1. Beni Asllani University of Tennessee at Chattanooga
Chapter 12
Forecasting
Operations Management - 6th Edition
Roberta Russell & Bernard W. Taylor, III
Beni Asllani University of Tennessee at Chattanooga
Copyright 2009 John Wiley & Sons, Inc.

2. Lecture Outline
Strategic Role of Forecasting in Supply Chain Management
Components of Forecasting Demand
Time Series Methods
Forecast Accuracy
Time Series Forecasting Using Excel
Regression Methods
Copyright 2009 John Wiley & Sons, Inc.

3. Forecasting Predicting the future Qualitative forecast methods
subjective
Quantitative forecast methods
based on mathematical formulas
Copyright 2009 John Wiley & Sons, Inc.

4. Forecasting and Supply Chain Management
Accurate forecasting determines how much inventory a company must keep at various points along its supply chain
Continuous replenishment
supplier and customer share continuously updated data
typically managed by the supplier
reduces inventory for the company
speeds customer delivery
Variations of continuous replenishment
quick response
JIT (just-in-time)
VMI (vendor-managed inventory)
stockless inventory
Copyright 2009 John Wiley & Sons, Inc.

5. Forecasting Quality Management Strategic Planning
Accurately forecasting customer demand is a key to providing good quality service
Strategic Planning
Successful strategic planning requires accurate forecasts of future products and markets
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6. Types of Forecasting Methods
Depend on
time frame
demand behavior
causes of behavior
Copyright 2009 John Wiley & Sons, Inc.

7. Time Frame Indicates how far into the future is forecast
Short- to mid-range forecast
typically encompasses the immediate future
daily up to two years
Long-range forecast
usually encompasses a period of time longer than two years
Copyright 2009 John Wiley & Sons, Inc.

8. Demand Behavior Trend Random variations Cycle Seasonal pattern
a gradual, long-term up or down movement of demand
Random variations
movements in demand that do not follow a pattern
Cycle
an up-and-down repetitive movement in demand
Seasonal pattern
an up-and-down repetitive movement in demand occurring periodically
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9. Forms of Forecast Movement
Time
(a) Trend
(d) Trend with seasonal pattern
(c) Seasonal pattern
(b) Cycle
Demand
Random movement
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10. Forecasting Methods Time series Regression methods Qualitative
statistical techniques that use historical demand data to predict future demand
Regression methods
attempt to develop a mathematical relationship between demand and factors that cause its behavior
Qualitative
use management judgment, expertise, and opinion to predict future demand
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11. Qualitative Methods
Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts
Delphi method
involves soliciting forecasts about technological advances from experts
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12. Is accuracy of forecast acceptable?
Forecasting Process
1. Identify the purpose of forecast
2. Collect historical data
3. Plot data and identify patterns
6. Check forecast accuracy with one or more measures
5. Develop/compute forecast for period of historical data
4. Select a forecast model that seems appropriate for data 7.
Is accuracy of forecast acceptable? No
8b. Select new forecast model or adjust parameters of existing model
Yes
9. Adjust forecast based on additional qualitative information and insight
10. Monitor results and measure forecast accuracy
8a. Forecast over planning horizon
Copyright 2009 John Wiley & Sons, Inc.

13. Time Series
Assume that what has occurred in the past will continue to occur in the future
Relate the forecast to only one factor - time
Include
moving average
exponential smoothing
linear trend line
Copyright 2009 John Wiley & Sons, Inc.

14. Moving Average Naive forecast Simple moving average
demand in current period is used as next period’s forecast
Simple moving average
uses average demand for a fixed sequence of periods
stable demand with no pronounced behavioral patterns
Weighted moving average
weights are assigned to most recent data
Copyright 2009 John Wiley & Sons, Inc.

15. Moving Average: Naïve Approach
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
ORDERS
MONTH PER MONTH -
120 90
100 75
110 50
130
Nov
FORECAST
Copyright 2009 John Wiley & Sons, Inc.

16. n = number of periods in the moving average
Simple Moving Average
MAn = n
i = 1  Di
where
n = number of periods in the moving average
Di = demand in period i
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17. 3-month Simple Moving Average
MA3 = 3
i = 1  Di =
= 110 orders
for Nov
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
Nov -
ORDERS
MONTH PER MONTH –
103.3
88.3
95.0
78.3
85.0
105.0
110.0
MOVING
AVERAGE
Copyright 2009 John Wiley & Sons, Inc.

