Transcript PRODUCTIONS/OPERATIONS MANAGEMENT

3-1
Forecasting
Forecasting
3-2
Forecasting
FORECAST:


A statement about the future value of a variable of
interest such as demand.
Forecasts affect decisions and activities throughout
an organization
 Accounting, finance
 Human resources
 Marketing
 MIS
 Operations
 Product / service design
3-3
Forecasting
Uses of Forecasts
Accounting
Cost/profit estimates
Finance
Cash flow and funding
Human Resources
Hiring/recruiting/training
Marketing
Pricing, promotion, strategy
MIS
IT/IS systems, services
Operations
Schedules, MRP, workloads
Product/service design
New products and services
3-4
Forecasting

Assumes causal system
past ==> future

Forecasts rarely perfect because of
randomness

Forecasts more accurate for
groups vs. individuals

Forecast accuracy decreases
as time horizon increases
I see that you will
get an A this semester.
3-5
Forecasting
Elements of a Good Forecast
Timely
Reliable
Accurate
Written
3-6
Forecasting
Steps in the Forecasting Process
“The forecast”
Step 6 Monitor the forecast
Step 5 Prepare the forecast
Step 4 Gather and analyze data
Step 3 Select a forecasting technique
Step 2 Establish a time horizon
Step 1 Determine purpose of forecast
3-7
Forecasting
Types of Forecasts

Judgmental - uses subjective inputs

Time series - uses historical data
assuming the future will be like the past

Associative models - uses explanatory
variables to predict the future
3-8
Forecasting
Judgmental Forecasts

Executive opinions

Sales force opinions

Consumer surveys

Outside opinion
 Delphi
method

Opinions of managers and staff

Achieves a consensus forecast
3-9
Forecasting

Time Series Forecasts
Trend - long-term movement in data
 Seasonality - short-term regular variations in
data
 Cycle – wavelike variations of more than one
year’s duration
 Irregular variations - caused by unusual
circumstances
 Random variations - caused by chance
3-10 Forecasting
Forecast Variations
Figure 3.1
Irregular
variatio
n
Trend
Cycles
90
89
88
Seasonal variations
3-11 Forecasting
Naive Forecasts
Uh, give me a minute....
We sold 250 wheels last
week.... Now, next week
we should sell....
The forecast for any period equals
the previous period’s actual value.
3-12 Forecasting

Naïve Forecasts
Simple to use
 Virtually no cost
 Quick and easy to prepare
 Data analysis is nonexistent
 Easily understandable
 Cannot provide high accuracy
 Can be a standard for accuracy
3-13 Forecasting
Techniques for Averaging

Moving average

Weighted moving average

Exponential smoothing
3-14 Forecasting

Moving Averages
Moving average – A technique that averages a
number of recent actual values, updated as new
values become available.
n
MAn =

Ai

i=1
n
Weighted moving average – More recent values in a
series are given more weight in computing the
forecast.
3-15 Forecasting

Moving Averages
Moving average –
n
MAn =
Period
1
2
3
4
5
6
Ai

i=1
n
Sales Average Forecast for next period
40
41
42
123/3
41
?
?
?
3-16 Forecasting

Moving Averages
Moving average –
n
MAn =
Period
1
2
3
4
5
6
Ai

i=1
n
Sales Average Forecast for next period
40
41
42
123/3
41
42
?
?
Actual
41
42
42
3-17 Forecasting

Moving Averages
Moving average –
n
MAn =
Period
1
2
3
4
5
6
Ai

i=1
n
Sales Average Forecast for next period
40
41
42
123/3
41
42
125/3
41.67
44
?
Actual
41
42
42
44
3-18 Forecasting

Moving Averages
Moving average –
n
MAn =
Period
1
2
3
4
5
6
Ai

i=1
Sales Average Forecast for next period
40
41
42
123/3
41
42
125/3
41.67
44
128/3
42.67
?
n
Actual
41
42
42
44
43
3-19 Forecasting

