MGTS 352 Operations Management
Forecasting Module
Extra Concepts, Techniques, & Practice
Exercises –
Part 1
1
Judgmental Methods
 Executive opinions
 pool opinions of high-level executives
 long term strategic or new product development
Expert opinions
Delphi method: iterative questionnaires
circulated until consensus is reached.
 technological forecasting
2
Judgmental Methods
 Sales force opinions
 based on direct customer contact
Consumer surveys
 questionnaires or focus groups
Historical analogies
 use demand for a similar product
3
What is a Time Series?
Time series:
 a time ordered sequence of observations taken at
regular intervals of time.
4
Six Patterns of Time Series
 Level: (average) horizontal pattern
 Trend: steady upward or downward movement
 Seasonality: regular variations related to time of year or day
 Cycles: wavelike variations lasting more than one year
 Irregular variations: caused by unusual circumstances, not
reflective of typical behaviour
 Random variations: residual variations after all other
behaviours are accounted for (called noise)
5
Patterns of a Time Series
Demand for snowboards
Seasonal peaks (winters)
Trend component
Actual
demand line
Random
variation
Year
1
6
Year
2
Year
3
Year
4
Time series models
 Naive methods
 Averaging methods
 Moving average
 Weighted moving average
 Exponential smoothing
 Trend models
 Linear and non-linear trend
 Trend adjusted exponential smoothing
 Techniques for seasonality
 Techniques for cycles
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Naive Methods




Next period = last period
Simple to use and understand
Very low cost
Low accuracy
Stable time series data : Ft  At 1
Seasonal variation s : Ft  At  n
Data with tren d : Ft  At 1   At 1  At  2 
F = forecast
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A = actual
Naive Method –
Example – stable and without trend
We sold 250 wheels last
week.... Now, next week we should sell....
What is your answer?
Discuss!
9
Naive Method with Trend: Example
2 years ago we sold 50 memberships. Last
year we sold 75 memberships. This year we
expect to sell …
What is your answer?
Discuss!
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Averaging Methods
Demand in previous n periods

:F 
Moving
t
Average
Weighted
Moving Average
n
Weight

:F 
t
Exponentia l
Smoothing
F = forecast
11
period n
 Demand
 Weights
: Ft  Ft 1    At 1  Ft 1 
A = actual
 = smoothing
constant
period n

Moving Average
 average of last few actual data values, updated each
period
 easy to calculate and understand
 smoothes bumps, lags behind changes
 choose number of periods to include
 fewer data points = more sensitive to changes
 more data points = smoother, less responsive
12
Moving Average – Example
 Compute a three-period moving average forecast
for period 6, given the demand below:
Period
1
2
3
4
5
Demand
42
40
43
40
41
13
Moving Average – Example
Solution
 Compute a three-period moving average forecast
for period 6, given the demand below
Period
1
2
3
4
5
Demand 
42 

40 
F3  F4  F5 43  40  41

 41 .33
 F6 
43 
3
3
40 

41 
14
Moving Average Example
Compute 3-period moving average forecast for
periods 4, 5, 6, and 7.
Period
Demand
1
2
3
4
5
6
7
9
12
14
16
19
23
26
15
Moving Average Example
Solution
Period
1
2
3
4
5
6
7
Demand
Forecast
9
12
14
16
19
23
26
(9 + 12 + 14)/3 = 11 2/3
(12 + 14 + 16)/3 = 14
(14 + 16 + 19)/3 = 16 1/3
(16 + 19 + 23)/3 = 19 1/3
16
Weighted Moving Average - Example
 Compute a 4-period weighted moving average forecast for
period 6,
 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.
 Compute and discuss!
 (Answer on next page. But do not check the answer before
you try.)
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Weighted Moving Average – Example
Solution
 Compute a 4-period weighted moving average forecast for
period 6 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.
Period
Demand
1
42
2
40
3
43
4
40
5
41
Weight 


