IMPROVING FORECAST ACCURACY FOR
CLIENT COURIER – FINAL REPORT
Client: Client Courier Ltd.
Capstone Consulting Group,
Prepared For: Ignacio Castillo
April 15, 2003
Final Report
April 15, 2003
Authors
This report was prepared by:
Adam Crowe
acrowe@ualberta.ca
Andrea Denney
adenney@ualberta.ca
David Fath
dfath@ualberta.ca
Elaine Siu
eysiu@ualberta.ca
Linda Tarshahani
lindat@ualberta.ca
Final Report
April 15, 2003
Table of Contents
Executive Summary ...................................................................................................... 1
Introduction ................................................................................................................... 2
Background ............................................................................................................. 2
Problem Definition ................................................................................................... 2
Objectives................................................................................................................ 3
Scope and Deliverables ........................................................................................... 4
Assumptions ............................................................................................................ 5
Methodology .................................................................................................................. 6
Phase One: Data Analysis ........................................................................................ 6
Current Methodology ............................................................................................... 6
Data Patterns and Trends........................................................................................ 7
Phase Two: Research & Modeling ........................................................................... 8
Research ................................................................................................................. 8
Modeling .................................................................................................................. 8
Our Modifications to the Triple Exponential Smoothing Model ............................... 10
Results .................................................................................................................. 13
Phase Three: Build Forecast Tool .......................................................................... 14
Tool Requirements ................................................................................................ 14
How it works .......................................................................................................... 15
Managerial Discussion ............................................................................................... 17
Cost analysis ........................................................................................................... 17
Forecasting Alternatives ........................................................................................ 17
Future considerations ............................................................................................. 18
Recommendations................................................................................................. 18
Integration with other tools ..................................................................................... 18
Conclusion............................................................................................................. 19
Exhibits ........................................................................................................................ 20
Exhibit 1 – Forecast activity areas ......................................................................... 20
Exhibit 2 – Example Impacts of Current Forecasting Methodology ........................ 20
Exhibit 3 – MAPE comparison for tested models ................................................... 21
Exhibit 4 – TES model in-depth – Initialization ....................................................... 21
Exhibit 5 – TES model in-depth – Learning Phase ................................................. 22
Exhibit 6 – TES model in-depth - Forecasting ........................................................ 23
Exhibit 7 – Solution and Modifications ................................................................... 24
Exhibit 8 – Monthly forecasting errors (1 month out) .............................................. 25
Exhibit 9 – Daily forecasting errors (4 weeks/20 working days out) ........................ 25
Exhibit 10 – Capstone vs. Forecast Pro Error rates ............................................... 26
Exhibit 11 – Tool Screenshot - The Welcome Splash Page ................................... 26
Exhibit 12 – Tool Screenshot - The Forecast Menu ............................................... 27
Exhibit 13 – Tool Screenshot - Reporting Structure ............................................... 28
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Exhibit 14 - Revisiting our Objectives for Client ..................................................... 29
Appendices .................................................................................................................. 30
Appendix 1: Detailed description of tested forecasting models .............................. 30
References ............................................................................................................ 33
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Executive Summary
Client Courier Ltd. has hired Capstone Consulting Group to support its efforts in
improving forecast accuracy and efficiency in its Western Canadian distribution
centres. Many of the Client’s employees have lost confidence in the current
corporate forecasts and are relying on their own personal judgment to make
important decisions. As a result, Client feels that inaccurate forecasts are
contributing to poor decisions on both strategic and tactical levels.
Client makes many forecasts that represent different regions, activities and
employee groups, and makes monthly, weekly, and daily forecasts for each of
them. Capstone has agreed to provide a comprehensive tool that will enable
managers and front-line staff alike to produce forecasts so that they can be easily
used to make important decisions
Capstone considered several new forecasting methods that could increase
forecasting accuracy, including: ARIMA, Time Series Decomposition, the Theta
model, and Triple Exponential Smoothing (TES). It was decided that TES was
the best method to use for Client’s monthly and daily forecasts as it produced the
best forecasts for 2002 when data from this year was held back.
To further improve Client’s forecasts, Capstone has customized the TES model
to incorporate several unique features of the company’s historical data. The
accuracy of this new model brought the average forecasting error down 56%
from Client’s previous forecast error. This difference was measured using mean
absolute percent error, and is an average of all forecasts.
Once a suitable methodology was agreed upon, Capstone began creating a user
friendly VBA tool that could be used across the organization. The tool is capable
of incorporating new data and modifying forecasts to reduce errors. Capstone
feels this tool will be incredibly useful for Client’s Western Canadian region and
hopes that its success will contribute to Client’s competitive advantage in the
courier industry.
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Introduction
Background
Client Courier Ltd. (Client) is Canada’s leader in overnight package delivery, and
is a major provider of integrated distribution solutions in North America. Client is
interested in formalizing and automating the volume forecasting process for its
distribution centers in western Canada. According to the Company, improving
forecast accuracy and efficiency is important because it will allow a more
organized approach to staff scheduling and resource allocation. As a result of
this new approach, Client feels that it can enhance its competitive advantage in
the Canadian courier industry by using their resources more effectively. Client
Courier Ltd. has hired Capstone Consulting Group (Capstone) to analyze its
historical volume, research mathematical methods for forecasting its demand,
and recommend a forecast method that improves forecast accuracy. Capstone
will also build a flexible and dynamic software application that will allow users to
forecast volume demand using a customized forecasting approach.
Problem Definition
The major problem that Client faces is that inaccurate forecasts are leading to
poor strategic and tactical decisions within the company. Front line employees
and regional managers have lost confidence in the corporate forecasts and are
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relying on their own personal judgment to make important decisions. Client
recognizes that more sophisticated forecasts are needed to create buy-in among
its employees and allow them to make informed decisions.
Objectives
Capstone Consulting outlined several objectives that would address Client’s
needs:

