPE = = 10.2%
81.3% 8
Mean absolute percent error:
Tracking signal = = =
CFE MAD

13. Causal Methods Linear Regression
Causal methods are used when historical data are available and the relationship between the factor to be forecasted and other external or internal factors can be identified.
Linear regression: A causal method in which one variable (the dependent variable) is related to one or more independent variables by a linear equation.
Dependent variable: The variable that one wants to forecast.
Independent variables: Variables that are assumed to affect the dependent variable and thereby “cause” the results observed in the past.

14. Causal Methods Linear Regression
Deviation,
or error {
Dependent variable
Independent variable X Y
Regression
equation:
Y = a + bX
Y = dependent variable
X = independent variable
a = Y-intercept of the line
b = slope of the line
Estimate of
Y from
regression
equation
Actual
value
of Y
Value of X used
to estimate Y 8

15. Linear Regression Example 13.1
The following are sales and advertising data for the past 5 months for brass door hinges. The marketing manager says that next month the company will spend $1,750 on advertising for the product. Use linear regression to develop an equation and a forecast for this product.
Sales Advertising
Month (000 units) (000 $) 14

16. Example 13.1 Causal Methods Linear Regression
Sales Advertising
Month (000 units) (000 $)
Regression equation for forecast = Y = a + bx, where
a = Y – bX
b =
XY – nXY
X 2 – nX 2
Example 13.1 15

17. Example 13.1 Causal Methods Linear Regression
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Example 13.1 16

18. Example 13.1 Causal Methods Linear Regression
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
n = 5 Y = 171 X = 1.64
Example 13.1 26

19. XY – nXY X 2 – nX 2 Example 13.1 Causal Methods Linear Regression
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
a = Y – bX
b =
XY – nXY
X 2 – nX 2
Example 13.1 17

20. Example 13.1 Causal Methods Linear Regression
a = Y – bX
b =
– 5(1.64)(171)
14.90 – 5(1.64)2
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
This slide advances automatically.
Example 13.1 18

21. Example 13.1 Causal Methods Linear Regression
a = Y – bX
b =
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
Example 13.1 19

22. Example 13.1 Causal Methods Linear Regression
b =
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
This slide advances automatically.
Example 13.1 20

23. Example 13.1 Causal Methods Linear Regression
b =
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
Example 13.1 21

24. Example 13.1 Causal Methods Linear Regression
b =
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
Y = – (X)
Example 13.1 22

25. Example 13.1 Causal Methods Linear Regression
Advertising (thousands of dollars)
| | | |
300 —
250 —
200 —
150 —
100 — 50
Sales (thousands of units)
a =
b =
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
Y = – (X)
This slide advances automatically.
Figure 13.3 23

26. Example 13.1 Causal Methods Linear Regression
b =
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
Y = – (X)
| | | |
Advertising (thousands of dollars)
300 —
250 —
200 —
150 —
100 — 50
Sales (thousands of units)
This slide advances automatically.
Figure 13.3 24

27. Example 13.1 Causal Methods Linear Regression
b =
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
Y = – (X)
Sales (thousands of units)
| | | |
Advertising (thousands of dollars)
300 —
250 —
200 —
150 —
100 — 50
Figure 13.3 24

28. Example 13.1 Causal Methods Linear Regression
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
Example 13.1 25

29. [nX 2 – (X) 2][nY 2 – (Y) 2]
Example 13.1 Causal Methods Linear Regression
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
nXY – X Y
[nX 2 – (X) 2][nY 2 – (Y) 2]
r =
Example 13.1 26

30. Example 13.1 Causal Methods Linear Regression
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
r = 0.98
Example 13.1 27

31. Example 13.1 Causal Methods Linear Regression
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
r = r 2 = 0.96
Example 13.1 28

32. Example 13.1 Causal Methods Linear Regression
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
r = r 2 = 0.96
Forecast for Month 6:
Advertising expenditure = $1750
Y = (1.75)
Example 13.1 29

