1. Chapter 12
Forecasting

2. Copyright 2011 John Wiley & Sons, Inc.
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
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3. Copyright 2011 John Wiley & Sons, Inc.
Forecasting
Predicting the future
Qualitative forecast methods
subjective
Quantitative forecast methods
based on mathematical formulas
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4. Supply Chain Management
Accurate forecasting determines inventory levels in the supply chain
Continuous replenishment
supplier & 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
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5. The Effect of Inaccurate Forecasting
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6. Copyright 2011 John Wiley & Sons, Inc.
Forecasting
Quality Management
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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7. Types of Forecasting Methods
Depend on
time frame
demand behavior
causes of behavior
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8. Copyright 2011 John Wiley & Sons, Inc.
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
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9. Copyright 2011 John Wiley & Sons, Inc.
Demand Behavior
Trend
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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10. Forms of Forecast Movement
Time
(a) Trend
(d) Trend with seasonal pattern
(c) Seasonal pattern
(b) Cycle
Demand
Random movement
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11. Copyright 2011 John Wiley & Sons, Inc.
Forecasting Methods
Time series
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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12. Copyright 2011 John Wiley & Sons, Inc.
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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13. Forecasting Process No Yes
6. Check forecast accuracy with one or more measures
4. Select a forecast model that seems appropriate for data
5. Develop/compute forecast for period of historical data
8a. Forecast over planning horizon
9. Adjust forecast based on additional qualitative information and insight
10. Monitor results and measure forecast accuracy
8b. Select new forecast model or adjust parameters of existing model 7.
Is accuracy of forecast acceptable?
1. Identify the purpose of forecast
3. Plot data and identify patterns
2. Collect historical data No
Yes
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14. Copyright 2011 John Wiley & Sons, Inc.
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
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15. Copyright 2011 John Wiley & Sons, Inc.
Moving Average
Naive forecast
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
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16. 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
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17. Simple Moving Average  Di MAn = where
n = number of periods in the moving average
Di = demand in period i
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18. 3-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
MA3 = 3
i = 1  Di =
= 110 orders for Nov –
103.3
88.3
95.0
78.3
85.0
105.0
110.0
MOVING
AVERAGE
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19. 5-month Simple Moving Average
ORDERS
MONTH PER MONTH
MOVING
AVERAGE
MA5 = 5
i = 1  Di =
= 91 orders for Nov
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
Nov - –
99.0
85.0
82.0
88.0
95.0
91.0
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20. Copyright 2011 John Wiley & Sons, Inc.
Smoothing Effects
150 –
125 –
100 –
75 –
50 –
25 –
0 –
| | | | | | | | | | |
Jan Feb Mar Apr May June July Aug Sept Oct Nov
Actual
Orders
Month
5-month
3-month
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21. Weighted Moving Average
Adjusts moving average method to more closely reflect data fluctuations
WMAn =
i = 1 
Wi Di
where
Wi = the weight for period i, between 0 and 100 percent
 Wi = 1.00 n
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22. 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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23. Exponential Smoothing
Averaging method
Weights most recent data more strongly
Reacts more to recent changes
Widely used, accurate method
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24. Exponential Smoothing
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
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25. 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
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26. Exponential Smoothing (α=0.30)
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
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
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27. Exponential Smoothing
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 –
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28. Exponential Smoothing
70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | | | | | | | |
Actual
Orders
Month
 = 0.50
 = 0.30
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29. 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
0 ≤  ≤ 1
Copyright 2011 John Wiley & Sons, Inc.

30. 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
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31. Adjusted Exponential Smoothing
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 –
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32. Adjusted Exponential Smoothing Forecasts
70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | | | | | | | |
Actual
Demand
Period
Forecast ( = 0.50)
Adjusted forecast ( = 0.30)
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33. Copyright 2011 John Wiley & Sons, Inc.
Linear Trend Line
y = a + bx
where
a = intercept
b = slope of the line
x = time period
y = forecast for demand for period x
b =
a = y - b x
n = number of periods
x = = mean of the x values
y = = mean of the y values
xy - nxy
x2 - nx2
x n
y
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34. Copyright 2011 John Wiley & Sons, Inc.