Formalize a forecasting method by providing a mathematical basis from which
forecasts can be produced. We planned to exploit the relationships and
patterns that exist in historical data and use them to predict future demand.

Improve forecasting accuracy and efficiency for forecasts relating to all
regional distribution centres, business types and carriers as listed in Exhibit I.

Provide a user interface that will allow a wide variety of people within the
company to access forecast information to make decisions. This would
enable:
1. Senior managers to use long-range forecasts to make strategic
decisions.
2. Operational managers to use month-to-month forecasts
3. Enable tactical decision making based on changes to day-to-day
forecasts
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Scope and Deliverables
Capstone Consulting and Client Courier agreed the scope of this project would
be as follows:

Investigate:
o Underlying patterns and trends in daily, weekly and monthly data
o Forecast methods suitable for Client’s business

Produce daily, weekly and monthly forecasts using the most suitable
method for:
o Seven regions within Western Canada
o Four business activities (Exhibit 1)
o Two types of carriers (Exhibit 1)

Develop:
o A user-friendly, stand-alone forecasting tool
o A descriptive user manual for the tool

Evaluate:
o The performance of the forecasts for all regions, all types
o
The strengths and limitations of the model and tool
Our scope was limited to generating forecasts and did not include:

Integration of the delivered forecasting tool with other decision support
tools
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
Providing recommendations based on our findings about operational
activities, such as staff scheduling

Implementation of our tool into Client’s corporate structure, which includes
training of front-line staff
Assumptions
Capstone Consulting made the following assumptions in developing the forecast
models and tool:

Each business type in each region has its own percentage allocation of
work between PCL and Agents but these percentages remain relatively
stable; therefore, forecasting for total volume and then breaking the
forecast down by carrier type is acceptable.

The model must use historical data to generate forecasts

Forecasts produced by Forecast Pro provide an adequate benchmark by
which forecast results can be compared.

Mean Absolute Percent Error is the most suitable forecast error to
measure since it normalizes the errors across demand volumes of
different sizes and is the measurement currently used by Client.

