The paper proposes a new hybrid model for forecasting project total duration in earned value management that combines artificial neural networks, random number simulation, and statistical methods. The model uses an artificial neural network to forecast the next period's earned schedule value based on prior periods' actual values. It then uses the forecast along with statistical methods to calculate confidence intervals and point estimates for total project duration at each period. The model was tested on real project data and found to outperform traditional earned value management forecasting methods in terms of accuracy.
Software of Time Series Forecasting based on Combinations of Fuzzy and Statis...ITIIIndustries
The developed software is a web application with open access and is aimed on forecasting of time series stored in database. We proposed approach of time series forecasting, combined ARIMA models with fuzzy techniques: three fuzzy time series models, fuzzy transformation (F-transform) and ACL-scale. Applications of a proposed web service have demonstrated efficiency in practical time series predictions with suitable accuracy.
A single stage single constraints linear fractional programming problem an ap...orajjournal
In the present paper we present a new method for solving a class of single stage single constraints linear fractional programming (LFP) problem. The proposed method is based on transformation the objective value and the constraints also. After reducing the fractional program in to equivalent linear program with the help of transformation technique, after that we apply Simplex method to find objective value. Numerical examples are constructed to show the applicability of the above technique
Study of Probability Distributions of Cpi and Spi in Earned Value Analysistheijes
Earned Value analysis (EVA) is the most efficient tool used for transitional review of project execution .It is helpful to project managers and management team to value the progress of project work throughout the project life cycle. The Earned Schedule (ES) is used to approximate the time or duration of project/ s for appropriate evaluation of project execution. ES also help to forecast the time required to complete the project. When combined with schedule analysis, ES can enhance the project. EVA provides the controlling tool for better decision making in project management. The paper discuss about the probability distribution of Cost performance Index (CPI) and Schedule performance Index (SPI). Best fitted distribution will help for forecasting project duration effectively. This helps the Project Manager to prevent the over budgeted cost in future. So an attempt is made to find the alternative distribution of CPI and SPI for better decision making. If the project schedule performance shows poor results then manager need to take the corrective action with the help of this tool. Weibull, Gamma and Exponentiated Exponential Distribution functions are used to study the effect of SPI on CPI. For making better decision in project scheduling, Project managers can review the parameters using EVM tool. The tool is useful in all types of civil engineering and software engineering projects.
Software of Time Series Forecasting based on Combinations of Fuzzy and Statis...ITIIIndustries
The developed software is a web application with open access and is aimed on forecasting of time series stored in database. We proposed approach of time series forecasting, combined ARIMA models with fuzzy techniques: three fuzzy time series models, fuzzy transformation (F-transform) and ACL-scale. Applications of a proposed web service have demonstrated efficiency in practical time series predictions with suitable accuracy.
A single stage single constraints linear fractional programming problem an ap...orajjournal
In the present paper we present a new method for solving a class of single stage single constraints linear fractional programming (LFP) problem. The proposed method is based on transformation the objective value and the constraints also. After reducing the fractional program in to equivalent linear program with the help of transformation technique, after that we apply Simplex method to find objective value. Numerical examples are constructed to show the applicability of the above technique
Study of Probability Distributions of Cpi and Spi in Earned Value Analysistheijes
Earned Value analysis (EVA) is the most efficient tool used for transitional review of project execution .It is helpful to project managers and management team to value the progress of project work throughout the project life cycle. The Earned Schedule (ES) is used to approximate the time or duration of project/ s for appropriate evaluation of project execution. ES also help to forecast the time required to complete the project. When combined with schedule analysis, ES can enhance the project. EVA provides the controlling tool for better decision making in project management. The paper discuss about the probability distribution of Cost performance Index (CPI) and Schedule performance Index (SPI). Best fitted distribution will help for forecasting project duration effectively. This helps the Project Manager to prevent the over budgeted cost in future. So an attempt is made to find the alternative distribution of CPI and SPI for better decision making. If the project schedule performance shows poor results then manager need to take the corrective action with the help of this tool. Weibull, Gamma and Exponentiated Exponential Distribution functions are used to study the effect of SPI on CPI. For making better decision in project scheduling, Project managers can review the parameters using EVM tool. The tool is useful in all types of civil engineering and software engineering projects.
