Forecasting chapter Presentation by Jay Heizer.

Forecasting chapter from Operations Management slides by Jay Heizer

1. 1
Forecasting

2. Demand Forecast:
•is an estimate of the expected demand during a specific periodof time.
•Process of predicting a future event
•Underlying basis of all business decisions
Production (sales quantities)
Inventory
Personnel
Facilities
•How big a facility do I need to manufacture a new phone?
•How much money do I need to run operations of my accounting
office?
•How many operators should I schedule next month for my call
centre?
•How much lettuce should I buy for next week in my restaurant?
Forecast Examples

3. Forecasting Approaches
2. Quantitative Methods
•Used when situation is ‘stable’and historical data
exist
•Existing products
•Current technology
•Involves mathematical techniques
1. Qualitative Methods
•Used when situation is vague and little data exist
•Great starting & ending point
•Common uses: New products, New technology

4. Topic Exploration

5. Forecasting Time Horizons
•Short-range forecast
•Up to 1 year, generally less than 3 months
•tend to be more accurate than medium/longer-term forecasts
•Purchasing, job scheduling, workforce levels, job assignments, production
levels
•Medium-range forecast
•3 months to 3 years
•Sales and production planning, budgeting
•Long-range forecast
•3+ years
•New product planning, facility location, research and development

6. Qualitative Approaches
•Jury of executive opinion / Expert Panel
•Delphi method
•Sales force composite insights
•Consumer Market Survey -Ask the customer
Quantitative Approaches
•Time-series models
•Associative model
Trend Patterns
Seasonality Patterns
Cycle Patterns
Random Variations
Linear Regression
Multiple Linear Regression

7. Quantitative Approaches
1. Time-series models
•based on sequence of evenly spaced data points
•models that base predictions on historical patterns of numerical
data.
•Data can be represented via a TREND PATTERN, SEASONALITY
PATTERN, CYCLE PATTERN, or RANDOM VARIATION
?

8. TREND PATTERNS
•Develop an equation that describes the trend
•Look at historical data
•Linear vs Non-Linear Trends
Linear Trend
Non-Linear Trend

9. SEASONALITY PATTERN
•models that base predictions on historical patterns of numerical data but
incorporate amplitudeof seasonal variation
•Last less than one year

10. •models that base predictions on historical patterns of numerical data
•Last more than one year
CYCLE PATTERN

11. •Blips in data caused by chance or unusual situations
RANDOM VARIATIONS

12. •create equations with explanatory variables to predict the future
2. Associative model
LINEAR REGRESSION
MULTIPLE REGRESSION

13. CONCEPT APPLICATION
“Time Series Models”

14. Naive Methods
•Next period = last period
•Simple to use and understand
•Very low cost
•Low accuracy ( )
211
1
:d with trenData
:s variationSeasonal
:data series timeStable
−−−
−
−
−+=
=
=
tttt
ntt
tt
AAAF
AF
AF
F= forecast A= actual
Period of
time since
‘Last Season’
2 periods
ago
1
2
3

15. Stable Time Series
Example
What is the forecast for Period 9?
F9 = A9-8 orF9 = A8or F9 = 10
n A F
1 10
2 10
3 10
4 10
5 10
6 10
7 10
8 10
9

16. Seasonal Variation
Example
What is the forecast for Periods 9, 10, 11, 12 ?
F9 = A9-4 or F9 = A5 or F9 = 10
F10 = A10-4 or F10 = A6or F10 = 28
F11 = A11-4 orF11 = A7 or F11 = 7
F12 = A12-4 orF12 = A8 orF12 = 0
Season n A F
Spring 1 12
Summer 2 25
Fall 3 8
Winter 4 2
Spring 5 10
Summer 6 28
Fall 7 7
Winter 8 0
Spring 9
Summer 10
Fall 11
Winter 12

17. Data with Trend
Example
What is the forecast for Period 17?
F17 = A17-1 + (A17-1 –A17-2)
or
F17 = A16 + (A16 –A15)
or
F17 = 32 + (32-30)
or
F17 = 34
n A F
1 2
2 4
3 6
4 8
5 10
6 12
7 14
8 16
9 18
10 20
11 22
12 24
13 26
14 28
15 30
16 32
17

18. Averaging Methods( )
111
:
Smoothing
lExponentia
−−−
−+=
tttt
FAFF  n
n
F
t

=
periods previousin Demand
:
Average
Moving
F= forecast A= actual = smoothing
1.Moving average
2.Weighted moving average
3.Exponential smoothing
•Smoothing of random variation
•3 techniques:
Relevance %
1
2
3
constant

19. Moving Average
Example 1
What is the 4-Period Moving Average forecast for
Period 17?
F17 = Sum (32+30+28+26) / 4
or
F17 = 29
Example 2
What is the 6-Period Moving Average forecast for
Period 17?
F17 = Sum (32+30+28+26+24+24) / 6
or
F17 = 27
n A F
1 2
2 4
3 6
4 8
5 10
6 12
7 14
8 16
9 18
10 20
11 22
12 24
13 26
14 28
15 30
16 32
17n
n
F
t

