The document provides an overview of time-series forecasting techniques and their application to forecasting call volume for a computer warehouse. It discusses several forecasting methods including last-value, averaging, and moving average. For each method, it shows how to adjust for seasonality, apply the method to historical call volume data, and calculate forecast errors. The best method will be selected based on accuracy in predicting future call volume.
PowerPoint presentation on Agile software development and Scrum. First and foremost it´s not about tools or processes. It´s about the mindset needed to be successful in delivering valuable software to the customer
What is the purpose of Sprint planning meeting in Agile?Mario Lucero
What is the purpose of the Sprint planning meeting?
When you’re working within an agile management framework, you accomplish discrete tasks within the framework of a sprint. On the first day of each sprint the scrum team holds the sprint planning meeting.
CPFR - Model for Supply Chain Co-ordinationCHIN Kok Poh
Collaborative Planning Forecast and Replenishment is a supply chain management practice for multi-tier co-ordination. This slides incoporate CPFR, Unified Communications, RFID, RTLS and Portal Collaboration technologies to execute advanced CPFR.
Stuck with your Forecasting Assignment? Get 24/7 help from tutors with Phd in the subject. Email us at support@helpwithassignment.com
Reach us at http://www.HelpWithAssignment.com
PowerPoint presentation on Agile software development and Scrum. First and foremost it´s not about tools or processes. It´s about the mindset needed to be successful in delivering valuable software to the customer
What is the purpose of Sprint planning meeting in Agile?Mario Lucero
What is the purpose of the Sprint planning meeting?
When you’re working within an agile management framework, you accomplish discrete tasks within the framework of a sprint. On the first day of each sprint the scrum team holds the sprint planning meeting.
CPFR - Model for Supply Chain Co-ordinationCHIN Kok Poh
Collaborative Planning Forecast and Replenishment is a supply chain management practice for multi-tier co-ordination. This slides incoporate CPFR, Unified Communications, RFID, RTLS and Portal Collaboration technologies to execute advanced CPFR.
Stuck with your Forecasting Assignment? Get 24/7 help from tutors with Phd in the subject. Email us at support@helpwithassignment.com
Reach us at http://www.HelpWithAssignment.com
Interventions required to meet business objectives from Forecasting Methods,
Quantitative & Qualitative Methods,
Forecast Accuracy , Error Reduction to
CPFR
Interventions required to meet business objectives - from Forecasting Methods,
Forecast Accuracy / Error Reduction,
Integrate – Sales Forecast / Production to undertaking a CPFR
New Clustering-based Forecasting Method for Disaggregated End-consumer Electr...Peter Laurinec
This paper presents a new method for forecasting the load of individual electricity consumers using smart grid data and clustering. The data from all consumers are used for clustering to create more suitable training sets to forecasting methods. Before clustering, time series are efficiently preprocessed by normalisation and the computation of representations of time series using a multiple linear regression model. Final centroid-based forecasts are scaled by saved normalisation parameters to create forecast for every consumer. Our method is compared with the approach that creates forecasts for every consumer separately. Evaluation and experiments were conducted on two large smart meter datasets from residences of Ireland and factories of Slovakia.
The achieved results proved that our clustering-based method improves forecasting accuracy and decreases high rates of errors (maximum). It is also more scalable since it is not necessary to train the model for every consumer.
Lecture Capture Summary (LCS) #11. Chapter Title Containin.docxjesssueann
Lecture Capture Summary (LCS) #1
1. Chapter Title Containing Video: Overview of Valuation
2. Video Topic: The video explained and showed the certain processes and procedures for evaluating investment decisions. The video pictured the Three-Phase Investment Evaluation Process that consisted of the 8 detailed steps, and he explained that there is much more to making an investment decision than “by estimating a set of cash flows or doing some calculations”. His statement is backed up by the 3 phase 8 step evaluation process that we will be using.
3. Two Finance Concepts/Terms from Video with Definitions:
· Capital Expenditure: Funds used by a company to acquire or upgrade physical assets such as property, industrial buildings or equipment. It is often used to undertake new projects or investments by the firm.
· Net Present Value (NPV): NPV is the difference between the present value of cash inflows and the present value of cash outflows. It is used in capital budgeting to analyze the profitability of a projected investment or project.
4. Video’s Relevance to Corporate Finance Decision-Making: In this video, we briefly go over the steps of investment evaluation process and it is very relevant to corporate finance decision-making. We have gone over terms such as capital expenditure and net present value. When making corporate finance decisions, we have to evaluate whether or not a project or investment will be profitable because the goal is to make money and maximize shareholder return. In order to evaluate a project or investment, we use NPV. In finance, we know that money in the future is not worth as much as money today; by using NPV, we see how much future cash flow is equivalent to today’s cash flow. Capital expenditure is also important because we want to know how much money we have to spend in order to generate profit. Capital expenditure is also used to calculate NPV. In sum, it is very important for us to know how projects are evaluated and how we use these evaluations and results to make decisions.