Earned Value Management (EVM) is a technique
that forecasts the project giving an early warning of cost &
schedule. It not onely measures the project performance but also
measure the progress of the schedule. It is an effective tool to
measure cost, schedule & performance of the project. The EVA is
useful in various fields such as IT, Industries and Construction
companies etc.
The value of Earned Value Analysis (EVA) is dependent on
two key areas i.e. Precise Cost information and pragmatic
progress of project. If these two key areas are efficient then
benefit of the project will definitely get valued. This paper
summarizes the evolution, basic terminologies of Earned value
Analysis and effective use of it in the construction industries by
MS Project. There are many ways to implement EVA in the
construction project. MS Project is a tool to determine the EV
and its parameters in an efficient way with accuracy and within
time constraints.
Performance Evaluation of Construction Projects by EVM Method, Using Primaver...Mohammad Lemar ZALMAİ
Most of the construction projects are exposed to time and cost overruns due to various factors and this is a major problem. As a solution to this, the Earned Value Management (EVM) method is considered. EVM is a powerful and well-known method used in monitoring and controlling the project. EVM gives an early indication that either project is delayed or not and the project is either over budget or under budget at any particular day by tracking it. Thus, it helps to improve the management control system of a construction project, to detect and control the problems in potential risk areas and to suggest the importance and purpose of monitoring the construction work.
This paper explains the main parameters of the EVM system involved in the calculation of time and cost for construction projects. In this study, the Primavera P6 software is used to deals with the project monitoring process of a seven-storeyed (G+6) faculty building whose construction is in progress at Istanbul, Turkey. A comparison between the planned progress of construction activities and actual progress is performed and the analysis results are interpreted. This case study justifies the benefits of using EVM for project cash flow analysis and forecasting.
Performance Evaluation of Construction Projects by EVM Method, Using Primaver...Mohammad Lemar ZALMAİ
Abstract
Most of the construction projects are exposed to time and cost overruns due to various factors and this is a major problem. As a solution to this, the Earned Value Management (EVM) method is considered. EVM is a powerful and well-known method used in monitoring and controlling the project. EVM gives an early indication that either project is delayed or not and the project is either over budget or under budget at any particular day by tracking it. Thus, it helps to improve the management control system of a construction project, to detect and control the problems in potential risk areas and to suggest the importance and purpose of monitoring the construction work. This paper explains the main parameters of the EVM system involved in the calculation of time and cost for construction projects. In this study, the Primavera P6 software is used to deals with the
project monitoring process of a seven-storey (G+6) faculty building whose construction is in progress at Istanbul, Turkey. A comparison between the planned progress of construction activities and actual progress is performed and the analysis results are interpreted. This case study justifies the benefits of using EVM for project cash flow analysis and forecasting.
Keywords: construction cost management, construction planning, earned value management (EVM), Primavera p6, project management, project scheduling.
Polynomial Function and Fuzzy Inference for Evaluating the Project Performanc...IJERA Editor
The objectives of this paper are two folds. The first one is to improve the time forecasting produced from the well known Earned Value Management (EVM), using the polynomial function. The time prediction observed from the polynomial model, which is compared against that observed from the most common method for time forecasting (critical path method), is a more accurate (mean absolute percentage of error is less than 2%) than that observed from the conventional deterministic forecasting methods (CDFMs). The second is to evaluate and forecast the overall project performance under uncertainty using the fuzzy inference. As the uncertainty is inherent in real life projects, the polynomial function and fuzzy inference model (PFFI) can assist the project managers, to estimate the future status of the project in a more robust and reliable way. Two examples are used to illustrate how the new method can be implemented in reality.