33. Example 13.1 Causal Methods Linear Regression
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
r = r 2 = 0.96
Forecast for Month 6:
Advertising expenditure = $1750
Y = or 183,015 hinges
Example 13.1 30

34. Components of a Time Series
Time Series: The repeated observations of demand for a service or product in their order of occurrence.
There are four basic patterns of most time series.
Trend. The systematic increase or decrease in the mean of the series over time.
Seasonal. A repeatable pattern of increases or decreases in demand, depending on the time of day, week, month, or season.
Cyclical. The less predictable gradual increases or decreases over longer periods of time (years or decades).
Random. The unforecastable variation in demand.

35. Demand Patterns
Horizontal
Trend
Seasonal
Cyclical

36. Time Series Methods
Naive forecast: A time-series method whereby the forecast for the next period equals the demand for the current period, or Forecast = Dt
Simple moving average method: A time-series method used to estimate the average of a demand time series by averaging the demand for the n most recent time periods.
It removes the effects of random fluctuation and is most useful when demand has no pronounced trend or seasonal influences. …

37. Moving Average Method Example 13.2
a. Compute a three-week moving average forecast for
the arrival of medical clinic patients in week 4.
The numbers of arrivals for the past 3 weeks were:
Patient
Week Arrivals
1 400
2 380
3 411
b. If the actual number of patient arrivals in week
4 is 415, what is the forecast error for week 4?
c. What is the forecast for week 5?

38. Example 13.2 Solution
The moving average method may involve the use of as many periods of past demand as desired. The stability of the demand series generally determines how many periods to include.
Week
450 —
430 —
410 —
390 —
370 —
| | | | | |
Patient arrivals
Actual patient
arrivals 31

39. Example 13.2 Solution continued
Forecast for week 4 is the average of the arrivals for weeks 1,2 and 3
F4 = 3
Week
Arrivals
Average 1
400 2
380 3
411
397 4
415
402 5 ?
Forecast for week 5 is the average of the arrivals for weeks 2,3 and 4 b. c.
Forecast error for week 4 is 18. It is the difference between the actual arrivals (415) for week 4 and the average of 397 that was used as a forecast for week 4. (415 – 397 = 18)

40. Comparison of 3- and 6-Week MA Forecasts
Patient Arrivals
Actual patient arrivals
3-week moving average forecast
6-week moving average forecast

41. Application 13.1
We will use the following customer-arrival data in this moving average application:

42. Application 13.1a Moving Average Method
© 2007 Pearson Education
Application 13.1a Moving Average Method
780 customer arrivals
802 customer arrivals

43. Weighted Moving Averages
Weighted moving average method: A time-series method in which each historical demand in the average can have its own weight; the sum of the weights equals 1.0.
Ft+1 = W1Dt + W2Dt-1 + …+ WnDt-n+1

44. Application 13.1b Weighted Moving Average
© 2007 Pearson Education
Application 13.1b Weighted Moving Average
786 customer arrivals
802 customer arrivals

45. Exponential Smoothing
Exponential smoothing method: A sophisticated weighted moving average method that calculates the average of a time series by giving recent demands more weight than earlier demands.
Ft+1 = (Demand this period) + (1 – )(Forecast calculated last period)
=  Dt + (1–)Ft
Or an equivalent equation: Ft+1 = Ft + (Dt – Ft )
Where alpha (is a smoothing parameter with a value between 0 and 1.0
Exponential smoothing is the most frequently used formal forecasting method because of its simplicity and the small amount of data needed to support it.