Professor Dr. TREVOR HALE
MGT 3332
CASE STUDY #1
Highline Financial Service offers three types of service to its client. Freddie Mack (Managing partner) has a data from three categories of services over the past eight quarters. Seem like other company’s factors have not changes “in terms of advertising or promotion, and competition doesn’t change” (Stevenson, William (2011-02-15). This data will be utilized to estimate demand for each service for the subsequent four quarters using Naive Forecast and Moving Average. Naive forecast “uses a single previous value of a time series as the basis of a forecast. But naïve forecast has one weakness of the naive method is that the forecast just traces the actual data, with a lag of one period; it does not smooth at all.” Stevenson, William (2011-02-15). Moving Average forecast “uses a number of the most recent actual data values in generating a forecast” Stevenson, William (2011-02-15).
As we c.
VAT Registration Outlined In UAE: Benefits and Requirementsuae taxgpt
Vat Registration is a legal obligation for businesses meeting the threshold requirement, helping companies avoid fines and ramifications. Contact now!
https://viralsocialtrends.com/vat-registration-outlined-in-uae/
Interventions required to meet business objectives from Forecasting Methods,
Quantitative & Qualitative Methods,
Forecast Accuracy , Error Reduction to
CPFR
Interventions required to meet business objectives - from Forecasting Methods,
Forecast Accuracy / Error Reduction,
Integrate – Sales Forecast / Production to undertaking a CPFR
New Clustering-based Forecasting Method for Disaggregated End-consumer Electr...Peter Laurinec
This paper presents a new method for forecasting the load of individual electricity consumers using smart grid data and clustering. The data from all consumers are used for clustering to create more suitable training sets to forecasting methods. Before clustering, time series are efficiently preprocessed by normalisation and the computation of representations of time series using a multiple linear regression model. Final centroid-based forecasts are scaled by saved normalisation parameters to create forecast for every consumer. Our method is compared with the approach that creates forecasts for every consumer separately. Evaluation and experiments were conducted on two large smart meter datasets from residences of Ireland and factories of Slovakia.
The achieved results proved that our clustering-based method improves forecasting accuracy and decreases high rates of errors (maximum). It is also more scalable since it is not necessary to train the model for every consumer.
Lecture Capture Summary (LCS) #11. Chapter Title Containin.docxjesssueann
Lecture Capture Summary (LCS) #1
1. Chapter Title Containing Video: Overview of Valuation
2. Video Topic: The video explained and showed the certain processes and procedures for evaluating investment decisions. The video pictured the Three-Phase Investment Evaluation Process that consisted of the 8 detailed steps, and he explained that there is much more to making an investment decision than “by estimating a set of cash flows or doing some calculations”. His statement is backed up by the 3 phase 8 step evaluation process that we will be using.
3. Two Finance Concepts/Terms from Video with Definitions:
· Capital Expenditure: Funds used by a company to acquire or upgrade physical assets such as property, industrial buildings or equipment. It is often used to undertake new projects or investments by the firm.
· Net Present Value (NPV): NPV is the difference between the present value of cash inflows and the present value of cash outflows. It is used in capital budgeting to analyze the profitability of a projected investment or project.
4. Video’s Relevance to Corporate Finance Decision-Making: In this video, we briefly go over the steps of investment evaluation process and it is very relevant to corporate finance decision-making. We have gone over terms such as capital expenditure and net present value. When making corporate finance decisions, we have to evaluate whether or not a project or investment will be profitable because the goal is to make money and maximize shareholder return. In order to evaluate a project or investment, we use NPV. In finance, we know that money in the future is not worth as much as money today; by using NPV, we see how much future cash flow is equivalent to today’s cash flow. Capital expenditure is also important because we want to know how much money we have to spend in order to generate profit. Capital expenditure is also used to calculate NPV. In sum, it is very important for us to know how projects are evaluated and how we use these evaluations and results to make decisions.
Professor Dr. TREVOR HALE
MGT 3332
CASE STUDY #1
Highline Financial Service offers three types of service to its client. Freddie Mack (Managing partner) has a data from three categories of services over the past eight quarters. Seem like other company’s factors have not changes “in terms of advertising or promotion, and competition doesn’t change” (Stevenson, William (2011-02-15). This data will be utilized to estimate demand for each service for the subsequent four quarters using Naive Forecast and Moving Average. Naive forecast “uses a single previous value of a time series as the basis of a forecast. But naïve forecast has one weakness of the naive method is that the forecast just traces the actual data, with a lag of one period; it does not smooth at all.” Stevenson, William (2011-02-15). Moving Average forecast “uses a number of the most recent actual data values in generating a forecast” Stevenson, William (2011-02-15).
As we c.
VAT Registration Outlined In UAE: Benefits and Requirementsuae taxgpt
Vat Registration is a legal obligation for businesses meeting the threshold requirement, helping companies avoid fines and ramifications. Contact now!
https://viralsocialtrends.com/vat-registration-outlined-in-uae/
Tata Group Dials Taiwan for Its Chipmaking Ambition in Gujarat’s DholeraAvirahi City Dholera
The Tata Group, a titan of Indian industry, is making waves with its advanced talks with Taiwanese chipmakers Powerchip Semiconductor Manufacturing Corporation (PSMC) and UMC Group. The goal? Establishing a cutting-edge semiconductor fabrication unit (fab) in Dholera, Gujarat. This isn’t just any project; it’s a potential game changer for India’s chipmaking aspirations and a boon for investors seeking promising residential projects in dholera sir.