A Formal Method for Mapping Software Engineering Practices to Essence ijseajournal
Essence Framework (EF) aims at addressing the core problems of software engineering (SE) and its practices. As a relatively new framework, one important issue for EF has been mapping software practices to its conceptual domain. Although there are several works describing systematic procedures, a review of literature cannot suggest a study using a formal method. The study is conducted according to the guidelines of Design Science Research (DSR) Method. The research contribution is classified as an “application of a new solution (the formal method) to a new problem (mapping software practices to EF). The formal method
employs an algorithm based on Concept Algebra and it is applied in a Scrum case study. The results are promising and they differ from the ones exist in the current EF related literature.
The relatively new concept of #EarnedSchedule explained by Whizible PMP as a part of the #projectmanagementtraining series. Useful for #projectmanagers and PMO. Also useful for PMP exam as per PMBOK version 6
A project consists of interconnected activities that are to be executed in a certain order before the entire task is completed. The activities are interrelated in a logical sequence which is known as precedence relationship. The project is represented in the form of a network for analytical treatment to get a solution for scheduling and controlling activities.
In this project, To schedule the activities, we have applied the "CPM " and "PERT" method.
project management-cpm and pert methods for managersNaganna Chetty
A project is a one shot, time limited, goal directed, major undertaking, requiring the commitment of varied skills & resources.
A project:
Has a unique purpose.
Is temporary.
Is developed using progressive elaboration.
Requires resources, often from various areas.
Should have a primary customer or sponsor.
The project sponsor usually provides the direction and funding for the project.
Involves uncertainty.
Project managers work with project sponsors, project teams, and other people involved in projects to meet project goals.
Program: “A group of related projects managed in a coordinated way to obtain benefits and control not available from managing them individually.”
Program managers oversee programs and often act as bosses for project managers.
Project management is “the application of knowledge, skills, tools and techniques to project activities to meet project requirements.”
Particle Swarm Optimization in the fine-tuning of Fuzzy Software Cost Estimat...Waqas Tariq
Software cost estimation deals with the financial and strategic planning of software projects. Controlling the expensive investment of software development effectively is of paramount importance. The limitation of algorithmic effort prediction models is their inability to cope with uncertainties and imprecision surrounding software projects at the early development stage. More recently, attention has turned to a variety of machine learning methods, and soft computing in particular to predict software development effort. Fuzzy logic is one such technique which can cope with uncertainties. In the present paper, Particle Swarm Optimization Algorithm (PSOA) is presented to fine tune the fuzzy estimate for the development of software projects . The efficacy of the developed models is tested on 10 NASA software projects, 18 NASA projects and COCOMO 81 database on the basis of various criterion for assessment of software cost estimation models. Comparison of all the models is done and it is found that the developed models provide better estimation
Financial time series forecasting has received
tremendous interest by both the individual and institutional
investors and hence by the researchers. But the high noise and
complexity residing in the financial data makes this job extremely
challenging. Over the years many researchers have used support
vector regression (SVR) quite successfully to conquer this
challenge. As the latent high noise in the data impairs the
performance, reducing the noise could be effective while
constructing the forecasting model. To accomplish this task,
integration of principal component analysis (PCA) and SVR is
proposed in this research work. In the first step, a set of technical
indicators are calculated from the daily transaction data of the
target stock and then PCA is applied to these values aiming to
extract the principle components. After filtering the principal
components, a model is finally constructed to forecast the future
price of the target stocks. The performance of the proposed
approach is evaluated with 16 years’ daily transactional data of
three leading stocks from different sectors listed in Dhaka Stock
Exchange (DSE), Bangladesh. Empirical results show that the
proposed model enhances the performance of the prediction
model and also the short-term prediction gains more accuracy
than long-term prediction.
Abstract— Execution of engineering projects are tracked against critical metrics such as safety, quality,
delivery cost and inventory. Earned value is a key parameter that helps in assessing delivery (schedule) and cost.
Static shows that 70% of projects are over budget behind schedule, 52% of all projects finish at 189% of their
initial budget and some, after huge investments of time and money, are simply never completed. The rest of this
paper gives a perspective on monitoring project health by Earned value analysis.
Forecasting cost and schedule performanceGlen Alleman
For credible decisions to be made, we need confidence intervals on all the numbers we use to make decisions.