Moving Averages
Moving average –
n
MAn =
Period
1
2
3
4
5
6
Ai

i=1
n
Sales Average Forecast for next period
40
41
42
123/3
41
42
125/3
41.67
44
128/3
42.67
43
129/3
43
Actual
41
42
42
44
43
43
3-20 Forecasting
Simple Moving Average
Actual
MA5
47
45
43
41
39
37
MA3
35
1
2
3
4
5
6
7
8
n
MAn =
9
Ai

i=1
n
10 11 12
3-21 Forecasting
Weighted Moving Averages

Weighted Moving average –
WMAn=
Period
1
2
3
4
5
6
Sales
40
41
42
?
?
?
Weight
20%
30%
50%
Result
n
A*wi

i=1
Forecast
Actual
3-22 Forecasting
Weighted Moving Averages

Weighted Moving average –
WMAn=
Period
1
2
3
4
5
6
Sales
40
41
42
?
?
?
Weight
20%
30%
50%
n
A*wi

i=1
Result Forecast Actual
8
12.3
21
41.3
42
3-23 Forecasting
Weighted Moving Averages

Weighted Moving average –
n
WMAn=
Period
1
2
3
4
5
6
Sales
40
41
42
42
?
?
Weight
20%
30%
50%
A*wi

i=1
Result Forecast Actual
8.2
12.6
21
41.8
44
3-24 Forecasting
Weighted Moving Averages

Weighted Moving average –
n
WMAn=
Period
1
2
3
4
5
6
Sales
40
41
42
42
44
?
Weight
20%
30%
50%
A*wi

i=1
Result Forecast Actual
8.4
12.6
22
43
43
3-25 Forecasting
Weighted Moving Averages

Weighted Moving average –
n
WMAn=
Period
1
2
3
4
5
6
Sales
40
41
42
42
44
43
Weight
20%
30%
50%
A*wi

i=1
Result Forecast Actual
8.4
13.2
21.5
43.1
43
3-26 Forecasting
Exponential Smoothing
Ft = Ft-1 + (At-1 - Ft-1)
• Premise--The most recent observations might
have the highest predictive value.

Therefore, we should give more weight to the
more recent time periods when forecasting.
3-27 Forecasting
Exponential Smoothing
Ft = Ft-1 + (At-1 - Ft-1)

Weighted averaging method based on previous
forecast plus a percentage of the forecast error
 A-F is the error term,  is the % feedback
3-28 Forecasting
Exponential Smoothing
Ft = Ft-1 + (At-1 - Ft-1)
 Ft
= Next Period
 Ft-1= Previous Period
  = Smoothing Constant
 At-1 = Actual Result
Previous Period
3-29 Forecasting
Exponential Smoothing - Problem
Ft = Ft-1 + (At-1 - Ft-1)
Ft = Result of formula
Ft-1= 42
 = Smoothing = .10
At-1 = 44
3-30 Forecasting
Exponential Smoothing - Problem
Ft = Ft-1 + (At-1 - Ft-1)
Ft = 42 + .10(44-42)
Ft = 42 + .10(2)
Ft = 42 + .20
Ft = 42.20
3-31 Forecasting
Exponential Smoothing - Problem
Ft = Ft-1 + (At-1 - Ft-1)
Ft = 43 + .10(42.20-43)
Ft = 43 + .10(-.80)
Ft = 43 + -.080
Ft = 42.92
3-32 Forecasting
Example 3 - Exponential Smoothing
Period
Actual
1
2
3
4
5
6
7
8
9
10
11
12
Alpha = 0.1 Error
42
40
43
40
41
39
46
44
45
38
40
42
41.8
41.92
41.73
41.66
41.39
41.85
42.07
42.36
41.92
41.73
Alpha = 0.4 Error
-2.00
1.20
-1.92
-0.73
-2.66
4.61
2.15
2.93
-4.36
-1.92
42
41.2
41.92
41.15
41.09
40.25
42.55
43.13
43.88
41.53
40.92
-2
1.8
-1.92
-0.15
-2.09
5.75
1.45
1.87
-5.88
-1.53
3-33 Forecasting
Picking a Smoothing Constant
Actual
Demand
50
 = .4
45
 = .1
40
35
1
2
3
4
5
6
7
Period
8
9 10 11 12
3-34 Forecasting
Common Nonlinear Trends
Figure 3.5
Parabolic
Exponential
Growth
3-35 Forecasting
Linear Trend Equation
Ft
Ft = a + bt