Visit : https://www.avirahi.com/blog/tata-group-dials-taiwan-for-its-chipmaking-ambition-in-gujarats-dholera/
Personal Brand Statement:
As an Army veteran dedicated to lifelong learning, I bring a disciplined, strategic mindset to my pursuits. I am constantly expanding my knowledge to innovate and lead effectively. My journey is driven by a commitment to excellence, and to make a meaningful impact in the world.
Attending a job Interview for B1 and B2 Englsih learnersErika906060
It is a sample of an interview for a business english class for pre-intermediate and intermediate english students with emphasis on the speking ability.
3.0 Project 2_ Developing My Brand Identity Kit.pptxtanyjahb
A personal brand exploration presentation summarizes an individual's unique qualities and goals, covering strengths, values, passions, and target audience. It helps individuals understand what makes them stand out, their desired image, and how they aim to achieve it.
Digital Transformation and IT Strategy Toolkit and TemplatesAurelien Domont, MBA
This Digital Transformation and IT Strategy Toolkit was created by ex-McKinsey, Deloitte and BCG Management Consultants, after more than 5,000 hours of work. It is considered the world's best & most comprehensive Digital Transformation and IT Strategy Toolkit. It includes all the Frameworks, Best Practices & Templates required to successfully undertake the Digital Transformation of your organization and define a robust IT Strategy.
Editable Toolkit to help you reuse our content: 700 Powerpoint slides | 35 Excel sheets | 84 minutes of Video training
This PowerPoint presentation is only a small preview of our Toolkits. For more details, visit www.domontconsulting.com
Memorandum Of Association Constitution of Company.pptseri bangash
www.seribangash.com
A Memorandum of Association (MOA) is a legal document that outlines the fundamental principles and objectives upon which a company operates. It serves as the company's charter or constitution and defines the scope of its activities. Here's a detailed note on the MOA:
Contents of Memorandum of Association:
Name Clause: This clause states the name of the company, which should end with words like "Limited" or "Ltd." for a public limited company and "Private Limited" or "Pvt. Ltd." for a private limited company.
https://seribangash.com/article-of-association-is-legal-doc-of-company/
Registered Office Clause: It specifies the location where the company's registered office is situated. This office is where all official communications and notices are sent.
Objective Clause: This clause delineates the main objectives for which the company is formed. It's important to define these objectives clearly, as the company cannot undertake activities beyond those mentioned in this clause.
www.seribangash.com
Liability Clause: It outlines the extent of liability of the company's members. In the case of companies limited by shares, the liability of members is limited to the amount unpaid on their shares. For companies limited by guarantee, members' liability is limited to the amount they undertake to contribute if the company is wound up.
https://seribangash.com/promotors-is-person-conceived-formation-company/
Capital Clause: This clause specifies the authorized capital of the company, i.e., the maximum amount of share capital the company is authorized to issue. It also mentions the division of this capital into shares and their respective nominal value.
Association Clause: It simply states that the subscribers wish to form a company and agree to become members of it, in accordance with the terms of the MOA.
Importance of Memorandum of Association:
Legal Requirement: The MOA is a legal requirement for the formation of a company. It must be filed with the Registrar of Companies during the incorporation process.
Constitutional Document: It serves as the company's constitutional document, defining its scope, powers, and limitations.
Protection of Members: It protects the interests of the company's members by clearly defining the objectives and limiting their liability.
External Communication: It provides clarity to external parties, such as investors, creditors, and regulatory authorities, regarding the company's objectives and powers.
https://seribangash.com/difference-public-and-private-company-law/
Binding Authority: The company and its members are bound by the provisions of the MOA. Any action taken beyond its scope may be considered ultra vires (beyond the powers) of the company and therefore void.
Amendment of MOA:
While the MOA lays down the company's fundamental principles, it is not entirely immutable. It can be amended, but only under specific circumstances and in compliance with legal procedures. Amendments typically require shareholder
RMD24 | Retail media: hoe zet je dit in als je geen AH of Unilever bent? Heid...BBPMedia1
Grote partijen zijn al een tijdje onderweg met retail media. Ondertussen worden in dit domein ook de kansen zichtbaar voor andere spelers in de markt. Maar met die kansen ontstaan ook vragen: Zelf retail media worden of erop adverteren? In welke fase van de funnel past het en hoe integreer je het in een mediaplan? Wat is nu precies het verschil met marketplaces en Programmatic ads? In dit half uur beslechten we de dilemma's en krijg je antwoorden op wanneer het voor jou tijd is om de volgende stap te zetten.
Kseniya Leshchenko: Shared development support service model as the way to ma...Lviv Startup Club
Kseniya Leshchenko: Shared development support service model as the way to make small projects with small budgets profitable for the company (UA)
Kyiv PMDay 2024 Summer
Website – www.pmday.org
Youtube – https://www.youtube.com/startuplviv
FB – https://www.facebook.com/pmdayconference
Premium MEAN Stack Development Solutions for Modern BusinessesSynapseIndia
Stay ahead of the curve with our premium MEAN Stack Development Solutions. Our expert developers utilize MongoDB, Express.js, AngularJS, and Node.js to create modern and responsive web applications. Trust us for cutting-edge solutions that drive your business growth and success.