These confidence intervals come from the underlying statistics and the related probabilities.
Statistical forecasting, using time series analysis of past performance, is mandatory for any credible discussion of project performance in the future.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Earned Value Management (EVM) is a technique
that forecasts the project giving an early warning of cost &
schedule. It not onely measures the project performance but also
measure the progress of the schedule. It is an effective tool to
measure cost, schedule & performance of the project. The EVA is
useful in various fields such as IT, Industries and Construction
companies etc.
The value of Earned Value Analysis (EVA) is dependent on
two key areas i.e. Precise Cost information and pragmatic
progress of project. If these two key areas are efficient then
benefit of the project will definitely get valued. This paper
summarizes the evolution, basic terminologies of Earned value
Analysis and effective use of it in the construction industries by
MS Project. There are many ways to implement EVA in the
construction project. MS Project is a tool to determine the EV
and its parameters in an efficient way with accuracy and within
time constraints.
Performance Evaluation of Construction Projects by EVM Method, Using Primaver...Mohammad Lemar ZALMAİ
Most of the construction projects are exposed to time and cost overruns due to various factors and this is a major problem. As a solution to this, the Earned Value Management (EVM) method is considered. EVM is a powerful and well-known method used in monitoring and controlling the project. EVM gives an early indication that either project is delayed or not and the project is either over budget or under budget at any particular day by tracking it. Thus, it helps to improve the management control system of a construction project, to detect and control the problems in potential risk areas and to suggest the importance and purpose of monitoring the construction work.
This paper explains the main parameters of the EVM system involved in the calculation of time and cost for construction projects. In this study, the Primavera P6 software is used to deals with the project monitoring process of a seven-storeyed (G+6) faculty building whose construction is in progress at Istanbul, Turkey. A comparison between the planned progress of construction activities and actual progress is performed and the analysis results are interpreted. This case study justifies the benefits of using EVM for project cash flow analysis and forecasting.
Performance Evaluation of Construction Projects by EVM Method, Using Primaver...Mohammad Lemar ZALMAİ
Abstract
Most of the construction projects are exposed to time and cost overruns due to various factors and this is a major problem. As a solution to this, the Earned Value Management (EVM) method is considered. EVM is a powerful and well-known method used in monitoring and controlling the project. EVM gives an early indication that either project is delayed or not and the project is either over budget or under budget at any particular day by tracking it. Thus, it helps to improve the management control system of a construction project, to detect and control the problems in potential risk areas and to suggest the importance and purpose of monitoring the construction work. This paper explains the main parameters of the EVM system involved in the calculation of time and cost for construction projects. In this study, the Primavera P6 software is used to deals with the
project monitoring process of a seven-storey (G+6) faculty building whose construction is in progress at Istanbul, Turkey. A comparison between the planned progress of construction activities and actual progress is performed and the analysis results are interpreted. This case study justifies the benefits of using EVM for project cash flow analysis and forecasting.
Keywords: construction cost management, construction planning, earned value management (EVM), Primavera p6, project management, project scheduling.
Polynomial Function and Fuzzy Inference for Evaluating the Project Performanc...IJERA Editor
The objectives of this paper are two folds. The first one is to improve the time forecasting produced from the well known Earned Value Management (EVM), using the polynomial function. The time prediction observed from the polynomial model, which is compared against that observed from the most common method for time forecasting (critical path method), is a more accurate (mean absolute percentage of error is less than 2%) than that observed from the conventional deterministic forecasting methods (CDFMs). The second is to evaluate and forecast the overall project performance under uncertainty using the fuzzy inference. As the uncertainty is inherent in real life projects, the polynomial function and fuzzy inference model (PFFI) can assist the project managers, to estimate the future status of the project in a more robust and reliable way. Two examples are used to illustrate how the new method can be implemented in reality.