All the data provided by Client Courier Ltd is accurate, reliable and
complete.
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Methodology
The methodology undertaken by Capstone Consulting can be broken into three
distinct phases. The initial phase was to analyze historical data to find recurring
patterns and trends. The second phase was to research forecast models,
analyze their respective properties and error rates and then build a forecast
model that produced the smallest forecast errors. The third phase was to
develop a forecasting tool based on the forecast model.
Phase One: Data Analysis
Current Methodology
Client is utilizing a last point method of forecasting which is then adjusted based
on managerial judgment.
However, Client has noticed the following symptoms
from using this approach (see Exhibit 2 for visual explanation):

Consistently lower forecasts – Management’s adjustments to the
forecasts are typically conservative

High degree of variation in forecast errors – Forecasts rely on a single
historical data point; therefore, Client is assuming that each data point
will represent future demand

Unreasonable forecasts – Special causes of variation that affected last
year’s demand such as severe snowstorms, terrorist attacks, and other
unpredictable events, are not adjusted for in predicting future demand.
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Data Patterns and Trends
Capstone Consulting utilized forecasting tools, data set graphing, and percent
errors to test characteristics in Client’s historic data. The following patterns were
found:
1. Seasonality - Historical volume demand for Client Courier contained daily,
weekly and monthly seasonality for most regions and activities. Since
many of Client’s clients are retailers, monthly seasonality is closely
related to the annual consumer purchasing cycles that exist within the
industry. Weekly and daily seasonality can be attributed to a variety of
factors that are specific to each region and type of activity.
2. Insignificant trend - Capstone also observed that there has been no
significant increase or decrease in annual demand volume for Client over
the last four years for most regions. However, some regions did exhibit
annual trends, but these fluctuations were small and inconsistent.
3. Weekly groupings – We also discovered that Client would group months
by number of weeks (4 or 5). This meant that the last two days of a
month could be considered part of the first week of the following month.
When compared to the methodology of grouping dates to compile a
month (eg. Feb.1-Feb.28), we found that that Client’s weekly method
produced lower errors and showed a higher seasonality, thus this method
was chosen for future modeling.
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4. Working days in a month – We found that the number of working days in
a particular month had a high correlation to that month’s volume. For
example, if January 2001 had 19 working days and January 2002 had 20,
the monthly volume difference would be expected to differ by one working
day’s volume.
Phase Two: Research & Modeling
Research
Capstone Consulting’s research centered around four forecasting models. Three
of these, ARIMA, Time Series decomposition and Triple Exponential Smoothing
(TES) were chosen due to their proven capabilities and widespread acceptance
as forecasting tools. The fourth, the Theta model, is relatively new and had an
intriguing premise. Detailed descriptions of these four models are listed in
Appendix 1.
Modeling
The modeling component combined a qualitative and quantitative analysis of the
four models chosen to test. The qualitative analysis comprised a suitability test
to the data series provided by Client Courier based on model characteristics.
The quantitative analysis was conducted by holding back a period of 12 months
from our original data set of 4 years. Forecasts were then prepared for those 12
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months based on the remaining 3 years of data. Next, the forecasts were
compared to the actual monthly figures and a Mean Absolute Percent Error
(MAPE) was generated. This performance measure was chosen because the
percentage component of it standardizes errors, which are based on different
sample sizes of n. Since each month had a different demand volume, this
measure was ideal. In addition, Client uses MAPE on a corporate-wide basis for
benchmarking purposes.
Modeling analysis and comparative results
The characteristics of Client’s data were such that most of the forecasting models
tested could be eliminated. Two characteristics in particular eliminated the
practicality of the models:
1. Limited data - Certain regions had very limited amounts of data because
of their recent change to a distribution centre.
2. Outliers - All regions contained outliers, which were explained by weather
problems, loss or gains of clients and other factors that are not accounted
for.
These reasons made the ARIMA Box Jenkins model an obvious choice for
omission. ARIMA does not work well with outliers, as they violate the stationary
assumption. As well, ARIMA requires lengthy time-series data, which was not
available for some regions. The ARIMA model would not be effective without
extensive data cleaning, which would have enlarged the scope of the project
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immensely. Time series decomposition proved to be effective in identifying
components present in the series but was also quite susceptible to outliers and
ultimately did not forecast well. The Theta model produced relatively accurate
results but required another forecasting method to forecast the Theta data series.