Know more: https://www.synapseindia.com/technology/mean-stack-development-company.html
Improving profitability for small businessBen Wann
In this comprehensive presentation, we will explore strategies and practical tips for enhancing profitability in small businesses. Tailored to meet the unique challenges faced by small enterprises, this session covers various aspects that directly impact the bottom line. Attendees will learn how to optimize operational efficiency, manage expenses, and increase revenue through innovative marketing and customer engagement techniques.
[Note: This is a partial preview. To download this presentation, visit:
https://www.oeconsulting.com.sg/training-presentations]
Sustainability has become an increasingly critical topic as the world recognizes the need to protect our planet and its resources for future generations. Sustainability means meeting our current needs without compromising the ability of future generations to meet theirs. It involves long-term planning and consideration of the consequences of our actions. The goal is to create strategies that ensure the long-term viability of People, Planet, and Profit.
Leading companies such as Nike, Toyota, and Siemens are prioritizing sustainable innovation in their business models, setting an example for others to follow. In this Sustainability training presentation, you will learn key concepts, principles, and practices of sustainability applicable across industries. This training aims to create awareness and educate employees, senior executives, consultants, and other key stakeholders, including investors, policymakers, and supply chain partners, on the importance and implementation of sustainability.
LEARNING OBJECTIVES
1. Develop a comprehensive understanding of the fundamental principles and concepts that form the foundation of sustainability within corporate environments.
2. Explore the sustainability implementation model, focusing on effective measures and reporting strategies to track and communicate sustainability efforts.
3. Identify and define best practices and critical success factors essential for achieving sustainability goals within organizations.
CONTENTS
1. Introduction and Key Concepts of Sustainability
2. Principles and Practices of Sustainability
3. Measures and Reporting in Sustainability
4. Sustainability Implementation & Best Practices
To download the complete presentation, visit: https://www.oeconsulting.com.sg/training-presentations
What are the main advantages of using HR recruiter services.pdfHumanResourceDimensi1
HR recruiter services offer top talents to companies according to their specific needs. They handle all recruitment tasks from job posting to onboarding and help companies concentrate on their business growth. With their expertise and years of experience, they streamline the hiring process and save time and resources for the company.
2. Forecasting at Fastchips
• Fastchips is a leading producer of microprocessors.
• Six months ago, it launched the sales of its latest microprocessor.
• Month-by-month sales (in thousands) over the initial six months have been
17 25 24 26 30 28
Question: What is the forecast for next month’s sales?
10-2
3. The Last-Value Forecasting Method
The last-value forecasting method ignores all data points in a time series except
the last one.
Forecast = Last value
Fastchips: Month-by-month sales (in thousands) over the initial six months:
17 25 24 26 30 28
Forecast = 28
10-3
4. The Averaging Forecasting Method
The averaging forecasting method uses all the data points in the time series and
simply averages these points.
Forecast = Average of all data to date
Fastchips: Month-by-month sales (in thousands) over the initial six months:
17 25 24 26 30 28
Forecast = (17+25+24+26+30+28) / 6 = 25
10-4
5. The Moving-Average Forecasting Method
The moving-average forecasting method averages the data for only the most
recent time periods.
n = Number of recent periods to consider as relevant for forecasting
Forecast = Average of last n values
Fastchips: Month-by-month sales (in thousands) over the initial six months:
17 25 24 26 30 28
Forecast (n=3) = (26+30+28) / 3 = 28
10-5
6. The Exponential Smoothing Forecasting Method
• The exponential smoothing forecasting method provides a more
sophisticated version of the moving-average method.
• It gives the greatest weight to the last month and then progressively smaller
weights to the older months.
• Exponential smoothing with trend adjusts exponential smoothing by also
directly considering any current upward or downward trend in sales.
10-6
7. Linear Regression
• Linear regression uses a two-dimensional graph with sales measured along
the vertical axis and time measured along the horizontal axis.
• After plotting the sales data, this method finds a line passing through the midst
of the data as closely as possible.
• The extension of the line into future months provides the forecast of sales in
these future months.
10-7
8. Measuring the Forecast Error
• The mean absolute deviation (called MAD) measures the average forecasting
error.
MAD = (Sum of forecasting errors) / (Number of forecasts)
• The mean square error (often abbreviated MSE) measures the average of the
square of the forecasting error.
MSE = (Sum of square of forecasting errors) / (Number of forecasts).
• The MSE increases the weight of large errors relative to the weight of small
errors.
10-8
9. The Computer Club Warehouse (CCW)
• The Computer Club Warehouse (CCW) sells computer products at bargain
prices by taking telephone orders (as well as website and fax orders) directly
from customers.
• Products include computers, peripherals, supplies, software, and computer
furniture.
• The CCW call center is never closed. It is staffed by dozens of agents to take
and process customer orders.
• A large number of telephone trunks are provided for incoming calls. If an
agent is not free when a call arrives, it is placed on hold. If all the trunks are in
use (called saturation), the call receives a busy signal.