A Formal Method for Mapping Software Engineering Practices to Essence ijseajournal
Essence Framework (EF) aims at addressing the core problems of software engineering (SE) and its practices. As a relatively new framework, one important issue for EF has been mapping software practices to its conceptual domain. Although there are several works describing systematic procedures, a review of literature cannot suggest a study using a formal method. The study is conducted according to the guidelines of Design Science Research (DSR) Method. The research contribution is classified as an “application of a new solution (the formal method) to a new problem (mapping software practices to EF). The formal method
employs an algorithm based on Concept Algebra and it is applied in a Scrum case study. The results are promising and they differ from the ones exist in the current EF related literature.
The relatively new concept of #EarnedSchedule explained by Whizible PMP as a part of the #projectmanagementtraining series. Useful for #projectmanagers and PMO. Also useful for PMP exam as per PMBOK version 6
A project consists of interconnected activities that are to be executed in a certain order before the entire task is completed. The activities are interrelated in a logical sequence which is known as precedence relationship. The project is represented in the form of a network for analytical treatment to get a solution for scheduling and controlling activities.
In this project, To schedule the activities, we have applied the "CPM " and "PERT" method.
project management-cpm and pert methods for managersNaganna Chetty
A project is a one shot, time limited, goal directed, major undertaking, requiring the commitment of varied skills & resources.
A project:
Has a unique purpose.
Is temporary.
Is developed using progressive elaboration.
Requires resources, often from various areas.
Should have a primary customer or sponsor.
The project sponsor usually provides the direction and funding for the project.
Involves uncertainty.
Project managers work with project sponsors, project teams, and other people involved in projects to meet project goals.
Program: “A group of related projects managed in a coordinated way to obtain benefits and control not available from managing them individually.”
Program managers oversee programs and often act as bosses for project managers.
Project management is “the application of knowledge, skills, tools and techniques to project activities to meet project requirements.”
Particle Swarm Optimization in the fine-tuning of Fuzzy Software Cost Estimat...Waqas Tariq
Software cost estimation deals with the financial and strategic planning of software projects. Controlling the expensive investment of software development effectively is of paramount importance. The limitation of algorithmic effort prediction models is their inability to cope with uncertainties and imprecision surrounding software projects at the early development stage. More recently, attention has turned to a variety of machine learning methods, and soft computing in particular to predict software development effort. Fuzzy logic is one such technique which can cope with uncertainties. In the present paper, Particle Swarm Optimization Algorithm (PSOA) is presented to fine tune the fuzzy estimate for the development of software projects . The efficacy of the developed models is tested on 10 NASA software projects, 18 NASA projects and COCOMO 81 database on the basis of various criterion for assessment of software cost estimation models. Comparison of all the models is done and it is found that the developed models provide better estimation
Financial time series forecasting has received
tremendous interest by both the individual and institutional
investors and hence by the researchers. But the high noise and
complexity residing in the financial data makes this job extremely
challenging. Over the years many researchers have used support
vector regression (SVR) quite successfully to conquer this
challenge. As the latent high noise in the data impairs the
performance, reducing the noise could be effective while
constructing the forecasting model. To accomplish this task,
integration of principal component analysis (PCA) and SVR is
proposed in this research work. In the first step, a set of technical
indicators are calculated from the daily transaction data of the
target stock and then PCA is applied to these values aiming to
extract the principle components. After filtering the principal
components, a model is finally constructed to forecast the future
price of the target stocks. The performance of the proposed
approach is evaluated with 16 years’ daily transactional data of
three leading stocks from different sectors listed in Dhaka Stock
Exchange (DSE), Bangladesh. Empirical results show that the
proposed model enhances the performance of the prediction
model and also the short-term prediction gains more accuracy
than long-term prediction.
Abstract— Execution of engineering projects are tracked against critical metrics such as safety, quality,
delivery cost and inventory. Earned value is a key parameter that helps in assessing delivery (schedule) and cost.
Static shows that 70% of projects are over budget behind schedule, 52% of all projects finish at 189% of their
initial budget and some, after huge investments of time and money, are simply never completed. The rest of this
paper gives a perspective on monitoring project health by Earned value analysis.
Forecasting cost and schedule performanceGlen Alleman
For credible decisions to be made, we need confidence intervals on all the numbers we use to make decisions.