0 1 2
Ft = Forecast for period t
t = Specified number of time periods
a = Value of Ft at t = 0
b = Slope of the line
3 4 5
t
3-36 Forecasting
Calculating a and b
n  (ty) -  t  y
b =
2
2
n t - (  t)
 y - b t
a =
n
3-37 Forecasting
Linear Trend Equation Example
t
Week
1
2
3
4
5
2
t
1
4
9
16
25
 t = 15
 t = 55
2
( t) = 225
2
y
Sales
150
157
162
166
177
ty
150
314
486
664
885
 y = 812  ty = 2499
3-38 Forecasting
b =
Linear Trend Calculation
5 (2499) - 15(812)
5(55) - 225
=
12495-12180
275 -225
812 - 6.3(15)
a =
= 143.5
5
y = 143.5 + 6.3t
= 6.3
3-39 Forecasting
Associative Forecasting

Predictor variables - used to predict values of
variable interest

Regression - technique for fitting a line to a set
of points

Least squares line - minimizes sum of squared
deviations around the line
3-40 Forecasting
Linear Model Seems Reasonable
X
7
2
6
4
14
15
16
12
14
20
15
7
Y
15
10
13
15
25
27
24
20
27
44
34
17
Computed
relationship
50
40
30
20
10
0
0
5
10
15
20
25
A straight line is fitted to a set of sample points.
3-41 Forecasting
Forecast Accuracy

Error - difference between actual value and predicted
value

Mean Absolute Deviation (MAD)


Mean Squared Error (MSE)


Average absolute error
Average of squared error
Mean Absolute Percent Error (MAPE)

Average absolute percent error
3-42 Forecasting
MAD, MSE, and MAPE
MAD
=
 Actual
 forecast
n
MSE
=
 ( Actual
 forecast)
2
n -1
MAPE =
( Actual
 forecas
nt
/ Actual*100)
3-43 Forecasting
Period
1
2
3
4
5
6
7
8
MAD=
MSE=
MAPE=
Example 10
Actual
217
213
216
210
213
219
216
212
2.75
10.86
1.28
Forecast
215
216
215
214
211
214
217
216
(A-F)
2
-3
1
-4
2
5
-1
-4
-2
|A-F|
2
3
1
4
2
5
1
4
22
(A-F)^2
4
9
1
16
4
25
1
16
76
(|A-F|/Actual)*100
0.92
1.41
0.46
1.90
0.94
2.28
0.46
1.89
10.26
3-44 Forecasting

Controlling the Forecast
Control chart

A visual tool for monitoring forecast errors
 Used to detect non-randomness in errors

Forecasting errors are in control if

All errors are within the control limits
 No patterns, such as trends or cycles, are
present
3-45 Forecasting
Sources of Forecast errors

Model may be inadequate
 Irregular variations
 Incorrect use of forecasting technique
3-46 Forecasting
Choosing a Forecasting Technique

No single technique works in every situation
 Two most important factors

Cost
 Accuracy

Other factors include the availability of:

Historical data
 Computers
 Time needed to gather and analyze the data
 Forecast horizon
3-47 Forecasting
Exponential Smoothing
3-48 Forecasting
Linear Trend Equation
3-49 Forecasting
Simple Linear Regression