• An accurate forecast of the demand for agents is needed.
Question: How should the demand for agents be forecasted?
10-9
10. 25 Percent Rule (Current Forecasting Method)
Since sales are relatively stable through the year except for a substantial increase
during the Christmas season, assume that each quarter’s call volume will be the
same as the preceding quarter, except for adding 25 percent for Quarter 4.
Forecast for Quarter 2 = Call volume for Quarter 1
Forecast for Quarter 3 = Call volume for Quarter 2
Forecast for Quarter 4 = 1.25(Call volume for Quarter 3)
Forecast for next Quarter 1 = (Call volume for Quarter 4) / 1.25
10-10
11. Average Daily Call Volume (3 Years of Data)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
A B C D E
CCW's Average Daily Call Volume
Year Quarter Call Volume
1 1 6,809
1 2 6,465
1 3 6,569
1 4 8,266
2 1 7,257
2 2 7,064
2 3 7,784
2 4 8,724
3 1 6,992
3 2 6,822
3 3 7,949
3 4 9,650
10-11
12. Applying the 25-Percent Rule
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
A B C D E F G H I
Current Forecasting Method for CCW's Average Daily Call Volume
Forecasting
Year Quarter Data Forecast Error Mean Absolute Deviation
1 1 6,809 MAD = 424
1 2 6,465 6,809 344
1 3 6,569 6,465 104 Mean Square Error
1 4 8,266 8,211 55 MSE = 317,815
2 1 7,257 6,613 644
2 2 7,064 7,257 193
2 3 7,784 7,064 720
2 4 8,724 9,730 1,006
3 1 6,992 6,979 13
3 2 6,822 6,992 170
3 3 7,949 6,822 1,127
3 4 9,650 9,936 286
4 1 7,720
4 2
4 3
4 4
10-12
13. Measuring the Forecast Error
• The mean absolute deviation (called MAD) measures the average forecasting
error.
MAD = (Sum of forecasting errors) / (Number of forecasts)
• The mean square error (often abbreviated MSE) measures the average of the
square of the forecasting error.
MSE = (Sum of square of forecasting errors) / (Number of forecasts).
• The MSE increases the weight of large errors relative to the weight of small
errors.
10-13
14. Considering Seasonal Effects
• When there are seasonal patterns in the data, they can be addressed by
forecasting methods that use seasonal factors.
• The seasonal factor for any period of a year (a quarter, a month, etc.) measures
how that period compares to the overall average for an entire year.
Seasonal factor = (Average for the period) / (Overall average)
• It is easier to analyze data and detect new trends if the data are first adjusted to
remove the seasonal patterns.
Seasonally adjusted data = (Actual call volume) / (Seasonal factor)
10-14
16. Excel Template for Calculating Seasonal Factors
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
A B C D E F G
Estimating Seasonal Factors for CCW
True
Year Quarter Value Type of Seasonality
1 1 6,809 Quarterly
1 2 6,465
1 3 6,569
1 4 8,266 Estimate for
2 1 7,257 Quarter Seasonal Factor
2 2 7,064 1 0.9323
2 3 7,784 2 0.9010
2 4 8,724 3 0.9873
3 1 6,992 4 1.1794
3 2 6,822
3 3 7,949
3 4 9,650
10-16
17. Seasonally Adjusted Time Series for CCW
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
A B C D E F
Seasonally Adjusted Time Series for CCW
Seasonal Actual Seasonally Adjusted
Year Quarter Factor Call Volume Call Volume
1 1 0.93 6,809 7,322
1 2 0.90 6,465 7,183
1 3 0.99 6,569 6,635
1 4 1.18 8,266 7,005
2 1 0.93 7,257 7,803
2 2 0.90 7,064 7,849
2 3 0.99 7,784 7,863
2 4 1.18 8,724 7,393
3 1 0.93 6,992 7,518
3 2 0.90 6,822 7,580
3 3 0.99 7,949 8,029
3 4 1.18 9,650 8,178
10-17
18. Outline for Forecasting Call Volume
1. Select a time-series forecasting method.
2. Apply this method to the seasonally adjusted time series to obtain a forecast of
the seasonally adjusted call volume for the next time period.
3. Multiply this forecast by the corresponding seasonal factor to obtain a forecast
of the actual call volume (without seasonal adjustment).
10-18
19. The Last-Value Forecasting Method
• The last-value forecasting method ignores all data points in a time series
except the last one.
Forecast = Last value
• The last-value forecasting method is sometimes called the naïve method,
because statisticians consider it naïve to use just a sample size of one when
other data are available.
• However, when conditions are changing rapidly, it may be that the last value is
the only relevant data point.