This data series exhibited many of the same basic features of the original series,
therefore the ARIMA and decomposition models were not appropriate. This left
the Triple Exponential Smoothing model, which worked quite well to forecast the
Theta data series. Our last test, and model of choice, was the Triple
Exponential Smoothing (TES) model independently. TES does not have the
strict basic assumptions of the ARIMA model and it is not as susceptible to
outliers, therefore large scale data cleaning is not necessary. Comparing the
mean average percent error results from the 4 models validated our choice to
use TES (see Exhibit 3). The basic components (Initialization, Learning and
Forecasting) of the Triple Exponential Smoothing model can be found in Exhibits
4, 5 and 6.
Our Modifications to the Triple Exponential Smoothing Model
Initial trend smoothing parameter
After some initial analysis it was noticed that the initial trend component in the
TES model was not always indicative of future trend and was skewing our
forecast. The initial trend in the basic Triple Exponential Smoothing Model is
calculated by subtracting the first term of the second period from the first term of
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the first period. To make our forecasts more accurate, we multiplied the
calculated trend to a value between zero and one. This trend smoothing
parameter is then calculated using non-linear programming to minimize the fitted
errors of the data series. If a value of zero was computed, it meant that the
calculated trend was highly skewed and would not be value added for future
forecasts. A value of one would indicate that the calculated trend was accurate
in determining future forecasts. We also found that when dealing monthly totals
there was a high correlation between the number of working days in a month
relative to that month’s average number of working days (see Exhibit 7).
Number of working days index
As discussed previously, the number of working days in a particular month
fluctuates slightly from year to year depending on where the weekends fall and
on holidays such as Easter. To take this into account for our forecasts, we
created an index of the number of working days in a particular month divided by
that month’s average number of working days (see Exhibit 7). This index was
multiplied by a smoothing parameter and then by the forecast. This smoothing
parameter was adjusted using non-linear programming as with the other
parameters. These modifications greatly improved our forecast accuracy relative
to the traditional Triple Exponential Smoothing Model.
Holiday Adjustments
Holidays pose a number of problems for our daily forecasts. First, because our
daily forecasts use Triple Exponential Smoothing with five seasons, it is
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impossible for our model to automatically pick up annual holiday patterns.
Second, because the actual demand for holidays is often zero, the seasonality
index for that day of the week will be drastically affected, and can severely
impact the forecasts for subsequent weeks. For example, if the volume on the
first Monday of August (Victoria day) is zero, our model will assign the
subsequent Monday a seasonality index that is very low. However, actual
demand for that Monday will most likely be far higher than such an index would
predict. Our model does not know that the first Monday was a holiday that
represents an irregular demand volume.
To combat these problems, we make two important adjustments: first, we adjust
the series of data that represents historical demand. The volume on holidays is
changed to represent the average volume that would be expected on that day of
the week if a holiday had not taken place. We do this by taking an average of the
same day of the week over the preceding two weeks. This prevents our model
from adjusting the seasonality parameter to account for the irregular demand that
is experienced on holidays. The second adjustment that is made reduces the
forecasted demand that would be expected on a particular day to zero if that day
is a holiday. We do this by attaching a binary variable to each future day in the
forecast, and assigning a value of 0 to days that are holidays. We then multiply
the binary variable to the Triple Exponential Smoothing forecast, which gives us
our final forecast for that day.
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Weekends
Our model does not forecast demand for weekends. This is because the
historical demand volume on weekends is very low and highly sporadic. Client
tries to handle all volume during the regular workweek and its activity during
weekends is often determined by management on a short-term basis. Because
of this, Capstone feels that it is better to leave weekend forecasts to the
discretion of managers than to time series analysis. Client’s management has
supported this approach.
Results
Results for our methodology were measured using the mean absolute percent
error for each forecast, and were averaged across forecasts to obtain summary
metrics for reporting purposes. We compared our forecast errors to those
produced by other forecasts, including those made by Client and those
generated using specialized software.
Client: Compared to Client’s last point method, our forecasts reduce overall
errors by the following amounts:
Monthly – 56% (see Exhibit 8)
Daily -- 2.2% (see Exhibit 9)
* Weekly forecasts errors for Client have not yet been given to Capstone for comparison.
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For a detailed breakdown of Capstone’s forecast errors compared to Client’s