=
periods previousin Demand
:
Average
Moving

20. Weighted Moving
Average
Example 1
What is the 4-period weighted moving average
forecast for period 17 using a weight of 0.4 for the
most recent period, 0.3 for the next, 0.2 for the
next, and 0.1 for the next.
F17 = Sum (32x0.4) + (30x0.3) + (28*0.2) + (26*0.1)
Or
F17 = 30
n A Weight % F
1 2 0
2 4 0
3 6 0
4 8 0
5 10 0
6 12 0
7 14 0
8 16 0
9 18 0
10 20 0
11 22 0
12 24 0
13 26 10
14 28 20
15 30 30
16 32 40
17

21. Weighted Moving
Average
Example 1
What is the 4-period weighted moving average
forecast for period 17 using a weight of 0.4 for the
most recent period, 0.3 for the next, 0.2 for the
next, and 0.1 for the next.
F17 = Sum (32x0.4) + (30x0.3) + (28*0.2) + (26*0.1)
Or
F17 = 30
n A Weight % F
1 2 0
2 4 0
3 6 0
4 8 0
5 10 0
6 12 0
7 14 0
8 16 0
9 18 0
10 20 0
11 22 0
12 24 0
13 26 10
14 28 20
15 30 30
16 32 40
17

22. Exponential Smoothing
Example 1
What is the Period 5 forecast using smoothing
constant of 0.40 ?
or
F5 = 60.83
n ActualForecast
1 65 60
2 55
3 58
4 64
5( )
111
:
Smoothing
lExponentia
−−−
−+=
tttt
FAFF 
Period Actual Forecast Calculations
1 65 60
2 55 62 = 60 + 0.4(65-60)
3 58 59.2 = 62 + 0.4(55-62)
4 64 58.72= 59.2 + 0.4(58-59.2)
5 60.83= 58.72 + 0.4(64-58.72)

23. Exponential Smoothing
Example 2
What is the Period 5 forecast using smoothing
constant of 0.40 ?
(**If no forecast is given –start using Naïve Method)
or
F5 = 61.48
n ActualForecast
1 65
2 55
3 58
4 64
5( )
111
:
Smoothing
lExponentia
−−−
−+=
tttt
FAFF 
Period Actual Forecast Calculations
1 65
2 55 65
3 58 61 = 65 + 0.4(55-65)
4 64 59.8 = 61 + 0.4(58-61)
5 61.48=59.8 + 0.4(64-59.8)

24. ( )
n
tby
a
ttn
yttyn
b
btay
t


 
−
=
−
−
=
+=
:intercept-y
:Slope
:Equation
2
2
 What is the linear equation for the following data set?
n t
1 2
2 4
3 6
4 8
5 10
6 12
7 14
8 16
9 18
10 20
11 22
12 24
13 26
14 28
15 30
16 32
17 34
18 36
19 38
20 40
21 42
22 44
23 46
24 48
25 50
26 52
27 54
28 56
29 58
30 60

25. ( )
n
tby
a
ttn
yttyn
b
btay
t


 
−
=
−
−
=
+=
:intercept-y
:Slope
:Equation
2
2
 y = a + bt
b = 30(30938) –930(1045)
30(37820) –(930)(930)
a = 1045-(-0.16207*930)
30
= -0.16207
= 39.875
n t y tyt squared
1 2 40 80 4
2 4 36 144 16
3 6 46 276 36
4 8 32 256 64
5 10 57 570 100
6 12 38 456 144
7 14 34 476 196
8 16 52 832 256
9 18 26 468 324
10 20 34 680 400
11 22 27 594 484
12 24 40 960 576
13 26 32 832 676
14 28 36 1008 784
15 30 37 1110 900
16 32 32 1024 1024
17 34 26 884 1156
18 36 36 1296 1296
19 38 32 1216 1444
20 40 28 1120 1600
21 42 26 1092 1764
22 44 30 1320 1936
23 46 28 1288 2116
24 48 32 1536 2304
25 50 40 2000 2500
26 52 32 1664 2704
27 54 36 1944 2916
28 56 32 1792 3136
29 58 30 1740 3364
30 60 38 2280 3600
SUM 930 1045 3093837820
y =39.875 -0.16207t

26. 0
10
20
30
40
50
60
0 10 20 30 40 50 60 70

27. Accuracy and Control of Forecasts
Four measures of forecasts are used:
•Mean absolute deviation (MAD)
Lower Values indicate Accurate Forecast
•Mean squared error (MSE)
Lower Values indicate Accurate Forecast
•Mean absolute percent error (MAPE)
Lower Values indicate Accurate Forecast
•Control Charts
Are ACTUAL vs FORECAST Errors within acceptable
Control Limits?
N = # of
samples
95% of all errors
should be within
2s
97.7% of all errors
should be within
3s
E = # of
errors
Absolute

28. Mean Absolute Deviation (MAD)
Example
What is the MAD of this forecast?
MAD = 10 / 4 or 2.5

29. Mean Squared Errors (MSE)
Example
What is the MSE of this forecast?
MAD = 30 / 4 or 7.5

30. Mean Absolute Percent Errors (MAPE)
Example
What is the MAPE of this forecast?
MAD = 4.69 / 4or 1.17

31. Control Chart
A F A -F
Month (Sales) (Forecast) Error
1 90 100 -10 100
2 95 100 -5 25
3 115 100 +15 225
4 100 110 -10 100
5 125 110 +15 225
6 140 110 +30 900
1575s= = =
1575
6
2625162. .
Errors should be within ±2(16.2).
Lower limit = -32.4 Upper limit = 32.4
Acceptable Range 2
e
Example
Is this forecast within control limits?