18. 5-month Simple Moving Average
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
Nov -
ORDERS
MONTH PER MONTH –
99.0
85.0
82.0
88.0
95.0
91.0
MOVING
AVERAGE
MA5 = 5
i = 1  Di =
= 91 orders
for Nov
Copyright 2009 John Wiley & Sons, Inc.

19. Smoothing Effects 150 – 125 – 100 – 5-month 75 – 50 – 25 – 0 – Orders
| | | | | | | | | | |
Jan Feb Mar Apr May June July Aug Sept Oct Nov
Actual
Orders
Month
5-month
3-month
Copyright 2009 John Wiley & Sons, Inc.

20. Weighted Moving Average
WMAn =
i = 1 
Wi Di
where
Wi = the weight for period i, between 0 and 100 percent
 Wi = 1.00
Adjusts moving average method to more closely reflect data fluctuations
Copyright 2009 John Wiley & Sons, Inc.

21. Weighted Moving Average Example
MONTH WEIGHT DATA
August 17% 130
September 33% 110
October 50% 90
WMA3 = 3
i = 1 
Wi Di
= (0.50)(90) + (0.33)(110) + (0.17)(130)
= orders
November Forecast
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22. Exponential Smoothing
Averaging method
Weights most recent data more strongly
Reacts more to recent changes
Widely used, accurate method
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23. Exponential Smoothing (cont.)
Ft +1 = Dt + (1 - )Ft
where:
Ft +1 = forecast for next period
Dt = actual demand for present period
Ft = previously determined forecast for present period
= weighting factor, smoothing constant
Copyright 2009 John Wiley & Sons, Inc.

24. Effect of Smoothing Constant
0.0  1.0 If = 0.20, then Ft +1 = 0.20Dt Ft
If = 0, then Ft +1 = 0Dt + 1 Ft = Ft Forecast does not reflect recent data
If = 1, then Ft +1 = 1Dt + 0 Ft =Dt Forecast based only on most recent data
Copyright 2009 John Wiley & Sons, Inc.

25. Exponential Smoothing (α=0.30)
PERIOD MONTH DEMAND
1 Jan 37
2 Feb 40
3 Mar 41
4 Apr 37
5 May 45
6 Jun 50
7 Jul 43
8 Aug 47
9 Sep 56
10 Oct 52
11 Nov 55
12 Dec 54
F2 = D1 + (1 - )F1
= (0.30)(37) + (0.70)(37)
= 37
F3 = D2 + (1 - )F2
= (0.30)(40) + (0.70)(37)
= 37.9
F13 = D12 + (1 - )F12
= (0.30)(54) + (0.70)(50.84)
= 51.79
Copyright 2009 John Wiley & Sons, Inc.

26. Exponential Smoothing (cont.)
FORECAST, Ft + 1
PERIOD MONTH DEMAND ( = 0.3) ( = 0.5)
1 Jan 37 – –
2 Feb
3 Mar
4 Apr
5 May
6 Jun
7 Jul
8 Aug
9 Sep
10 Oct
11 Nov
12 Dec
13 Jan –
Copyright 2009 John Wiley & Sons, Inc.

27. Exponential Smoothing (cont.)
70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | | | | | | | |
Actual
Orders
Month
 = 0.50
 = 0.30
Copyright 2009 John Wiley & Sons, Inc.

28. Adjusted Exponential Smoothing
AFt +1 = Ft +1 + Tt +1
where
T = an exponentially smoothed trend factor
Tt +1 = (Ft +1 - Ft) + (1 - ) Tt
Tt = the last period trend factor
= a smoothing constant for trend
Copyright 2009 John Wiley & Sons, Inc.

29. Adjusted Exponential Smoothing (β=0.30)
PERIOD MONTH DEMAND
1 Jan 37
2 Feb 40
3 Mar 41
4 Apr 37
5 May 45
6 Jun 50
7 Jul 43
8 Aug 47
9 Sep 56
10 Oct 52
11 Nov 55
12 Dec 54
T3 = (F3 - F2) + (1 - ) T2
= (0.30)( ) + (0.70)(0)
= 0.45
AF3 = F3 + T3 =
= 38.95
T13 = (F13 - F12) + (1 - ) T12
= (0.30)( ) + (0.70)(1.77)
= 1.36
AF13 = F13 + T13 = = 54.97
Copyright 2009 John Wiley & Sons, Inc.