errors, please see Exhibits 8 and 9 (note that these forecast horizons have been
specified by the client as being the most common and widely-used internally).
Forecast Pro: Forecast Pro is a leading forecasting software that is used by
thousands of businesses across the world, and has won several forecasting
awards. Forecast Pro uses several conventional forecasting methods including
ARIMA, Time Series Decomposition and Triple Exponential Smoothing. It fits
each method of forecasting to the historical data, and chooses the forecasting
method that reduces errors the most. Compared to Forecast Pro, our Errors are
as follows:
Monthly – 19 %
Daily --
27 %
For a detailed breakdown of Capstone’s forecast errors compared to Forecast
Pro’s errors, please see Exhibit 10.
Phase Three: Build Forecast Tool
Tool Requirements
1. Based in Microsoft Excel
2. User friendly interface
3. Capability to forecast all regions and all types within a reasonable time
period
4. Clean reporting structure for graphs and tables
5. Option to update data
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6. Easy to install
7. User manual
How it works
The forecasting tool is an Excel file that can easily be transferred and saved on
different computers. Everything that is needed to run the tool is in Microsoft
Excel 1997, 1998, 2000 or XP. Users need to be aware that an Excel Add-in
known as Solver, which comes standard with Microsoft Office, is also needed in
order for the program to work correctly. Therefore if users cannot find Solver
under Tools  Add-Ins in Excel, they will need to find the Microsoft Office
installation CD to add the feature before continuing.
Starting up
Upon running the program a welcome splash page is presented to the user (see
Exhibit 11). From the splash page the user has three options: 1. Update the data
in the tool, 2. Forecast, or 3. End the program.
Updating data
If the user chooses to update the data they must also choose whether it is daily,
weekly or monthly data that they would like to update. Once a choice is made
the user will be brought to a spreadsheet containing the dates, region, business
type and carrier type information. The user can copy and paste the data or
manually enter data into this spreadsheet and the tool will use this information
next time the user chooses to forecast. Once the user is finished entering the
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data the user will select the “Done” button on the spreadsheet to be brought back
to the splash page.
Forecasting
The forecast component of the tool is chosen when the user selects the “Start”
button from the splash page. A user form will appear allowing the user to select
the type of forecast he/she intends to do. This user form contains all the
combinations of forecasts the user can choose from. The user may choose from;
daily, weekly, monthly forecasts, the business types, carrier types, regions, and
the starting and ending dates for the forecast period (see Exhibit 12). Once a
selection has been made the model will use data from the most recent three
years from the starting date of the forecast period. This data is used for the
initializing and learning phases of the TES forecast model. From what the user
has entered the tool will figure out how many combinations of forecasts it needs
to perform and will update the formulas in the TES model as required. It will then
run solver for each combination of forecasts to minimize MAPE from the learning
phase to produce forecasts for the selected periods. Each time solver computes
values for the LS, TS and SS weights, the forecast and data are copied and
pasted onto a separate results sheet.
Viewing results
From the results sheet, graphs and tables are produced and used to initialize
another user form as the reporting output for managerial use (see Exhibit 13).
The user can use a list box on the right hand side of the form to select which
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graph and data he/she would like to view or save to a separate file with the
system date and “Forecast” text as the filename.
When the user is finished forecasting he/she will be brought back to the splash
page where they can select the “End” button to save and exit the program.
Managerial Discussion
Cost analysis
As with any feasible project, there needs to be a benefit to the client. In the case
of this project, the intended benefit was derived from the ability to have more
complex mathematical methods as a foundation for a forecasting model, which in
turn would increase forecasting accuracy and return confidence to the front-line
staff. In developing the forecasting model, it was found that significant
improvements in accuracy resulted. Assuming a $1.00 cost per package over or
under forecasted, Capstone estimates annual cost savings to be approximately
$100,000 for the upcoming year.
Forecasting Alternatives
Other alternatives Client could have considered for this project were two of the
most prominent forecasting tools as listed:
1. Forecast X - $1075 per license
2. Forecast Pro - $1800 per license,
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Based on 9 users (1 senior manager, 1 regional manager, 7 distribution center
managers), Client would save $5675 or $12,200 respectively by using our
proposed tool. As shown in Exhibit 10 our model produced more accurate
results than Forecast Pro.
Future considerations
This model will last as long as the user requires it to. TES will always take into
account all available data and fit the forecasts so that error is minimized. As
changes occur, the TES model will adjust its future data.
Recommendations
Our recommendations for the most effective results are the following:

