EPT 432 Production Management
Laboratory Module
LAB 1
FORECASTING
1.0
OBJECTIVE
1. Describe quantitative and qualitative methods.
2. Describe MA, MWA, Exponential smoothing, MAD, MSE, MAPE and
Exponential smoothing with trend adjustments.
3. How to calculate MA, MWA, MAD, MSE, MAPE, Exponential smoothing and
Exponential smoothing with trend adjustments
4. Using software(ex:Excel) to calculate all the problems given
2.0
INTRODUCTION
Quantitative methods (forecast is made subjectively by the forecaster) are different from
qualitative methods because they are based on mathematical modeling.
In quantitative methods, there are a few type of model to shown this method, as in Table
1:1. Executive Opinion
- Forecasting method in which group of managers collectively develop
2. Market Research
- Approach to forecasting that relies on surveys and interviews to determine
customer preferences
3. Delphi Method
- Approach to forecasting in which a forecast is the product of a consensus among
a group of experts
Table 1: Qualitative Forecasting Models
Type
Executive
Opinion
Market
Research
Delphi Method
Characteristics
A group of managers
meet and come up with
a forecast
Uses surveys and
interviews to identify
customer preferences
Seeks to develop a
consensus among a
group of experts
Strength
Weaknesses
Good for strategic or new
product forecasting
One person’s opinion can
dominate the forecast
Good determinant of
customer preferences
It can be difficult to
develop a good
questionnaire
Time consuming to
develop
Excellent for forecasting
long-term product demand,
technological changes and
scientific advances.
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Quantitative methods can also be divided into two categories (see table 2):1. Time series models
- Based on the assumption that a forecast can be generated from the information
contained in a time series of data. Time series is a series of observation taken over
time
2. Casual models
- based on the assumption that the variable being forecast is related to other
variables in the environment
Table 2: Quantitative Forecasting Models
Type
Description
Strength
Weakness
Time Series Models
Naive
Use last period’s actual
value as a forecast
Simple and easy to use
Simple Mean
Uses an average of past
data as a forecast
Good for level pattern
Simple Moving
Average
A forecasting method
in which only n of the
most recent
observations are
averaged
Only good for level pattern
Important to select the
proper moving average
Weighted Moving A forecasting method
Average
where n of the most
recent observations are
averaged and past
observations may have
different weights
Good for level pattern;
allows placing different
weights on past demands
Selection of weights
requires good judgment
Exponential
Smoothing
A weighted average
procedure with weights
declining exponentially
as data become older
Provides excellent forecast
results for short to medium
length forecast
Choice of alpha is critical
Trend Adjusted
Exponential
Smoothing
An exponential
smoothing model
which separate
equations for
forecasting the level
and trend
Provides good results for
trend data
Should only be used for
data with trend
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Only good if data change
little from period to
period
Requires carrying a lot of
data
EPT 432 Production Management
Laboratory Module
Linear Trend Line Technique uses the
least squares method to
fit a straight line to past
data over time
Easy to use and understand
Data should display a
clear trend over time
Seasonal Indexes
Simple and logical
procedure for computing
seasonality
Make sure seasonality is
actually present
Linear Regression Uses the least squares
method to model a
linear relationship
between two variables
Easy to understand;
provides good forecast
accuracy
Make sure a linear
relationship is present.
Multiple
Regression
A powerful tool in
forecasting when multiple
variables are between
considered
Significantly increases
data and computational
requirements.
Computed the
percentage amount by
which data for each
season are above or
below the mean
Casual ( Associative) Models
Similar to linear
regression, but models
the relationship of
multiple variables with
the variable being
forecast.