30. Adjusted Exponential Smoothing: Example
FORECAST TREND ADJUSTED
PERIOD MONTH DEMAND Ft +1 Tt +1 FORECAST AFt +1
1 Jan – –
2 Feb
3 Mar
4 Apr
5 May
6 Jun
7 Jul
8 Aug
9 Sep
10 Oct
11 Nov
12 Dec
13 Jan –
Copyright 2009 John Wiley & Sons, Inc.

31. Adjusted Exponential Smoothing Forecasts
70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | | | | | | | |
Actual
Demand
Period
Adjusted forecast ( = 0.30)
Forecast ( = 0.50)
Copyright 2009 John Wiley & Sons, Inc.

32. Linear Trend Line y = a + bx xy - nxy x2 - nx2 b = a = y - b x
where
n = number of periods
x = = mean of the x values
y = = mean of the y values
xy - nxy
x2 - nx2
x n
y
y = a + bx
where
a = intercept
b = slope of the line
x = time period
y = forecast for demand for period x
Copyright 2009 John Wiley & Sons, Inc.

33. Least Squares Example x(PERIOD) y(DEMAND) xy x2 1 73 37 1 2 40 80 4
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34. Least Squares Example (cont.)
y = = 46.42
b = = =1.72
a = y - bx
= (1.72)(6.5) = 35.2
(12)(6.5)(46.42)
(6.5)2
xy - nxy
x2 - nx2 78 12
557
Copyright 2009 John Wiley & Sons, Inc.

35. Linear trend line y = 35.2 + 1.72x Forecast for period 13
= units
70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | | | | | | | |
Actual
Demand
Period
Copyright 2009 John Wiley & Sons, Inc.

36. Seasonal Adjustments Repetitive increase/ decrease in demand
Use seasonal factor to adjust forecast
Seasonal factor = Si = Di D
Copyright 2009 John Wiley & Sons, Inc.

37. Seasonal Adjustment (cont.)
Total
DEMAND (1000’S PER QUARTER)
YEAR Total
S1 = = = 0.28 D1 D
42.0
148.7
S2 = = = 0.20 D2
29.5
S4 = = = 0.37 D4
55.3
S3 = = = 0.15 D3
21.9
Copyright 2009 John Wiley & Sons, Inc.

38. Seasonal Adjustment (cont.)
SF1 = (S1) (F5) = (0.28)(58.17) = 16.28
SF2 = (S2) (F5) = (0.20)(58.17) = 11.63
SF3 = (S3) (F5) = (0.15)(58.17) = 8.73
SF4 = (S4) (F5) = (0.37)(58.17) = 21.53
y = x = (4) = 58.17
For 2005
Copyright 2009 John Wiley & Sons, Inc.

39. Forecast Accuracy Forecast error
difference between forecast and actual demand
MAD
mean absolute deviation
MAPD
mean absolute percent deviation
Cumulative error
Average error or bias
Copyright 2009 John Wiley & Sons, Inc.

40. Mean Absolute Deviation (MAD)
 Dt - Ft  n
MAD =
where
t = period number
Dt = demand in period t
Ft = forecast for period t
n = total number of periods
 = absolute value
Copyright 2009 John Wiley & Sons, Inc.

41. MAD Example  Dt - Ft  n MAD = = 53.39 11 = 4.85
– –
PERIOD DEMAND, Dt Ft ( =0.3) (Dt - Ft) |Dt - Ft|
 Dt - Ft  n
MAD = =
= 4.85
53.39 11
Copyright 2009 John Wiley & Sons, Inc.

42. Other Accuracy Measures
Mean absolute percent deviation (MAPD)
MAPD =
|Dt - Ft|
Dt
Cumulative error
E = et
Average error
E =
et n
Copyright 2009 John Wiley & Sons, Inc.

43. Comparison of Forecasts
FORECAST MAD MAPD E (E)
Exponential smoothing (= 0.30) %
Exponential smoothing (= 0.50) %
Adjusted exponential smoothing %
(= 0.50, = 0.30)
Linear trend line % – –
Copyright 2009 John Wiley & Sons, Inc.

