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 2011 John Wiley & Sons, Inc. 12-2
3. Forecasting
• Predicting the future
• Qualitative forecast methods
• subjective
• Quantitative forecast methods
• based on mathematical formulas
Copyright 2011 John Wiley & Sons, Inc. 12-3
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
Copyright 2011 John Wiley & Sons, Inc. 12-4
5. The Effect of Inaccurate Forecasting
Copyright 2011 John Wiley & Sons, Inc. 12-5
6. 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
Copyright 2011 John Wiley & Sons, Inc. 12-6
7. Types of Forecasting Methods
• Depend on
• time frame
• demand behavior
• causes of behavior
Copyright 2011 John Wiley & Sons, Inc. 12-7
8. 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 2011 John Wiley & Sons, Inc. 12-8
9. 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
Copyright 2011 John Wiley & Sons, Inc. 12-9
10. Forms of Forecast Movement
Copyright 2011 John Wiley & Sons, Inc. 12-10
Time
(a) Trend
Time
(d) Trend with seasonal pattern
Time
(c) Seasonal pattern
Time
(b) Cycle
DemandDemand
DemandDemand
Random
movement
11. 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
Copyright 2011 John Wiley & Sons, Inc. 12-11
12. Qualitative Methods
• Management, marketing, purchasing, and
engineering are sources for internal qualitative
forecasts
• Delphi method
• involves soliciting forecasts about technological
advances from experts
Copyright 2011 John Wiley & Sons, Inc. 12-12
13. Forecasting Process
Copyright 2011 John Wiley & Sons, Inc. 12-13
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
14. 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 2011 John Wiley & Sons, Inc. 12-14
15. 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
Copyright 2011 John Wiley & Sons, Inc. 12-15
16. Moving Average: Naïve Approach
Copyright 2011 John Wiley & Sons, Inc. 12-16
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
75
130
110
90Nov -
FORECAST
17. Simple Moving Average
Copyright 2011 John Wiley & Sons, Inc. 12-17
MAn =
n
i = 1
Di
n
where
n = number of periods in
the moving average
Di = demand in period i
18. 3-month Simple Moving Average
Copyright 2011 John Wiley & Sons, Inc. 12-18
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
3
=
90 + 110 + 130
3
= 110 orders for Nov
–
–
–
103.3
88.3
95.0
78.3
78.3
85.0
105.0
110.0
MOVING
AVERAGE
19. 5-month Simple Moving Average
Copyright 2011 John Wiley & Sons, Inc. 12-19
MA5 =
5
i = 1
Di
5
=
90 + 110 + 130+75+50
5
= 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 -
ORDERS
MONTH PER MONTH
–
–
–
–
–
99.0
85.0
82.0
88.0
95.0
91.0
MOVING
AVERAGE
20. Smoothing Effects
Copyright 2011 John Wiley & Sons, Inc. 12-20
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
21. Weighted Moving Average
Copyright 2011 John Wiley & Sons, Inc. 12-21
• 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
22. Weighted Moving Average Example
Copyright 2011 John Wiley & Sons, Inc. 12-22
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)
= 103.4 orders
November Forecast
23. Exponential Smoothing
Copyright 2011 John Wiley & Sons, Inc. 12-23
• Averaging method
• Weights most recent data more strongly
• Reacts more to recent changes
• Widely used, accurate method
24. Exponential Smoothing
Copyright 2011 John Wiley & Sons, Inc. 12-24
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
25. 0.0 1.0
If = 0.20, then Ft +1 = 0.20 Dt + 0.80 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