These confidence intervals come from the underlying statistics and the related probabilities.
Statistical forecasting, using time series analysis of past performance, is mandatory for any credible discussion of project performance in the future.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
2. Hybrid artificial neural network and statistical model 403
1 Introduction and overview
Earned value management (EVM) is a convenient and effective method of project
management. It cuts a project into several equal basic periods (generally the basic time
unit, e.g., month or day), and puts the cumulative planned workload (scaled in money
unit) into each period as planned value (PV); as the project is performing, the actual
finished PV of each period is filled into earned value (EV); plus the actual cost (AC) of
each period and several related derived indicators, e.g., CPI, SPI, CV, SV, etc., EVM
builds up a framework to weigh and forecast a project performance status. However, with
the development of EVM, researchers find that EVM performs poorly in the aspect of
weighing project schedule because the indicator SPI is defined by EV/PV and SV is
defined by EV – PV which makes them approach to 1 and 0 respectively in the latter part
of the project even if its performance is behind the planned schedule. This is
unacceptable when forecast the project total duration cause the result generally
approaches to the planned duration no matter if a project’s performance is good or bad
(Vandevoorde and Vanhoucke, 2006; Lipke et al., 2008); besides, the two indicators
cannot reflect the project performance status properly. Based on EVM, Lipke et al.
develops earned schedule (ES) method that it scales the workload in time unit and solves
the above problem, which is an extension to EVM. Based on ES method, Lipke et al.
(2008) apply statistical methods and their well established schedule performance
analysing technique-IEACt to predict total cost and total duration of a project.
Based on IEACt, the paper proposes a new hybrid method for project total duration
forecasting, which combines artificial neural network (ANN), random number simulation
method and statistical method. Experiments and test results show our hybrid method
outperforms the classic IEACt method in aspect of forecasting accuracy.
The paper’s structure is arranged as follows: Section 2 is a brief introduction to EVM,
and then our hybrid model is put force and experiments are carried out in Section 3,
Section 4 is accuracy test for the comparison of our hybrid model and classic IEACt and
conclusions are drawn in Section 5.
2 Review of EVM
An understanding of EVM is assumed in this paper. For convenience, we list the basic
EVM terminology including ES that portrays the project status and forecasts the total
duration.
We need to make an explanation that PV, EV, AC, ES with the performance indicators
CPI and SPI are all cumulative expressions in default situations, that is to say for each
period, these values are calculated by the cumulative values. The periodic expressions
can easily obtained by the difference of the adjacent two cumulative values. In this paper,
we denote periodic expressions of above terminology by adding suffix p and period
suffix t, e.g., the EV value of the 5th period itself is denoted by EVp,5. Earned schedule
framework is a recent extension to EVM, designed for providing reliable and useful
schedule performance information (Lipke et al., 2008; Cioffi, 2006). In earned schedule
framework, the basic metric is ES, which means the schedule duration earned, can be
calculated as follows:
3. 404 Y. Li and L. Liu
ESt = i + ( EVt − PVi ) ( PVi +1 − PVi ) (1)
In the above definition, the tth ES is described as the workload of already finished (i, time
unit) plus a linear interpolation value which is the amount of ES accrued within the
increment of i from PVi to PVi+1. Compared with EVM metrics, ES is specially designed
to cover the needs for time scale forecasting, which in traditional EVM metrics SPI
approximates to 1 no matter the performance of EV when a project is nearly finished;
hence the indicator SPI could not reflect the project performance properly. However, in
ES metrics, ES is calculated by the periodic actual finished proportion of planned
workload, wherever the project is performing, ES could properly express the performance
status of a project.