46. Exponential Smoothing Example 13.3
Week
Arrivals 1
400 2
380 3
411 4
415 5 ?
Reconsider the medical clinic patient arrival data. It is now the end of week a. Using  = 0.10, calculate the exponential smoothing forecast for week Ft+1 =  Dt + (1-)Ft
F4 = 0.10(411) (390) = 392.1
b. What is the forecast error for week 4 if the actual demand turned out to be 415?
E4 = = 23
c. What is the forecast for week 5?
F5 = 0.10(415) (392.1) = 394.4

47. Application 13.1c Exponential Smoothing
© 2007 Pearson Education
Application 13.1c Exponential Smoothing
784 customer arrivals
789 customer arrivals

48. Trend-Adjusted Exponential Smoothing
A trend in a time series is a systematic increase or decrease in the average of the series over time.
Where a significant trend is present, exponential smoothing approaches must be modified; otherwise, the forecasts tend to be below or above the actual demand.
Trend-adjusted exponential smoothing method: The method for incorporating a trend in an exponentially smoothed forecast.
With this approach, the estimates for both the average and the trend are smoothed, requiring two smoothing constants. For each period, we calculate the average and the trend.

49. Trend-Adjusted Exponential Smoothing Formula
Ft+1 = At +Tt
where At = Dt + (1 – )(At-1 + Tt-1)
Tt = (At – At-1) + (1 – )Tt-1
At = exponentially smoothed average of the series in period t
Tt = exponentially smoothed average of the trend in period t
 = smoothing parameter for the average
 = smoothing parameter for the trend
Dt = demand for period t
Ft+1 = forecast for period t + 1

50. Trend-Adjusted Exponential Smoothing
Example Medanalysis ran an average of 28 blood tests per week during the past four weeks. The trend over that period was 3 additional patients per week. This week’s demand was for 27 blood tests. We use  = 0.20 and  = 0.20 to calculate the forecast for next week.
A0 = 28 patients and Tt = 3 patients
At = Dt + (1 – )(At-1 + Tt-1)
A1= 0.20(27) (28 + 3) = 30.2
Tt = (At – At-1) + (1 – )Tt-1
T1 = 0.20(30.2 – 2.8) (3) = 2.8
Ft+1 = At + Tt
F2 = = 33 blood tests

51. Example 13.4 Medanalysis Trend-Adjusted Exponential Smoothing
| | | | | | | | | | | | | | |
80 —
70 —
60 —
50 —
40 —
30 —
Patient arrivals
Week
Actual blood test requests
Trend-adjusted forecast 57

52. © 2007 Pearson Education
Forecast for Medanalysis Using the Trend-Adjusted Exponential Smoothing Model

53. Application 13.2
The forecaster for Canine Gourmet dog breath fresheners estimated (in March) the sales average to be 300,000 cases sold per month and the trend to be +8,000 per month.
The actual sales for April were 330,000 cases.
What is the forecast for May,
assuming  = 0.20 and  = 0.10?

54. Application 13.2 Solution thousand thousand
© 2007 Pearson Education
Application 13.2 Solution
thousand
thousand
To make forecasts for periods beyond the next period, multiply the trend estimate by the number of additional periods, and add the result to the current average

55. Seasonal Patterns
Seasonal patterns are regularly repeated upward or downward movements in demand measured in periods of less than one year.
An easy way to account for seasonal effects is to use one of the techniques already described but to limit the data in the time series to those time periods in the same season.
If the weighted moving average method is used, high weights are placed on prior periods belonging to the same season.
Multiplicative seasonal method is a method whereby seasonal factors are multiplied by an estimate of average demand to arrive at a seasonal forecast.
Additive seasonal method is a method whereby seasonal forecasts are generated by adding a constant to the estimate of the average demand per season.

56. Multiplicative Seasonal Method
Step 1: For each year, calculate the average demand for each season by dividing annual demand by the number of seasons per year.
Step 2: For each year, divide the actual demand for each season by the average demand per season, resulting in a seasonal index for each season of the year, indicating the level of demand relative to the average demand.
Step 3: Calculate the average seasonal index for each season using the results from Step 2. Add the seasonal indices for each season and divide by the number of years of data.
Step 4: Calculate each season’s forecast for next year.