10-19
20. The Last-Value Method Applied to CCW’s Problem
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
A B C D E F G H I J K
Last-Value Forecasting Method with Seasonality for CCW
Seasonally Seasonally
True Adjusted Adjusted Actual Forecasting
Year Quarter Value Value Forecast Forecast Error Type of Seasonality
1 1 6,809 7,322 Quarterly
1 2 6,465 7,183 7,322 6,589 124
1 3 6,569 6,635 7,183 7,112 543 Quarter Seasonal Factor
1 4 8,266 7,005 6,635 7,830 436 1 0.93
2 1 7,257 7,803 7,005 6,515 742 2 0.90
2 2 7,064 7,849 7,803 7,023 41 3 0.99
2 3 7,784 7,863 7,849 7,770 14 4 1.18
2 4 8,724 7,393 7,863 9,278 554
3 1 6,992 7,518 7,393 6,876 116
3 2 6,822 7,580 7,518 6,766 56
3 3 7,949 8,029 7,580 7,504 445
3 4 9,650 8,178 8,029 9,475 175
4 1 8,178 7,606
4 2
4 3
4 4
5 1 Mean Absolute Deviation
5 2 MAD = 295
5 3
5 4 Mean Square Error
6 1 MSE = 145,909
10-20
21. The Averaging Forecasting Method
• The averaging forecasting method uses all the data points in the time series
and simply averages these points.
Forecast = Average of all data to date
• The averaging forecasting method is a good one to use when conditions are
very stable.
• However, the averaging method is very slow to respond to changing
conditions. It places the same weight on all the data, even though the older
values may be less representative of current conditions than the last value
observed.
10-21
22. The Averaging Method Applied to CCW’s Problem
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
A B C D E F G H I J K
Averaging Forecasting Method with Seasonality for CCW
Seasonally Seasonally
True Adjusted Adjusted Actual Forecasting
Year Quarter Value Value Forecast Forecast Error Type of Seasonality
1 1 6,809 7,322 Quarterly
1 2 6,465 7,183 7,322 6,589 124
1 3 6,569 6,635 7,252 7,180 611 Quarter Seasonal Factor
1 4 8,266 7,005 7,047 8,315 49 1 0.93
2 1 7,257 7,803 7,036 6,544 713 2 0.90
2 2 7,064 7,849 7,190 6,471 593 3 0.99
2 3 7,784 7,863 7,300 7,227 557 4 1.18
2 4 8,724 7,393 7,380 8,708 16
3 1 6,992 7,518 7,382 6,865 127
3 2 6,822 7,580 7,397 6,657 165
3 3 7,949 8,029 7,415 7,341 608
3 4 9,650 8,178 7,471 8,816 834
4 1 7,530 7,003
4 2
4 3
4 4
5 1 Mean Absolute Deviation
5 2 MAD = 400
5 3
5 4 Mean Square Error
6 1 MSE = 242,876
10-22
23. The Moving-Average Forecasting Method
• The moving-average forecasting method averages the data for only the most
recent time periods.
n = Number of recent periods to consider as relevant for forecasting
Forecast = Average of last n values
• The moving-average forecasting method is a good one to use when conditions
don’t change much over the number of time periods included in the average.
• However, the moving-average method is slow to respond to changing
conditions. It places the same weight on each of the last n values even though
the older values may be less representative of current conditions than the last
value observed.
10-23
24. The Moving-Average Method Applied to CCW
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21
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27
28
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A B C D E F G H I J K
Moving Average Forecasting Method with Seasonality for CCW
Seasonally Seasonally
True Adjusted Adjusted Actual Forecasting Number of previous
Year Quarter Value Value Forecast Forecast Error periods to consider
1 1 6,809 7,322 n = 4
1 2 6,465 7,183
1 3 6,569 6,635 Type of Seasonality
1 4 8,266 7,005 Quarterly
2 1 7,257 7,803 7,036 6,544 713
2 2 7,064 7,849 7,157 6,441 623 Quarter Seasonal Factor
2 3 7,784 7,863 7,323 7,250 534 1 0.93
2 4 8,724 7,393 7,630 9,003 279 2 0.90
3 1 6,992 7,518 7,727 7,186 194 3 0.99
3 2 6,822 7,580 7,656 6,890 68 4 1.18
3 3 7,949 8,029 7,589 7,513 436
3 4 9,650 8,178 7,630 9,004 646
4 1 7,826 7,279
4 2
4 3
4 4
5 1
5 2
5 3
5 4 Mean Absolute Deviation
6 1 MAD = 437
6 2
6 3 Mean Square Error
6 4 MSE = 238,816
10-24
25. The Exponential Smoothing Forecasting Method
• The exponential smoothing forecasting method places the greatest weight on
the last value in the time series and then progressively smaller weights on the
older values.
Forecast = a (Last value) + (1 – a) (Last forecast)
a is the smoothing constant between 0 and 1.
• This method places a weight of a on the last value, a(1–a) on the next-to-last
value, a(1–a)2 on the next prior value, etc.
– For example, when a = 0.5, the method places a weight of 0.5 on the last value,
0.25 on the next-to-last, 0.125 on the next prior, etc.
– A larger value of a places more emphasis on the more recent values, a smaller
value places more emphasis on the older values.
• The choice of the value of the smoothing constant a has a substantial effect on
the forecast.
– A small value (say, a = 0.1) is appropriate if conditions are relatively stable.
– A larger value (say, a = 0.5) is appropriate if significant changes occur frequently.