Update data regularly - Since TES is based on historic data, the more data
the model has to base it’s forecasts on, the more accurately the model will
forecast.

Monitor major external changes - Once a significant impact has been
realized in Client’s demand, such as a key account changes, holidays and
weather disturbances. It will be up to managerial judgment to account for
these changes during the time period immediately after the impact.
Integration with other tools
Currently, our deliverable is a stand-alone tool. After testing its accuracy and
usefulness, one could begin integration with other corporate systems to reduce
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data entry errors and entry time. The tool has simple VBA coding which can be
added to, or changed depending on user preference. The provided user-manual
will assist programmers in understanding the operation of the tool and the
purpose of each command.
Conclusion
Capstone Consulting worked diligently with the client to ensure satisfaction and
deliverables that met the specified requirements. Likewise, Capstone met all of
it’s objectives as demonstrated in Exhibit 14. Capstone feels this project was
incredibly successful, which is reflected in the clients feedback.
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Exhibits
Exhibit 1 – Forecast activity areas
Purolator Courier
PCL
Agent
Pickup
Pieces
Delivery
Stops
Pieces
Pickup
Stops
Pieces
Delivery
Stops
Pieces
Stops
*Note: the above forecast activity exists for each of 7 different regions in Western Canada
Exhibit 2 – Example Impacts of Current Forecasting Methodology
P CL D e live ry S to p s - F o re c as ts vs A c tual, Mo nd ay-F rid ay
Proj.
Ac t.
4,500
4,000
3,500
3,000
Special cause
of
variation
Consistently lower
forecasts
2,500
Day s
20
241
229
217
205
193
181
169
157
145
133
121
109
97
85
73
61
49
37
25
13
2,000
1
N o. of D elivery S tops
5,000
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Exhibit 3 – MAPE comparison for tested models
Method
ARIMA
Decomposition
Theta
TES
% Error
5.3%
6.5%
5.1%
4.4%
Exhibit 4 – TES model in-depth – Initialization
Initialization
1 L
LL   Yi
L i 1
(TL  1  TL )
TL 
L
Yi
Si  , i  1,2,..., L
LL
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Exhibit 5 – TES model in-depth – Learning Phase
Level
Lt = α(Dt / St-p )+(1-α)(Lt-1+Tt-1 )
3000
Lt = Level of the series at time t
Dt = Data at time t
Volume
2500
St-p = Seasonal index at time t-p
P = Number of seasons per cycle
2000
α = Level smoothing parameter
1500
Tt-1 = Trend at time t-1
1000
500
0
1 2 3 4 1 2 3 4 1 2
3 4 1 2 3 4 1 2 3 4
Time Series