44. Forecast Control Tracking signal
monitors the forecast to see if it is biased high or low
1 MAD ≈ 0.8 б
Control limits of 2 to 5 MADs are used most frequently
Tracking signal = =
(Dt - Ft)
MAD E
Copyright 2009 John Wiley & Sons, Inc.

45. Tracking Signal Values
– – –
DEMAND FORECAST, ERROR E =
PERIOD Dt Ft Dt - Ft (Dt - Ft) MAD –
1.00
2.00
1.62
3.00
4.25
5.01
6.00
7.19
8.18
9.20
10.17
TRACKING
SIGNAL
TS3 = = 2.00
6.10
3.05
Tracking signal for period 3
Copyright 2009 John Wiley & Sons, Inc.

46. Tracking Signal Plot 3 – 2 – 1 – 0 –
Exponential smoothing ( = 0.30)
3 –
2 –
1 –
0 –
-1 –
-2 –
-3 –
Linear trend line
Tracking signal (MAD)
| | | | | | | | | | | | |
Period
Copyright 2009 John Wiley & Sons, Inc.

47. Statistical Control Charts
 =
(Dt - Ft)2
n - 1
Using  we can calculate statistical control limits for the forecast error
Control limits are typically set at  3
Copyright 2009 John Wiley & Sons, Inc.

48. Statistical Control Charts
Errors
18.39 –
12.24 –
6.12 –
0 –
-6.12 – – –
| | | | | | | | | | | | |
Period
UCL = +3
LCL = -3
Copyright 2009 John Wiley & Sons, Inc.

49. Time Series Forecasting using Excel
Excel can be used to develop forecasts:
Moving average
Exponential smoothing
Adjusted exponential smoothing
Linear trend line
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50. Exponentially Smoothed and Adjusted Exponentially Smoothed Forecasts
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51. Demand and exponentially smoothed forecast
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52. Data Analysis option
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53. Computing a Forecast with Seasonal Adjustment
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54. OM Tools
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55. Regression Methods Linear regression Correlation
a mathematical technique that relates a dependent variable to an independent variable in the form of a linear equation
Correlation
a measure of the strength of the relationship between independent and dependent variables
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56. Linear Regression y = a + bx a = y - b x b = xy - nxy x2 - nx2
where
a = intercept
b = slope of the line
x = = mean of the x data
y = = mean of the y data
xy - nxy
x2 - nx2
x n
y
Copyright 2009 John Wiley & Sons, Inc.

57. Linear Regression Example
x y
(WINS) (ATTENDANCE) xy x2
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58. Linear Regression Example (cont.)
y = =
b = =
= 4.06
a = y - bx
= (4.06)(6.125) = 49 8
346.9
xy - nxy2
x2 - nx2
(2,167.7) - (8)(6.125)(43.36)
(311) - (8)(6.125)2
Copyright 2009 John Wiley & Sons, Inc.

59. Linear Regression Example (cont.)
y = x
y = (7)
= 46.88, or 46,880
Regression equation
Attendance forecast for 7 wins
| | | | | | | | | | |
60,000 –
50,000 –
40,000 –
30,000 –
20,000 –
10,000 –
Linear regression line, y = x
Wins, x
Attendance, y
Copyright 2009 John Wiley & Sons, Inc.

60. Correlation and Coefficient of Determination
Correlation, r
Measure of strength of relationship
Varies between and +1.00
Coefficient of determination, r2
Percentage of variation in dependent variable resulting from changes in the independent variable
Copyright 2009 John Wiley & Sons, Inc.

61. Computing Correlation
n xy -  x y
[n x2 - ( x)2] [n y2 - ( y)2]
r =
Coefficient of determination
r2 = (0.947)2 = 0.897
r =
(8)(2,167.7) - (49)(346.9)
[(8)(311) - (49)2] [(8)(15,224.7) - (346.9)2]
r = 0.947
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62. Regression Analysis with Excel
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63. Regression Analysis with Excel (cont.)
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64. Regression Analysis with Excel (cont.)
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65. Multiple Regression
Study the relationship of demand to two or more independent variables
y = 0 + 1x1 + 2x2 … + kxk
where
0 = the intercept
1, … , k = parameters for the independent variables
x1, … , xk = independent variables
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66. Multiple Regression with Excel
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67. Copyright 2009 John Wiley & Sons, Inc. All rights reserved
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