10-25
26. The Exponential Smoothing Method Applied to CCW
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2
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9
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30
31
A B C D E F G H I J K
Exponential-Smoothing Forecasting Method with Seasonality for CCW
Seasonally Seasonally
True Adjusted Adjusted Actual Forecasting Smoothing Constant
Year Quarter Value Value Forecast Forecast Error a 0.5
1 1 6,809 7,322 7,500 6,975 166
1 2 6,465 7,183 7,411 6,670 205 Initial Estimate
1 3 6,569 6,635 7,297 7,224 655 Average = 7,500
1 4 8,266 7,005 6,966 8,220 46
2 1 7,257 7,803 6,986 6,497 760 Type of Seasonality
2 2 7,064 7,849 7,394 6,655 409 Quarterly
2 3 7,784 7,863 7,622 7,545 239
2 4 8,724 7,393 7,742 9,136 412 Quarter Seasonal Factor
3 1 6,992 7,518 7,568 7,038 46 1 0.93
3 2 6,822 7,580 7,543 6,789 33 2 0.90
3 3 7,949 8,029 7,561 7,486 463 3 0.99
3 4 9,650 8,178 7,795 9,199 451 4 1.18
4 1 7,987 7,428
4 2
4 3
4 4
5 1
5 2
5 3
5 4
6 1
6 2 Mean Absolute Deviation
6 3 MAD = 324
6 4
7 1 Mean Square Error
MSE = 157,836
10-26
27. A Time Series with Trend
(Population of a State over Time)
1995 2000 2005 Year
Population
(Millions)
4.8
5.0
5.2
5.4
Trend
line
10-27
28. Exponential Smoothing with Trend Forecasting Method
• The exponential smoothing with trend forecasting method uses the recent
values in the time series to estimate any current upward or downward trend in
these values.
Trend = Average change from one time-series value to the next
• The formula for forecasting the next value in the time series adds the estimated
trend.
Forecast = a (Last value) + (1 – a) (Last forecast) + Estimated trend
a is the smoothing constant between 0 and 1.
• Exponential smoothing also is used to obtain and update the estimated trend.
Estimated trend = b (Latest trend) + (1 – b) (Last estimate of trend)
b is the trend smoothing constant.
• The formula for forecasting n periods from now is
Forecast = a (Last value) + (1 – a) (Last forecast) + n (Estimated trend)
10-28
29. Exponential Smoothing with Trend Applied to CCW
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A B C D E F G H I J K L M
Exponential-Smoothing with Trend Forecasting Method with Seasonality for CCW
Seasonally Seasonally
True Adjusted Latest Estimated Adjusted Actual Forecasting Smoothing Constant
Year Quarter Value Value Trend Trend Forecast Forecast Error a 0.3
1 1 6,809 7,322 0 7,500 6,975 166 b 0.3
1 2 6,465 7,183 -54 -16 7,430 6,687 222
1 3 6,569 6,635 -90 -38 7,318 7,245 676 Initial Estimate
1 4 8,266 7,005 -243 -100 7,013 8,276 10 Average = 7,500
2 1 7,257 7,803 -102 -100 6,910 6,427 830 Trend = 0
2 2 7,064 7,849 167 -20 7,158 6,442 622
2 3 7,784 7,863 187 42 7,407 7,333 451 Type of Seasonality
2 4 8,724 7,393 179 83 7,627 9,000 276 Quarterly
3 1 6,992 7,518 13 62 7,619 7,085 93
3 2 6,822 7,580 32 53 7,642 6,877 55 Quarter Seasonal Factor
3 3 7,949 8,029 34 47 7,670 7,594 355 1 0.93
3 4 9,650 8,178 155 80 7,858 9,272 378 2 0.90
4 1 176 108 8,062 7,498 3 0.99
4 2 4 1.18
4 3
4 4
5 1
5 2
5 3
5 4
6 1
6 2
6 3
6 4 Mean Absolute Deviation
7 1 MAD = 345
Mean Square Error
MSE = 180,796
10-29
30. MAD and MSE for the Various Forecasting Method
Forecasting Method MAD MSE
CCW’s 25 percent rule 424 317,815
Last-value method 295 145,909
Averaging method 400 242,876
Moving-average method 437 238,816
Exponential smoothing 324 157,836
Exponential smoothing with trend 345 180,796
10-30
32. Typically Probability Distributions of Call Volume
in the Four Quarters (Assumes Annual Mean = 7,500)
6,500 7,000 7,500 8,000 8,500 9,000
Quarter 2 Quarter 1 Quarter 3 Quarter 4
10-32
33. Comparison of Typical Probability Distributions
of Seasonally-Adjusted Call Volumes in Years 1 and 2
6,500 7,000 7,500 8,000
Year 1 Year 2
10-33
34. Comparison of the Forecasting Methods
• Last value method: Suitable for a time series that is so unstable that even the
next-to-last value is not considered relevant for forecasting the next value.
• Averaging method: Suitable for a very stable time series where even its first
few values are considered relevant for forecasting the next value.
• Moving-average method: Suitable for a moderately stable time series where
the last few values are considered relevant for forecasting the next value.
• Exponential smoothing method: Suitable for a time series in the range from
somewhat unstable to rather stable, where the value of the smoothing constant
needs to be adjusted to fit the anticipated degree of stability.