Effect of Smoothing Constant
Copyright 2011 John Wiley & Sons, Inc. 12-25
26. Exponential Smoothing (α=0.30)
Copyright 2011 John Wiley & Sons, Inc. 12-26
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
27. Exponential Smoothing
Copyright 2011 John Wiley & Sons, Inc. 12-27
FORECAST, Ft + 1
PERIOD MONTH DEMAND ( = 0.3) ( = 0.5)
1 Jan 37 – –
2 Feb 40 37.00 37.00
3 Mar 41 37.90 38.50
4 Apr 37 38.83 39.75
5 May 45 38.28 38.37
6 Jun 50 40.29 41.68
7 Jul 43 43.20 45.84
8 Aug 47 43.14 44.42
9 Sep 56 44.30 45.71
10 Oct 52 47.81 50.85
11 Nov 55 49.06 51.42
12 Dec 54 50.84 53.21
13 Jan – 51.79 53.61
29. Adjusted Exponential Smoothing
Copyright 2011 John Wiley & Sons, Inc. 12-29
AFt +1 = Ft +1 + Tt +1
where
T = an exponentially smoothed trend factor
Tt +1 = (Ft +1 - Ft) + (1 - ) Tt
where
Tt = the last period trend factor
= a smoothing constant for trend
0 ≤ ≤
30. Adjusted Exponential Smoothing (β=0.30)
Copyright 2011 John Wiley & Sons, Inc. 12-30
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)(38.5 - 37.0) + (0.70)(0)
= 0.45
AF3 = F3 + T3 = 38.5 + 0.45
= 38.95
T13 = (F13 - F12) + (1 - ) T12
= (0.30)(53.61 - 53.21) + (0.70)(1.77)
= 1.36
AF13 = F13 + T13 = 53.61 + 1.36 = 54.97
31. Adjusted Exponential Smoothing
Copyright 2011 John Wiley & Sons, Inc. 12-31
FORECAST TREND ADJUSTED
PERIOD MONTH DEMAND Ft +1 Tt +1 FORECAST AFt +1
1 Jan 37 37.00 – –
2 Feb 40 37.00 0.00 37.00
3 Mar 41 38.50 0.45 38.95
4 Apr 37 39.75 0.69 40.44
5 May 45 38.37 0.07 38.44
6 Jun 50 38.37 0.07 38.44
7 Jul 43 45.84 1.97 47.82
8 Aug 47 44.42 0.95 45.37
9 Sep 56 45.71 1.05 46.76
10 Oct 52 50.85 2.28 58.13
11 Nov 55 51.42 1.76 53.19
12 Dec 54 53.21 1.77 54.98
13 Jan – 53.61 1.36 54.96
33. Linear Trend Line
Copyright 2011 John Wiley & Sons, Inc. 12-33
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
where
n = number of periods
x = = mean of the x values
y = = mean of the y values
xy - nxy
x2 - nx2
x
n
y
n
35. Least Squares Example
Copyright 2011 John Wiley & Sons, Inc. 12-35
x = = 6.5
y = = 46.42
b = = =1.72
a = y - bx
= 46.42 - (1.72)(6.5) = 35.2
3867 - (12)(6.5)(46.42)
650 - 12(6.5)2
xy - nxy
x2 - nx2
78
12
557
12
36. Copyright 2011 John Wiley & Sons, Inc. 12-36
Linear trend line y = 35.2 + 1.72x
Forecast for period 13 y = 35.2 + 1.72(13) = 57.56 units
70 –
60 –
50 –
40 –
30 –
20 –
10 – | | | | | | | | | | | | |
1 2 3 4 5 6 7 8 9 10 11 12 13
Actual
Demand
Period
Linear trend line
37. Seasonal Adjustments
Copyright 2011 John Wiley & Sons, Inc. 12-37
Repetitive increase/ decrease in demand
Use seasonal factor to adjust forecast
Seasonal factor = Si =
Di
D
38. Seasonal Adjustment
Copyright 2011 John Wiley & Sons, Inc. 12-38
2002 12.6 8.6 6.3 17.5 45.0
2003 14.1 10.3 7.5 18.2 50.1
2004 15.3 10.6 8.1 19.6 53.6
Total 42.0 29.5 21.9 55.3 148.7
DEMAND (1000’S PER QUARTER)
YEAR 1 2 3 4 Total
S1 = = = 0.28
D1
D
42.0
148.7
S2 = = = 0.20
D2
D
29.5
148.7
S4 = = = 0.37
D4
D
55.3
148.7
S3 = = = 0.15
D3
D
21.9
148.7
40. 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 2011 John Wiley & Sons, Inc. 12-40
41. Mean Absolute Deviation (MAD)
Copyright 2011 John Wiley & Sons, Inc. 12-41
where
t = period number
Dt = demand in period t
Ft = forecast for period t
n = total number of periods
= absolute value
Dt - Ft
nMAD =
44. Other Accuracy Measures
Copyright 2011 John Wiley & Sons, Inc. 12-44
Mean absolute percent deviation (MAPD)
MAPD =
|Dt - Ft|
Dt
Cumulative error