Trend
Tt = γ(Lt - Lt-1 )+(1-γ)Tt-1
3000
Tt = Trend of the series at time t
Lt = Level of the series at time t
Volume
2500
Lt-1 = Level of the series at time t-1
γ = Trend smoothing parameter
2000
Tt-1 = Trend at time t-1
1500
1000
500
0
1 2 3
4 1 2 3 4 1 2
3 4 1 2 3 4 1
Time Series
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Seasonality
St = β(Dt / Lt )+(1-β)St-p
St = Seasonal index at time t
3000
Lt = Level of the series at time t
St-p = Seasonal index at time t-p
2500
β = Seasonality smoothing parameter
Volume
2000
Dt = Data at time t
1500
1000
500
0
1 2
3 4 1 2 3
4 1 2 3 4
1 2 3 4 1
2 3 4
1 2 3 4 1
2 3 4
Time Series
Exhibit 6 – TES model in-depth - Forecasting
Ft+k = (Lt +kTt )St+k-p
Ft+k = k-step forecast at time t
3000
Lt = Level of the series at time t
St+k-p = Seasonal index at time t+k-p
2500
K = number of steps to forecast
Volume
2000
Tt = Trend at time t
1500
1000
500
0
1 2
3 4 1 2 3
4 1 2 3 4
Time Series
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Exhibit 7 – Solution and Modifications
Subject To
 , ,  ,  1
Minimizing Fitted Errors
 , ,  ,  0
t
Y
t
Min
 ( Lt  Tt ) St
 L
L
Yt
Initialization
1 L
LL   Yi
L i 1
(TL  1  TL )
TL 
L
Yi
Si  , i  1,2,..., L
LL
Objective Function
t
min  ( Lt  Tt ) St  L * 
L
*
Reduce initial
trend
Adjust totals by
the number of
working days
New Constraints
 ,  1
 ,  0
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Exhibit 8 – Monthly forecasting errors (1 month out)
Forecasting Error (MAPE)
9.0%
8.0%
7.0%
6.0%
5.0%
Client
Purolator
4.0%
Capstone
3.0%
2.0%
1.0%
0.0%
Pick Up
Pieces
Delivery
Pieces
Pick Up
Stops
Delivery
Stops
Exhibit 9 – Daily forecasting errors (4 weeks/20 working days out)
Forecast Error (MAPE)
14.0%
12.0%
10.0%
8.0%
Purolator
Client
6.0%
Capstone
4.0%
2.0%
0.0%
Pick Up
Pieces
Delivery
Pieces
Pick Up
Stops
25
Delivery
Stops
Final Report
April 15, 2003
Exhibit 10 – Capstone vs. Forecast Pro Error rates
12%
10%
8%
6%
4%
2%
0%
Monthly
Daily
Capstone
3%
8%
Forecast Pro
4%
11%
Exhibit 11 – Tool Screenshot - The Welcome Splash Page
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Exhibit 12 – Tool Screenshot - The Forecast Menu
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Exhibit 13 – Tool Screenshot - Reporting Structure
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Exhibit 14 - Revisiting our Objectives for Client
Capstones Objectives
Capstone Deliverables
Benefits to Client
Formalize a forecasting
method by providing a
mathematical basis from
which forecasts can be
produced.
 Developed a
customized triple
exponential
forecasting model
which can forecast
one year in
advance