• Exponential smoothing with trend: Suitable for a time series where the mean
of the distribution tends to follow a trend either up or down, provided that
changes in the trend occur only occasionally and gradually.
10-34
35. The Consultant’s Recommendations
1. Forecasting should be done monthly rather than quarterly.
2. Hiring and training of new agents also should be done monthly.
3. Recently retired agents should be offered the opportunity to work part time on an on-call
basis.
4. Since sales drive call volume, the forecasting process should begin by forecasting sales.
5. For forecasting purposes, total sales should be broken down into the major components:
a) The relatively stable market base of numerous small-niche products.
b) Each of the few (perhaps three or four) major new products.
6. Exponential smoothing with a relatively small smoothing constant is suggested for
forecasting sales of the marketing base of numerous small-niche products.
7. Exponential smoothing with trend, with relatively large smoothing constants, is
suggested for forecasting sales of each major new product.
8. Seasonally adjusted time series should be used for each application of the methods.
9. The forecasts in recommendation 5 should be summed to obtain a forecast of total sales.
10. Causal forecasting with linear regression should be used to obtain a forecast of call
volume from this forecast of total sales.
10-35
36. Causal Forecasting
Causal forecasting obtains a forecast of the quantity of interest (the dependent
variable) by relating it directly to one or more other quantities (the independent
variables) that drive the quantity of interest.
Type of Forecasting
Possible Dependent
Variable
Possible Independent
Variable
Sales Sales of a product Amount of advertising
Spare parts Demand for spare parts Usage of equipment
Economic trends Gross domestic product Various economic factors
CCW call volume Call volume Total sales
Any quantity This same quantity Time
10-36
37. Sales and Call Volume Data for CCW
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A B C D E
CCW's Average Daily Sales and Call Volume
Sales Call
Year Quarter ($thousands) Volume
1 1 4,894 6,809
1 2 4,703 6,465
1 3 4,748 6,569
1 4 5,844 8,266
2 1 5,192 7,257
2 2 5,086 7,064
2 3 5,511 7,784
2 4 6,107 8,724
3 1 5,052 6,992
3 2 4,985 6,822
3 3 5,576 7,949
3 4 6,647 9,650
10-37
38. Adding a Trendline to the Graph
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A B C D E
CCW's Average Daily Sales and Call Volume
Sales Call
Year Quarter ($thousands) Volume
1 1 4,894 6,809
1 2 4,703 6,465
1 3 4,748 6,569
1 4 5,844 8,266
2 1 5,192 7,257
2 2 5,086 7,064
2 3 5,511 7,784
2 4 6,107 8,724
3 1 5,052 6,992
3 2 4,985 6,822
3 3 5,576 7,949
3 4 6,647 9,650
10-38
39. Linear Regression
• When doing causal forecasting with a single independent variable, linear
regression involves approximating the relationship between the dependent
variable (call volume for CCW) and the independent variable (sales for CCW)
by a straight line.
• This linear regression line is drawn on a graph with the independent variable
on the horizontal axis and the dependent variable on the vertical axis. The line
is constructed after plotting a number of points showing each observed value
of the independent variable and the corresponding value for the dependent
variable.
• The linear regression line has the form
y = a + bx
where
y = Estimated value of the dependent variable
a = Intercept of the linear regression line with the y-axis
b = Slope of the linear regression line
x = Value of the independent variable
10-39
40. Excel Template for Linear Regression
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A B C D E F G H I J
Linear Regression of Call Volume vs. Sales Volume for CCW
Time Independent Dependent Estimation Square Linear Regression Line
Period Variable Variable Estimate Error of Error y = a + bx
1 4,894 6,809 6,765 43.85 1,923 a = -1,223.86
2 4,703 6,465 6,453 11.64 136 b = 1.63
3 4,748 6,569 6,527 42.18 1,780
4 5,844 8,266 8,316 49.93 2,493
5 5,192 7,257 7,252 5.40 29 Estimator
6 5,086 7,064 7,079 14.57 212 If x = 5,000
7 5,511 7,784 7,772 11.66 136
8 6,107 8,724 8,745 21.26 452 then y= 6,938.18
9 5,052 6,992 7,023 31.07 965
10 4,985 6,822 6,914 91.70 8,408
11 5,576 7,949 7,878 70.55 4,977
12 6,647 9,650 9,627 23.24 540
10-40
41. Judgmental Forecasting Methods
• Manager’s Opinion: A single manager uses his or her best judgment.
• Jury of Executive Opinion: A small group of high-level managers pool their
best judgment to collectively make the forecast.
• Salesforce Composite: A bottom-up approach where each salesperson
provides an estimate of what sales will be in his or her region. These estimates
are then aggregated into a corporate sales forecast.
• Consumer Market Survey: A grass-roots approach that surveys customers
and potential customers regarding their future purchasing plans and how they
would respond to various new features in products.
• Delphi Method: A panel of experts in different locations who independently
fill out a series of questionnaires. The results from each questionnaire are
provided with the next one, so each expert can evaluate the group information
in adjusting his or her responses next time.
10-41