In time-series model here, there are four basic patterns, which shown in figure 1:
1. Level or horizontal
- Pattern in which data values fluctuate around a constant mean
2. Trend
-pattern in which data exhibit increasing or decreasing values over time
3. Seasonality
- Any pattern that regularly repeats itself and is constant in length
4. Cycles
- Data patterns created by economic fluctuations
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Figure 1: Types of data patterns
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EPT 432 Production Management
(i)
Laboratory Module
Moving Average (MA)
A forecasting method in which only n of the most recent observations are averaged. It is
very useful if we can assume that market demands will stay fairly steady over time. This
can be expressed as:-
Moving Average = ∑ Demand in previous n periods
n
where n is the number of periods in the moving average
(ii)
Weighted Moving Average
In moving average, each observation is weighted equally. But sometimes the manager
want to use a moving average but gives higher or lower weights to some observations
based on knowledge of the industry. This is called a weighted moving average.
Weighted Moving Average = ∑ (Weight for period n) (Demand in period n)
∑ Weights
(iii)
Exponential Smoothing
A forecasting model that use a sophisticated weighted average procedure to obtain a
forecast. Even though it is sophisticated in the way it works, it is easy to use and
understand. To make a forecast for the next time period you need three pieces of
information:
1. the current period’s forecast
2. the current period’s actual value
3. the value of a smoothing coefficient, α, which varies between 0 and 1
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Laboratory Module
The basic exponential smoothing formula can be shown as:New Forecast = Last period’s forecast + α
where α = Last period’s actual demand – last period’s forecast
Equation shown can also be written mathematically as:
Ft = Ft-1 + α (At-1 – Ft-1)
where Ft = new forecast
Ft-1 = previous period’s forecast
α = smoothing ( or weighting) constant (0 ≤ α ≤ 1 )
At-1 = previous period’s actual demand
Measuring Forecast Error
Forecast error is the different between the forecast and actual value for a given period
Et = At - Ft
where Et = forecast error for period t
At = actual value for period t
Ft = forecast for period t
However error for one time period does not tell us very much. We need to measure
forecast accuracy over time. Three most popular error measures are the MAD, MSE and
MAPE.
(iv)
Mean Absolute Deviation (MAD)
Measure a forecast error that computes error as the average of the sum of the absolute
errors.
MAD = ∑ | Actual – Forecast |
n
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EPT 432 Production Management
(v)
Laboratory Module
Mean Squared Error
Measure a forecast error that computes error as the average of the squared root.
MSE = ∑ | Actual – Forecast | ²
n
(vi)
Mean Absolute Percent Error The average of the absolute differences
between the forecast and actual values, expressed as a percent of actual
values.
ⁿ
MAPE = ∑ 100 | Actual ί – Forecast ί | / Actual ί
ί=1
n
(vii)
Exponential Smoothing With Trend Adjustment
To improve our forecast, it can be done by using more complex exponential smoothing
model, one that adjusts for trend. The idea is to compute an exponentially smoothed
average of the data and then adjust for positive or negative lag in trend. The new formula
is:
Forecast including trend (FITt) = Exponentially smoothed forecast (Ft) +
Exponentially smoothed trend (Tt)
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With trend adjusted exponential smoothing, estimates for both the average and the trend
are smoothed. This procedure requires two smoothing constant: α for the average and β
for the trend. We then compute the average and the trend each period:
Ft = α (Actual demand last period) + (1 – α) (Forecast last period + Trend
estimate last period)
OR
Ft = α (At-1) + (1 – α ) (Ft-1 + Tt-1) --------------------------------------( 1 )
where,
Tt = β (Forecast this period – Forecast last period) + (1-β) (Trend estimate last period)
OR
Tt = β (Ft – Ft-1) + (1-β) Tt-1 --------------------------------------------- ( 2 )
where,
Ft = exponentially smoothed forecast of the data series in period t
Tt = exponentially smoothed trend in period t
At = Actual demand in period t
α = smoothing constant for the average ( 0 ≤ α ≤ 1)
β = smoothing constant for the trend ( 0 ≤ β ≤ 1 )
So the 3 steps to compute a trend adjusted forecast are:Step 1: Compute Ft, the exponentially smoothed forecast for period t, using equation (1)
Step 2: Compute the smoothed trend Tt, using equation (2)
Step 3: Calculate the forecast including trend, FITt, by the formula FITt = Ft + Tt
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EXAMPLE
(i) Moving Range
Sales forecasts for a product are made using a three period moving average. Given the
following sales figures for January, February and March, make a forecast for April.