Least Squares Example
x(PERIOD) y(DEMAND) xy x2
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35. Copyright 2011 John Wiley & Sons, Inc.
Least Squares Example
x = = 6.5
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
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36. Copyright 2011 John Wiley & Sons, Inc.
Linear trend line
y = x
Forecast for period 13
y = (13) = units
70 –
60 –
50 –
40 –
30 –
20 –
10 –
| | | | | | | | | | | | |
Actual
Demand
Period
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37. Copyright 2011 John Wiley & Sons, Inc.
Seasonal Adjustments
Repetitive increase/ decrease in demand
Use seasonal factor to adjust forecast
Seasonal factor = Si = Di D
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38. Copyright 2011 John Wiley & Sons, Inc.
Seasonal Adjustment
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
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39. Copyright 2011 John Wiley & Sons, Inc.
Seasonal Adjustment
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
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40. Copyright 2011 John Wiley & Sons, Inc.
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
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41. Mean Absolute Deviation (MAD)
where
t = period number
Dt = demand in period t
Ft = forecast for period t
n = total number of periods
 = absolute value
 Dt - Ft  n
MAD =
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42. Copyright 2011 John Wiley & Sons, Inc.
MAD Example
– –
PERIOD DEMAND, Dt Ft ( =0.3) (Dt - Ft) |Dt - Ft|
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43. Copyright 2011 John Wiley & Sons, Inc.
MAD Calculation
 Dt - Ft  n
MAD = =
= 4.85
53.39 11
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44. Other Accuracy Measures
Mean absolute percent deviation (MAPD)
MAPD =
|Dt - Ft|
Dt
Cumulative error
E = et
Average error
E =
et n
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45. 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 % – –
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46. Copyright 2011 John Wiley & Sons, Inc.
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
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47. 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
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48. Copyright 2011 John Wiley & Sons, Inc.
Tracking Signal Plot
3 –
2 –
1 –
0 –
-1 –
-2 –
-3 –
| | | | | | | | | | | | |
Tracking signal (MAD)
Period
Exponential smoothing ( = 0.30)
Linear trend line
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49. 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
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50. Statistical Control Charts
Errors
18.39 –
12.24 –
6.12 –
0 –
-6.12 – – –
| | | | | | | | | | | | |
Period
UCL = +3
LCL = -3
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51. 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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52. Exponentially Smoothed and Adjusted Exponentially Smoothed Forecasts
=B5*(C11-C10)+ (1-B5)*D10
=C10+D10
=ABS(B10-E10)
=SUM(F10:F20)
=G22/11
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53. Demand and Exponentially Smoothed Forecast
Click on “Insert” then “Line”
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54. Copyright 2011 John Wiley & Sons, Inc.
Data Analysis Option
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55. Forecasting With Seasonal Adjustment
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56. Forecasting With OM Tools
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57. Copyright 2011 John Wiley & Sons, Inc.
Regression Methods
Linear regression
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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58. Copyright 2011 John Wiley & Sons, Inc.
Linear Regression
y = a + bx
a = y - b x
b =
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
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59. Linear Regression Example
x y
(WINS) (ATTENDANCE) xy x2
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60. Linear Regression Example
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
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61. Linear Regression Example
60,000 –
50,000 –
40,000 –
30,000 –
20,000 –
10,000 –
Linear regression line, y = x
Attendance, y
Attendance forecast for 7 wins
y = (7)
= 46.88, or 46,880
| | | | | | | | | | |
Wins, x
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62. 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
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63. Computing Correlation
n xy -  x y
[n x2 - ( x)2] [n y2 - ( y)2]
r =
Coefficient of determination
r2 = (0.947)2 = 0.897
(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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64. Regression Analysis With Excel
=INTERCEPT(B5:B12,A5:A12)
=CORREL(B5:B12,A5:A12)
=SUM(B5:B12)
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65. Regression Analysis with Excel
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66. Regression Analysis With Excel
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67. Copyright 2011 John Wiley & Sons, Inc.
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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68. Multiple Regression With Excel
r2, the coefficient of determination
Regression equation coefficients for x1 and x2
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69. Multiple Regression Example
y = 19, x x2
y = 19, (7) (60,000)
= 46,229.35
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70. Copyright 2011 John Wiley & Sons, Inc.
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