Provides
consistency in
forecasts

Relieves staff of
dependence on
forecasting
manager
Improve forecasting
accuracy and efficiency
for forecasts relating to all
regional distribution
centres, business types
and carriers.
 Created a dynamic

tool cutting
forecasting
process time down
to 6 minutes(all
288 forecasts)
Decreased
forecasting errors
by 56%

Annual cost
savings of
$100,000
Provide a user interface
that will allow a wide
variety of people within
the company to access
forecast information to
make decisions.


Strategic planning,
long range
forecasts
Operational
planning, month to
month
Developed tool with
user-friendly
interface and
reporting structure


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Tactical
planning, day to
day
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Appendices
Appendix 1: Detailed description of tested forecasting models
ARIMA
The ARIMA Box Jenkins model consists of an AR (Autoregressive) component
and the MA (Moving Average component). The AR component is simply a linear
regression of the current value against one or more prior values, and can be
calculated using linear regression techniques like least squared error. The MA
component however is more complicated as it a linear regression on the white
noise of one or more prior values. This white noise is assumed to come from a
normal distribution and fitting it requires certain non-linear procedures. The
ARIMA model requires that the data series is stationary meaning that the level
and variation are constant; therefore any series with a trend component or
changing variation must be first made stationary before ARIMA can be applied.
This can be accomplished through differencing the series one or more times.
Seasonality can also be included in the data by applying the same ARIMA
components to the seasonal component of the series. It is generally not
recommended that ARIMA be used for data series that are dominated by trend or
seasonality. It is also recommended that ARIMA not be applied to data series
with less then 50 terms although other sources recommend at least 100 terms.
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Time Series Decomposition
Time series decomposition is the process of decomposing a time series
into its component parts. These components include the Seasonality, Trend and
Cycles. The first step is removing the seasonality by using a moving average of
length equal to the amount of seasons. The Centered moving average is then
taken. Seasonal indexes can then be calculated by dividing the actual values by
the de-seasonalized value. The trend is then calculated by fitting a line to the deseasonalized data. The Cycles are defined as wave like movements about the
long-term trend and occur most often in natural phenomenon such as sun spots
however there are virtually no multiple year cycles within Business data. Cycles
within a year are considered seasonality and do exist in business data. These
components are then forecasted separately and then recombined to achieve a
forecast for the original Time Series.
Theta Model
The Theta model consists of modifying the local curvature of the original
time series by the coefficient Theta. A Theta 0 and Theta 2 line are both
calculated. Theta 0 is a straight line moving through the original data and Theta
2 is a more extreme version of the original time series. The two lines are
calculated in such a way that the average of Theta 0 and Theta 2 at every point
is the original time series. Theta 0 and Theta 2 are then forecasted into the
future and then averaged to get a forecast for the original series. The Theta
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model is not actually a forecasting method but rather an adjustment to the series
that then must be forecasted using other methods. The resulting forecast has
proved very effective and even won the M3 forecasting competition in 2000.
Triple Exponential Smoothing
Like decomposition, Triple Exponential Smoothing also separates the
data series into a level, trend and seasonality component. After the initial values
for these components are calculated they are then updated as more data is
added using smoothing parameters. The smoothing parameters take the value
for zero to one and determine how much weight will be placed on the initial
calculations and how much weight on the updated data. The smoothing
parameters are calculated using non-linear programming that minimizes the
errors of the fitted series. This weighting on past and current data makes the
forecast quite robust and not very susceptible to outliers. The final values of
level, trend and seasonality are then used to forecast into the future.
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References
Websites:
Introduction to Time Series Analysis, National institute of standards and technology
http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm
Scientific Resources: Statistics, Econometrics, Forecasting, www.xycoon.com
Texts:
J. Holton Wilson - Barry Keating, (2002 McGraw-Hill Higher Education). Business
Forecasting Fourth Edition, “Time Series Decomposition”, pg 249.
J. Holton Wilson - Barry Keating, (2002 McGraw-Hill Higher Education). Business
Forecasting Fourth Edition, “ARIMA”, pg 287.
J. Holton Wilson - Barry Keating, (2002 McGraw-Hill Higher Education). Business
Forecasting Fourth Edition, “Winter’s”, pg 112.
S.Christian Albright (2001 Wadsworth Group). VBA for Modelers
Course package "Forecasting for Planners and Managers" MGTSC 405
Special Thanks:
Ignacio Castillo, University of Alberta
Susan Budge, University of Alberta
Abdullah Dasci, University of Alberta
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