Month
Actual sales
January
February
March
200
300
200
Solution:
Moving average = January + February + March = 200 + 300 + 200 = 233.3
3
3
If the actual sales for April turn out to be 300, let’s make a forecast for May. Using a
three period MA, we take an average of the latest 3 observations. Since we are now able
to include actual sales for April, we drop the sales for January:
MAMAy = February + March + April = 300 + 200 + 300 = 266.9
3
3
Similarly, if the actual sales for May turn out to be 400, we can make a forecast for June:
MAJune = March + April + May = 200 + 300 + 400 = 300.0
3
3
Then, if the actual sales for June turn out to be 500, the forecast July is computed as;
MAJuly = April + May + June = 300 + 400 + 500 = 400.0
3
3
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The other forecast follow in a similar fashion. If actual sales for July and August turn out
to be 600 and 650 respectively, the respective forecast for August and September are:
MAAugust = May + June + July = 400 + 500 + 600 = 500.0
3
3
MASeptember = June + July + August = 500 + 600 + 650 = 583.3
3
3
Here is the summary of the forecasts we have made and actual sales values:
Month
Actual Sales
Forecast Three Period MA
January
February
March
April
May
June
July
August
September
200
300
200
300
400
500
600
650
-
233.3
266.9
300.0
400.0
500.0
583.3
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MA is good only for a level pattern. The data shown in the example are level in the first
four periods. However, after the fourth period the data begin to show a trend. You can see
that the forecasts made with the MA begin to shown an upward trend. Form here, we can
see that the problem is that the forecast are trailing behind the actual data. We can say
that they are “lagging” the data. This is what happens when you apply a model that is
good only for a level pattern to data that have a trend.
(ii) Weighted Moving Average
A manager at Fit Well department store wants to forecasts sales of swimsuit for August
using a three period WMA. Sales for May, June and July are as below. The manager has
decide to weight May (.25), June (.25) and July (.50).
Month
Actual Sales
May
June
July
400
500
600
Forecast
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Solution:
WMAAugust = ∑(W. 400) + (W.500) + (W.600) = (.25*400) + (.25*500) + (.50*600)
1
1
= 525
(iii) Exponential Smoothing
The Hot Temple Mexican Restaurant uses exponential smoothing to forecast monthly
usage of Tabasco sauce. Its forecast for September was 200 bottles, whereas actual usage
in September was 300 bottles. If the restaurants managers use a α of 0.70, what is their
forecast for October?
Solution:
Ft = 200 + 0.7 (300-200) = 200 + 0.7(100) = 270 bottles
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EPT 432 Production Management
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(iv) Exponential Smoothing with Trend Adjustments
Green Grow is a lawn care company that uses exponential smoothing with trend to
forecast monthly usage of its lawn care products. At the end of July the company wishes
to forecast sales for August. The trend through June has been 15 additional gallons of
product sold per month. Average sales have been 57 gallons per month. The demand for
July was 62 gallons. The company uses α = 0.20 and β = 0.10. Make a forecast including
trend for the month of August.
Solution:
The information we have is

Ft = FJune = 57 gallons / month
Tt = TJune = 15 gallons / month
At = AJuly = 62 gallons
α = 0.20
β = 0.10
Step 1 – Forecast the month
Ft = FAugust = (0.20) (62) + (1 – 0.20) (57 + 15) = (12.4) + (0.80) (72)
= 70
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EPT 432 Production Management

Laboratory Module
Step 2 – Compute the trend
Tt = TAugust = (0.10) (70 – 57) + (1 – 0.10) (15) = (0.10) (13) + (0.90) (15)
= 14.8

Step 3 – Compute the forcast including trend
FIT = 70 + 14.8 = 84.8 gallons
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EPT 432 Production Management
Laboratory Module
(v) Mean Absolute Deviation & Mean Squared Error
Standard Parts Corporation is comparing the accuracy of two methods that it has used to
forecast sales of its popular valve. Forecast using method A and B are shown against the
actual values for January through May. Which methods provided better forecast
accuracy?