57. Using the Multiplicative Seasonal Method
Example 13.5: Stanley Steemer, a carpet cleaning company needs a quarterly forecast of the number of customers expected next year. The business is seasonal, with a peak in the third quarter and a trough in the first quarter.
Forecast customer demand for each quarter of year 5, based on an estimate of total year 5 demand of 2,600 customers.
Quarter Year 1 Year 2 Year 3 Year 4
Total
Demand has been increasing by an average of 400 customers each year. The forecast demand is found by extending that trend, and projecting an annual demand in year 5 of 2, = 2,600 customers. 60

58. Example 13.5 OM Explorer Solution
© 2007 Pearson Education
Example 13.5 OM Explorer Solution

59. Application 13.3 Multiplicative Seasonal Method
© 2007 Pearson Education
Application 13.3 Multiplicative Seasonal Method
1320/4 quarters = 330

60. Comparison of Seasonal Patterns
Multiplicative pattern
Additive pattern

61. Tracking Signal
Tracking signal: A measure that indicates whether a method of forecasting is accurately predicting actual changes in demand.
Tracking signal =
CFEt
MADt

62. Forecast Error Ranges
Forecasts stated as a single value can be less useful because they do not indicate the range of likely errors. A better approach can be to provide the manager with a forecasted value and an error range.
% of area of normal probability distribution within control limits of the tracking signal
Control Limit Spread Equivalent Percentage of Area
(number of MAD) Number of  within Control Limits
57.62
76.98
89.04
95.44
98.36
99.48
99.86
± 0.80
± 1.20
± 1.60
± 2.00
± 2.40
± 2.80
± 3.20
± 1.0
± 1.5
± 2.0
± 2.5
± 3.0
± 3.5
± 4.0 84

63. Computer Support CFE Tracking signal = MAD
Computer support, such as OM Explorer, makes error calculations easy when evaluating how well forecasting models fit with past data.
+2.0 —
+1.5 —
+1.0 —
+0.5 —
0 —
–0.5 —
–1.0 —
–1.5 —
| | | | |
Observation number
Tracking signal
Control limit
Out of control
Tracking signal =
CFE
MAD 86

64. Results Sheet Moving Average
Forecast for 7/17/06 83

65. Results Sheet Weighted Moving Average
Forecast for 7/17/06

66. Results Sheet Exponential Smoothing
Forecast for 7/17/06 83

67. Results Sheet Trend-Adjusted Exponential Smoothing
Forecast for 7/17/06
Forecast for 7/24/06
Forecast for 7/31/06
Forecast for 8/7/06
Forecast for 8/14/06
Forecast for 8/21/06 83

68. Criteria for Selecting Time-Series Methods
Forecast error measures provide important information for choosing the best forecasting method for a service or product.
They also guide managers in selecting the best values for the parameters needed for the method:
n for the moving average method, the weights for the weighted moving average method, and  for exponential smoothing.
The criteria to use in making forecast method and parameter choices include
minimizing bias
minimizing MAPE, MAD, or MSE
meeting managerial expectations of changes in the components of demand
minimizing the forecast error last period

69. Using Multiple Techniques
Research during the last two decades suggests that combining forecasts from multiple sources often produces more accurate forecasts.
Combination forecasts: Forecasts that are produced by averaging independent forecasts based on different methods or different data or both.
Focus forecasting: A method of forecasting that selects the best forecast from a group of forecasts generated by individual techniques.
The forecasts are compared to actual demand, and the method that produces the forecast with the least error is used to make the forecast for the next period. The method used for each item may change from period to period.

70. Forecasting as a Process
The forecast process itself, typically done on a monthly basis, consists of structured steps. They often are facilitated by someone who might be called a demand manager, forecast analyst, or demand/supply planner.

71. Denver Air-Quality Discussion Question 1
250 –
225 –
200 –
175 –
150 –
125 –
100 –
75 –
50 –
25 –
| | | | | | | | | | | | | |
Year 2
Year 1
July
August
Date
Visibility rating 83