E = et
Average error
E =
et
n
45. Comparison of Forecasts
Copyright 2011 John Wiley & Sons, Inc. 12-45
FORECAST MAD MAPD E (E)
Exponential smoothing ( = 0.30) 4.85 9.6% 49.31 4.48
Exponential smoothing ( = 0.50) 4.04 8.5% 33.21 3.02
Adjusted exponential smoothing 3.81 7.5% 21.14 1.92
( = 0.50, = 0.30)
Linear trend line 2.29 4.9% – –
46. 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
Copyright 2011 John Wiley & Sons, Inc. 12-46
Tracking signal = =
(Dt - Ft)
MAD
E
MAD
49. Statistical Control Charts
Copyright 2011 John Wiley & Sons, Inc. 12-49
=
(Dt - Ft)2
n - 1
Using we can calculate statistical
control limits for the forecast error
Control limits are typically set at 3
51. Time Series Forecasting Using Excel
• Excel can be used to develop forecasts:
• Moving average
• Exponential smoothing
• Adjusted exponential smoothing
• Linear trend line
Copyright 2011 John Wiley & Sons, Inc. 12-51
52. Exponentially Smoothed and Adjusted
Exponentially Smoothed Forecasts
Copyright 2011 John Wiley & Sons, Inc. 12-52
=B5*(C11-C10)+
(1-B5)*D10
=C10+D10
=ABS(B10-E10)
=SUM(F10:F20)
=G22/11
53. Demand and Exponentially Smoothed
Forecast
Copyright 2011 John Wiley & Sons, Inc. 12-53
Click on “Insert” then “Line”
57. 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
Copyright 2011 John Wiley & Sons, Inc. 12-57
58. Linear Regression
Copyright 2011 John Wiley & Sons, Inc. 12-58
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
n
59. Linear Regression Example
Copyright 2011 John Wiley & Sons, Inc. 12-59
x y
(WINS) (ATTENDANCE) xy x2
4 36.3 145.2 16
6 40.1 240.6 36
6 41.2 247.2 36
8 53.0 424.0 64
6 44.0 264.0 36
7 45.6 319.2 49
5 39.0 195.0 25
7 47.5 332.5 49
49 346.7 2167.7 311
60. Linear Regression Example
Copyright 2011 John Wiley & Sons, Inc. 12-60
x = = 6.125
y = = 43.36
b =
=
= 4.06
a = y - bx
= 43.36 - (4.06)(6.125)
= 18.46
49
8
346.9
8
xy - nxy2
x2 - nx2
(2,167.7) - (8)(6.125)(43.36)
(311) - (8)(6.125)2
61. Linear Regression Example
Copyright 2011 John Wiley & Sons, Inc. 12-61
| | | | | | | | | | |
0 1 2 3 4 5 6 7 8 9 10
60,000 –
50,000 –
40,000 –
30,000 –
20,000 –
10,000 –
Linear regression line, y
= 18.46 + 4.06x
Wins, x
Attendance,y
y = 18.46 + 4.06(7)
= 46.88, or 46,880
Attendance forecast for 7 wins
62. Correlation and Coefficient of
Determination
• Correlation, r
• Measure of strength of relationship
• Varies between -1.00 and +1.00
• Coefficient of determination, r2
• Percentage of variation in dependent variable
resulting from changes in the independent variable
Copyright 2011 John Wiley & Sons, Inc. 12-62
63. 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
Computing Correlation
Copyright 2011 John Wiley & Sons, Inc. 12-63
64. Regression Analysis With Excel
Copyright 2011 John Wiley & Sons, Inc. 12-64
=INTERCEPT(B5:B12,A5:A12)
=CORREL(B5:B12,A5:A12)=SUM(B5:B12)
67. Multiple Regression
Copyright 2011 John Wiley & Sons, Inc. 12-67
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
68. Multiple Regression With Excel
Copyright 2011 John Wiley & Sons, Inc. 12-68
r2, the coefficient
of determination
Regression equation
coefficients for x1 and x2
69. Multiple Regression Example
Copyright 2011 John Wiley & Sons, Inc. 12-69
y = 19,094.42 + 3560.99 x1 + .0368 x2
y = 19,094.42 + 3560.99 (7) + .0368 (60,000)
= 46,229.35
70. Copyright 2011 John Wiley & Sons, Inc. 12-70
Copyright 2011 John Wiley & Sons, Inc.
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