Solution:
Month
January
February
March
April
May
Total
Actual
Sales
Method A
Forecast Error Error
30
26
32
29
31
28
25
32
30
30
2
1
0
-1
1
3
2
1
0
1
1
5
Method B
Error²
Forecast
Error
Error
Error²
4
1
0
1
1
7
30
28
36
30
28
0
-2
-4
-1
3
-4
0
2
4
1
3
10
0
4
16
1
9
30
Accuracy for method A:
MAD = ∑ | actual – forecast | = 5 = 1
5
5
MSE = 7 = 1.5
5
Accuracy for method B:
MAD = 10 = 2
5
MSE = 30 = 6
5
One of the two methods, method a produced lower MAD and a lower MSE, which meant
that it provides better forecast accuracy. Note that the magnitude of difference in values
is grater for MSE than for MAD. Recall that MSE magnifies large errors through the
squaring process. For the month of March, method B had a magnitude of errors that was
much larger than for other periods, causing MSE to be high.
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EPT 432 Production Management
Laboratory Module
TUTORIAL
1. The following gives the number of pints of type A blood used at a Woodlawn
Hospitals in the past 6 weeks.
Week Of
Pints Used
August 31
September 7
September 14
September 21
September 28
October 5
360
389
410
381
368
374
(a) Forecast the demand for the week of October 12 using a 3 week moving average.
(b) Use a 3 week weighted moving average, with weights of 0.1, 0.3 and 0.6 and
using 0.6 for the most recent week. Forecast demand for the week of October 12.
(c) Compute the forecast for the week of October 12 using exponential smoothing
with a forecast for August 31 of 360 and α = 0.2
2. The Lucky Star Hospital is considering the purchase of a new ambulance. The decision
will rest partly on the anticipated mileage to be driven next year. The miles driven during
the past 5 years are as follows:
Year
Mileage
1
2
3
4
5
3000
4000
3400
3800
3700
(a) Forecast the mileage for next year using a 2 year moving average.
(b) Find the MAD based on the 2 year moving average forecast in part (a). ( Hint:
you will have only 3 years of matched data)
(c) Use a weighted 2 year moving average with weights of 0.4 and 0.6 to forecast
next year’s mileage. (The weight of 0.6 is for the most recent year. What MAD
results from using this approach to forecasting? (Hint: you will have only 3 years
of matched data)
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3. Daily high temperatures in Singapore for the last week were as follows: 93, 94, 93, 95,
96, 88, and 90 (yesterday).
(a)
(b)
(c)
(d)
(e)
Forecast the high temperature today using a 3 day moving average
Forecast the high temperature today using a 2 day moving average
Calculate the mean absolute deviation based on a 2 day moving average
Compute the mean squared error for the 2 day moving average
Calculate the mean absolute percent error for the 2 day moving average
4. Income at the law firm of Smith and Wesson for the period February to July was as
follows:-
Month
February
March
April
May
June
July
Income (in $
thousand)
70.0
68.5
64.8
71.7
71.3
72.8
Use trend adjusted exponential smoothing to forecast the law firm’s August income.
Assume that the initial forecast for February is $65,000 and the initial trend adjustment is
0. The smoothing constant selected are α = 0.1 and β = 0.2
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EPT 432 Production Management
Laboratory Module
LAB 1
FORECASTING
Lab Result
SCHOOL / PROGRAMME OF
:___________________________
DATE OF LABORATORY
:___________________________
GROUP MEMBERS NAME
:
(Reminder: Do not accept your group member to sign if his/her contribution is not satisfy)
1)_______________________________signature:__________
2)_______________________________signature:___________
3)_______________________________signature:__________
Marks:
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