0.1 
0.1  F2  0.2  F3  0.3  F4  0.4  F5
F

 41
 6
0.2 
0 . 1  0 .2  0 . 3  0 .4
0.3 

0.4 
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How do we determine the
weights?
The choice of weights may involve the use of trial and
error to find a suitable weighting scheme.
Weights must add up to 100%.
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Weighted Moving Average Example
Apply weights of .5 for most recent period, then .3, then .2
Period
Demand
9
12
14
16
19
23
26
1
2
3
4
5
6
7
20
Forecast
[(.5 x 14) + (.3 x 12) + (.2 x 9)] = 12.4
[(.5 x 16) + (.3 x 14) + (.2 x 12)] = 14.6
[(.5 x 19) + (.3 x 16) + (.2 x 14)] = 17.1
[(.5 x 23) + (.3 x 19) + (.2 x16)] = 20.4
Exponential Smoothing
 sophisticated weighted moving average
 weights decline exponentially
 most recent data weighted most
 subjectively choose smoothing constant 
  ranges from 0 to 1 (commonly .05 to .5)
 widely used
 easy to use
 easy to alter weighting
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Exponential Smoothing Formula
 Forecast = previous forecast plus a percentage of the
forecast error
 Actual - Forecast is the error term
  is the % feedback
Ft = Ft-1 + (At-1 - Ft-1)
F = forecast
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A = actual
Exponential Smoothing: Example
Forecasted demand = 142 video games
Actual demand = 153
Smoothing constant  = .20
New forecast
= .2 (153) + (1 - .2)(142)
= 30.6 + 113.6
= 144.2 ≈ 144 games
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Exponential Smoothing: Example
 Prepare a forecast using smoothing constant  = 0.40.
 What is the starting point?
 average of several periods of actual data
 subjective estimate (for this example, use 60)
 first actual value (naïve approach)
Period
Actual
Forecast
1
65
60
2
55
F2  F1  0.4A1  F1 
3
58
4
64
F3  F2  0.4A 2  F2 
Calculations
60  0.465 - 60  62
62  0.455 - 62  59.2
F4  F3  0.4A 3  F3  59.2  0.458 - 59.2  58.72
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Exponential Smoothing:
Practice Exercise
 What are the exponential smoothing forecasts for
periods 2-5 using  =0.7?
 Use naïve approach for 1st week
Week
1
2
3
4
Demand
820
775
680
655
25
Exponential Smoothing: Solution
F2=(.7)(820)+(1 - .7)(820) =820
F3=(.7)(775)+(1 - 0.7)(820)=788.5
Week
1
2
3
4
5
Demand
820
775
680
655
26
0.7
820.00
820.00
788.50
712.55
672.27
Trend-Adjusted Exponential Smoothing
 select values (usually through trial and error) for
  = smoothing constant for average
 b = smoothing constant for trend
 estimate starting smoothed average and smoothed
trend
 use most recent data
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Trend-Adjusted Exponential Smoothing
TAFt+1 = St + Tt
St = TAFt +α(At  TAFt)
Tt = Tt-1 + b( St  St-1 Tt-1)
where
St = smoothed average at the end of period t
Tt = smoothed trend at the end of period t
28
Example from Stevenson et al., 5th Canadian Edition
Trend-Adjusted Forecast: Example
29
Trend Adjusted Smoothing Example #1
(Solution on Next Page)
 Refer to data given next page (but do not look at the
answers before you have thought about the problem.) First,
think about how to resolve the problem manually, and
second, try to resolve it using Microsoft Excel
 Requirements:
 A) Develop a linear trend equation for the following data
on demand for white bread loaves at a bakery.
 B) Use trend-adjusted exponential smoothing with alpha =
0.3; and beta = 0.2 to model the bread demand. Use the
first 4 days to estimate the initial smoothed series (use the
average of the first 4 days) and smoothed trend (use the
increase from day 1 to day 4 divided by 3). Start forecasting
day 5. What is the forecast for day 16?
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Techniques for Seasonality –
Example #1
Predict quarterly demand for a certain loveseat
The series has both trend and seasonality.
Quarterly relatives:Q1= 1.20, Q2 = 1.10, Q3 = 0.75, Q4 =0.95.
Trend equation yt=124+7.5t (t = 1 in first quarter of 2012)
Predict demand for quarter 3 of 2015
for quarter 3 of 2015  t  15

y15  124  7.5  15  236 .5
F15  236 .5  0.75  177 .38
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Seasonality Practice Example #2
 Seasonality Example #2
 Given: refer to sales data of ice cream next page
 a) Develop seasonal indices for each month.
 b) Use the formulae Ft = 7,600 + 25t, and seasonal indices
to forecast demand for July and August of Year 4. (Assume
that the company developed the formulae based on past
sales data for forecasting monthly demand of Year 4.)
 First, resolve problem manually.
 Second, if you know how to do it manually, can you
automate it using Excel?
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