Operations Management: - Forecasting
Operations Management: - Forecasting
Operations Management: - Forecasting
Management
Chapter 4
Forecasting
Figure 2.5
2008 Prentice Hall, Inc. 4 10
Product Life Cycle
Introduction Growth Maturity Decline
Product design Forecasting Standardization Little product
and critical Less rapid differentiation
development Product and product changes Cost
OM Strategy/Issues
Figure 2.5
2008 Prentice Hall, Inc. 4 11
Types of Forecasts
Economic forecasts
Address business cycle inflation rate,
money supply, housing starts, etc.
Technological forecasts
Predict rate of technological progress
Impacts development of new products
Demand forecasts
Predict sales of existing products and
services
Trend Cyclical
Seasonal Random
Seasonal peaks
Actual
demand
Average
demand over
Random four years
variation
| | | |
1 2 3 4
Year Figure 4.1
2008 Prentice Hall, Inc. 4 25
Trend Component
Persistent, overall upward or
downward pattern
Changes due to population,
technology, age, culture, etc.
Typically several years
duration
0 5 10 15 20
2008 Prentice Hall, Inc. 4 28
Random Component
Erratic, unsystematic, residual
fluctuations
Due to random variation or
unforeseen events
Short duration and
nonrepeating
M T W T F
2008 Prentice Hall, Inc. 4 29
Naive Approach
22
20
18
16
14
12
10
| | | | | | | | | | | |
J F M A M J J A S O N D
20 Actual
sales
15
Moving
10 average
5
| | | | | | | | | | | |
J F M A M J J A S O N D
Figure 4.2
Ft = Ft 1 + (At 1 - Ft 1)
Weight Assigned to
Most 2nd Most 3rd Most 4th Most 5th Most
Recent Recent Recent Recent Recent
Smoothing Period Period Period Period Period
Constant () (1 - ) (1 - ) 2 (1 - ) 3 (1 - )4
Ft = Ft 1 + (At 1 - Ft 1)
= At 1 + (1-) Ft 1
= At 1 + (1-)[ At 2 + (1-)]
2008 Prentice Hall, Inc.
= At 1 + (1-)At 2 + (1-)2 Ft 2 4 43
Impact of Different
225
Actual = .5
200 demand
Demand
175
= .1
150 | | | | | | | | |
1 2 3 4 5 6 7 8 9
Quarter
Actual = .5
Chose
200 high values
demandof
Demand
n
100|Actuali - Forecasti|/Actuali
MAPE = i=1
n
Ft = Ft 1 + (At 1 - Ft 1)+ (1 - ) 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
Table 4.1
2008 Prentice Hall, Inc. 4 56
Exponential Smoothing with
Trend Adjustment Example
Forecast
Actual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.00
2 17
3 20
4 19
5 24 Step 1: Forecast for Month 2
6 21
7 31 F2 = A1 + (1 - )(F1 + T1)
8 28 F2 = (.2)(12) + (1 - .2)(11 + 2)
9 36
10 = 2.4 + 10.4 = 12.8 units
Table 4.1
2008 Prentice Hall, Inc. 4 57
Exponential Smoothing with
Trend Adjustment Example
Forecast
Actual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.00
2 17 12.80
3 20
4 19
5 24 Step 2: Trend for Month 2
6 21
7 31 T2 = b(F2 - F1) + (1 - b)T1
8 28 T2 = (.4)(12.8 - 11) + (1 - .4)(2)
9 36
10 = .72 + 1.2 = 1.92 units
Table 4.1
2008 Prentice Hall, Inc. 4 58
Exponential Smoothing with
Trend Adjustment Example
Forecast
Actual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.00
2 17 12.80 1.92
3 20
4 19
5 24 Step 3: Calculate FIT for Month 2
6 21
7 31 FIT2 = F2 + T1
8 28 FIT2 = 12.8 + 1.92
9 36
10 = 14.72 units
Table 4.1
2008 Prentice Hall, Inc. 4 59
Exponential Smoothing with
Trend Adjustment Example
Forecast
Actual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.00
2 17 12.80 1.92 14.72
3 20 15.18 2.10 17.28
