Outline: Forecasting

1
Outline Forecasting

• Introduction
• Types of Forecasts
• Time Series Models
• Causal Models
• Qualitative Models

2
Outline Forecasting (contd.)

• Time Series Forecasting
• Decomposition of a Time Series
• Naive Approach
• Moving Averages
• Exponential Smoothing
• Exponential Smoothing with Trend Adjustment
• Trend Projections
• Seasonal Variations in Data

3
Outline Forecasting (contd.)

• Causal Forecasting Methods
• Using Regression Analysis to Forecast
• Correlation Coefficients for Regression Lines
• Multiple Regression Analysis
• The Computers Role in Forecasting

4
Forecasting Time Horizons

• 1. Short-range forecast Time span of up to one
  year generally less than three months.
• Planning purchasing, job scheduling, work force
  levels, job assignments, and production levels.
• 2. Medium-range forecast Time span generally
  from three months to three years.
• Sales planning, production planning and
  budgeting, cash budgeting, and analyzing various
  operating plans.
• 3. Long-range forecast Time span generally five
  years or more.
• Planning for new products, capital expenditures,
  facility location or expansion, and research and
  development.

5
Eight Steps to Forecasting

• 1. Determine the use of the forecast - what are
  the objectives?
• 2. Select the items to be forecast
• 3. Determine the time horizon of the forecast
• 4. Select the forecasting model(s)
• 5. Gather the data
• 6. Validate the forecasting model
• 7. Make the forecast
• 8. Implement the results

6
Measures of Accuracy and Error

• MAD (Mean Absolute Deviation)
• MSE (Mean Square Error)
• MAPE (Mean Absolute Percent Error)

7
Moving Average
??Demand in previous n periods n
Moving Average
ACTUAL BICYCLE SALES
THREE-WEEK MOVING AVERAGE
WEEK
1 2 3 4 5 6 7
8 10 9 11 10 13 --
( 8 10 9)/3 9 (10 9 11)/3
10 ( 9 11 10)/3 10 (11 10 13)/3 11
1/3
8
Weighted Moving Average
WEIGHTS APPLIED PERIOD
3 2 1 6
Last week Two weeks ago Three weeks ago Sum of
weights
A three-week weighted moving average appears
below.
ACTUAL PIZZA SALES
THREE-WEEK MOVING AVERAGE
WEEK
8 10 9 11 10 13 --
1 2 3 4 5 6 7
(3 x 9) (2 x 10) (1 x 8)/6 9
1/6 (3 x 11) (2 x 9) (1 x 10)/6 10
1/6 (3 x 10) (2 x 11) (1 x 9)/6 10
1/6 (3 x 13) (2 x 10) (1 x 11)/6 11 2/3
9
Exponential Smoothing
Assume ? .1 The forecast for the week of
January 1 was 500 units, whereas actual demand
turned out to be 450 units. The demand
forecasted for the week of January 8 is F t F
t-1 ?(A t-1 - F t-1 ) 500 .1(450 -
500) 495 units
10
Error - MAD
ROUNDED FORECAST WITH ? .8
ABSOLUTE DEVIATION WITH ? .8
ROUNDED FORECAST WITH ? .5
ABSOLUTE DEVIATION WITH ? .5
ACTUAL BATTERY SALES
MONTH
January February March April May June
20 21 15 14 13 16
22 20 21 16 14 13
2 1 6 2 1 3 15
22 21 21 18 16 15
2 0 6 4 3 1 16
Sum of Absolute Deviations
? Deviations n
MAD
11
The Least Squares Method for Finding the Best
Fitting Straight Line
2
Dist


7
2
Dist


5
2

Dist

6
2
Dist


3
Values of Dependent Variable
2

Dist

2
4
Dist


1
2

Dist

2
Time
12
Four Values of the Correlation Coefficient
Y
Y
















X
X
(a) Perfect Positive Correlation r 1
(b) Positive Correlation 0 lt r lt 1
Y
Y


















X
X
(d) Perfect Negative Correlation r -1
(c) No Correlation r 0
13
Linear Regression
YEAR
TIME PERIOD
SALES (UNITS)
x2
xy
1989 1990 1991 1992 1993 1994 1995
1 2 3 4 5 6 7 28
100 110 122 130 139 152 164 917
1 4 9 16 25 36 49 140
110 220 366 520 695 912 1148 3971
?x??
?y??
?x??
?xy??
14
Linear Regression, cont
?x n
28 7
?y n
917 7
x
4
y
131


?xy - nxy ?x2 - nx 2
3971 - (7) (4) (131) 140 - (7)(42)
303 28
b
10.82


a y - bx 131 - 10.82(4) 87.72
Therefore, the least squares trend equation is, y
a bx 87.72 10.82x To project demand in
2005, we denote the year 2005 as x 8 Sales in
2005 87.72 10.82(8) 174.28

15
Linear Regression, alternative
RENUMBERED YEAR (x)
YEAR
CAPACITY (y)
x2
xy
1 2 3 4 5 6
- 2.5 - 1.5 - .5 .5 1.5 2.5
113 120 118 124 123 130
6.25 2.25 .25 .25 2.25 6.25
-287.5 -180 -59 62 184.5 325
?X 0
?X 730
?X2 17.5
?XY 45
Note this alternative way to recode years
simplifies the math since ?X 0.
?xy ?x2
45 17.5
Year 7 121.67 2.57(3.5) 131
b

2.57
?y n
730 6
a

121.67
y 121.67 2.57X
16
CAUSAL VARIABLES

• Independent variables must be known or
  controlled.
• Independent variables must be legitimate causal
  factors.
• Data can be unequally spaced.
• Data can have multiple sets.
• Independent variable can be coded

17
Causal Variables, cont

• Independent variables should be independent of
  each other.

18
Linear Regresion, causal
LEASES, y
AD, x
x2
xy
6 4 16 6 13 9 10 16
15 9 40 20 25 25 15 35
225 81 1600 400 625 625 225 1225
90 36 640 120 325 225 150 560
?y???80
?x???184
?x????5006
?xy???2146
19
Linear Regression, causal, cont
184 8
80 8
x
23
y
10
?xy - nxy ?x2 - nx2
2146 - (8)(23)(10) 5006 - (8)(232)
b

.395
a y - bx 1- - .395(23) .91
The estimates regression equation is

y .91 .395x or Apartments leased .91 .395
Ads placed If the number of ads is 30, we can
estimate the number of apartments rented with the
regression equation .91 .395(30) 12.76 13
apartments
20
Correlation of Ads to Leases
?x???184 ?y???80 ?xy???2146
?x2???5006 ?y2???80 ?xy???2146
Compute the correlation coefficient.
n?XY - ?X?Y
r
n?X2 - (?X)2n?Y2 - (?Y)2?
8(2,146) - (184)(80)

8(5,006) - (184)28(950) - (80)2
2,448

7,430,400
.90
21
Error
FORE- CAST DEMAND
FORE- CAST ERROR
CUMU- LATIVE ERROR
TRACK- ING SIGNAL
ACTUAL DEMAND
YEAR
ERROR
RSFE
MAD
1 2 3 4 5 6
78 75 83 84 88 85
71 80 101 84 60 73
7 5 18 0 28 12
7.0 6.0 10.0 7.5 11.6 11.7
-7 5 18 0 -28 -12
-7 -2 16 16 -12 -24
7 12 30 30 58 70
-1.0 -0.3 1.6 2.1 -1.0 -2.1
? ?Forecast errors n
70 6
MAD
11.7


RSFE MAD
-24 11.7
Tracking Signal

2.1 MADs