4 19 17.82 2.32 20.14
5 24 19.91 2.23 22.14
6 21 22.51 2.38 24.89
7 31 24.11 2.07 26.18
8 28 27.14 2.45 29.59
9 36 29.28 2.32 31.60
10 32.48 2.68 35.16
Table 4.1
2008 Prentice Hall, Inc. 4 60
Exponential Smoothing with
Trend Adjustment Example
35
25
20
15
0 | | | | | | | | |
1 2 3 4 5 6 7 8 9
Figure 4.3
Time (month)
2008 Prentice Hall, Inc. 4 61
Trend Projections
Fitting a trend line to historical data points
to project into the medium to long-range
Linear trends can be found using the least
squares technique
y^ = a + bx
^ = computed value of the variable to
where y
be predicted (dependent variable)
a = y-axis intercept
b = slope of the regression line
x = the independent variable
2008 Prentice Hall, Inc. 4 62
Values of Dependent Variable
Least Squares Method
Deviation5 Deviation6
Deviation3
Deviation4
Deviation1
(error) Deviation2
Trend line, y^ = a + bx
Deviation5 Deviation6
Deviation1
Deviation2
Trend line, y^ = a + bx
y^ = a + bx
Sxy - nxy
b=
Sx2 - nx2
a = y - bx
130
120
110
100
90
80
70
60
50
| | | | | | | | |
2001 2002 2003 2004 2005 2006 2007 2008 2009
Year
2008 Prentice Hall, Inc. 4 68
Seasonal Variations In Data
The multiplicative
seasonal model
can adjust trend
data for seasonal
variations in
demand
110
100
90
80
70
| | | | | | | | | | | |
J F M A M J J A S O N D
Time
2008 Prentice Hall, Inc. 4 76
San Diego Hospital
Trend Data
10,200
10,000
Inpatient Days
9,800 9745
9659 9702
9573 9616 9766
9,600 9530 9680 9724
9594 9637
9,400 9551
9,200
9,000 | | | | | | | | | | | |
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
67 68 69 70 71 72 73 74 75 76 77 78
Month
Figure 4.6
2008 Prentice Hall, Inc. 4 77
San Diego Hospital
Seasonal Indices
1.06
Index for Inpatient Days
1.04 1.04
1.04 1.03
1.02
1.02 1.01
1.00
1.00 0.99
0.98
0.98 0.99
0.96 0.97 0.97
0.96
0.94
0.92 | | | | | | | | | | | |
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
67 68 69 70 71 72 73 74 75 76 77 78
Month
Figure 4.7
2008 Prentice Hall, Inc. 4 78
San Diego Hospital
Combined Trend and Seasonal Forecast
10,200
10068
10,000 9911 9949
Inpatient Days
9,000 | | | | | | | | | | | |
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
67 68 69 70 71 72 73 74 75 76 77 78
Month
Figure 4.8
2008 Prentice Hall, Inc. 4 79
Associative Forecasting
Used when changes in one or more
independent variables can be used to predict
the changes in the dependent variable
1.0
| | | | | | |
0 1 2 3 4 5 6 7
Area payroll
| | | | | | |
0 1 2 3 4 5 6 7
Area payroll
2008 Prentice Hall, Inc. 4 84
Correlation
How strong is the linear
relationship between the
variables?
Correlation does not necessarily
imply causality!
Coefficient of correlation, r,
measures degree of association
Values range from -1 to +1
nSxy - SxSy
r=
[nSx 2 - (Sx)2][nSy2 - (Sy)2]
(a) Perfect positive x (b) Positive x
correlation: correlation:
r = +1 0<r<1
y y
y^ = a + b1x1 + b2x2
Tracking RSFE
signal =
MAD
(Actual demand in
period i -
Forecast demand
Tracking in period i)
signal = (|Actual - Forecast|/n)
0 MADs Acceptable
range
Lower control limit
Time
1 90-10/10
100= -1 -10 -10 10 10 10.0
2 95
-15/7.5
100= -2 -5 -15 5 15 7.5
3 115 0/10
100
= 0 +15 0 15 30 10.0
4 100-10/10
110= -1 -10 -10 10 40 10.0
5 125
+5/11110
= +0.5+15 +5 15 55 11.0
6 140
+35/14.2
110= +2.5
+30 +35 30 85 14.2