Table 1 Basic EVM and ES terminology
EVM ES
Status Earned value (EV) Earned schedule (ES)
Actual cost (AC) Actual time (AT)
Schedule variance (SV) Schedule variance (time) (SV(t))
SV = EV – PV SV(t) = ES – AT
Schedule performance index (SPI) Schedule performance index (time)
SPI = EV / PV (SPI(t))
SPI(t) = ES / AT
Cost performance index (CPI)
Cost variance (CV)
Forecasting Independent estimate at complete Independent estimate at complete time
(IEAC) (IEAC(t))
IEAC = BAC / CPI IEAC(t) = PD / SPI(t)
IEAC(t) = AT + (PD – ES) / PF
3 Methodology
According to the ES theory, the project total duration could be estimated by independent
estimate at completion time (IEAC(t)), it has two forms, short form and long form
respectively:
IEACt = PD / SPI (t ) (2)
IEACt = AT + ( PD − ES ) / PFt (3)
Where AT is the actual time, i.e., the current time; and PFt is the performance factor
which is generally SPI(t) for duration forecasting. IEACt provides us a convenient
forecasting method for project total duration. However, there is an underlying
assumption: the performance of future unfinished part of the project is equal to the
cumulative indicator SPI of finished part, i.e., the current SPI(t). Based on SPI(t), Lipke
et al. (2008) propose a statistical calculation method (Lipke et al., 2008; Lipke, 2002;
National Institute of Standards and Technology E-handbook of Statistical Methods,
2006), we summarise it as follows:
4. Hybrid artificial neural network and statistical model 405
CL = ln index(cum) ± Z * σ n * AF (4)
σ= ∑ ( ln index p (i ) − ln indexc )2 ( n − 1) (5)
AF = ( PD − ES ) ( PD − ES / n) (6)
IEACt = PD exp (CL) (7)
Where CL is the confidence limit, indexp refers to periodic index values and indexc refers
to cumulative index values. The index in our study refers to SPI, Z is the t distribution
value representing the level of confidence (95% in this paper), we use t distribution
instead of normal distribution because our data sample is less than 30. σ is the standard
deviation of SPI, n is the number of observations, and AF is the adjusted factors for finite
population, which is derived from the statistics formula (( N − n) / ( N −1)).
In this paper, we adopt this statistical method. However, we make a little change:
employing long forms instead of short forms; meanwhile, we make an extension to the
IEACt assumption as follows (the current time is t):
Assumption 1: The schedule performance index of future unfinished part of the project is
not exactly equal to the current cumulative SPIc,t as classic IEACt does, but equal to a
∧
forecasting value SPI c , t +1 , which could reflect the performance of unfinished part of the
project more properly than SPIc,t.
Assumption 2: The periodic EVp,t+1, ACp,t+1 and ESp,t+1 conform to normal distribution
respectively with parameters μ and σ2, where μ is the mean of the nearest T number of
periodic EVp,i, ACp,i, ESp,i (i = t – (T – 1,…,t) respectively, σ2 is their corresponding
deviation respectively.
The main idea of Assumption 2 lies in: we believe the performance of future unfinished
part of the project could be expressed by the nearest T number of EVp,i, ACp,i, ESp,i
(i = t – (T – 1,…,t) to it instead of the whole finished part from 1 to t, i.e., the latest
several periodic EV, AC, ES values could express better or have the greater possibility to
explain the future performance more than the whole finished periodic ones until t time.
Besides, we believe that for the periodic EV, AC, ES, the three metrics’ changing ranges
of future undone part (especially those of the next one period) have greater possibility to
fall in the regions formed by normal random numbers with the parameters of μ and σ2
respectively, instead of being simply equal to the means of t number of EV, AC, ES
respectively as traditional IEACt does.
For this consideration, we cut the whole forecasting process into two stages:
In the first stage we employ ANN back propagation algorithm to forecast the
next periodic earned schedule ESp,t+1 just one step further, and make
∧ ∧
SPI c ,t +1 = ( ES p ,t +1 + ESc ,t ) / (t + 1) as the future performance of the project. In Stage 2,
we put the forecasting value into the statistical framework to perform interval estimations
∧
for total duration; meantime, we make a replacement SPI c ,t +1 for PFt in formula (3) to
forecast the project total duration. The methodology of our hybrid model is summarised
as follows:
5. 406 Y. Li and L. Liu
1 Suppose the current time is t(t ≥ 3), set T =3.
2 Based on the available finished t number of periodic EVp,i, ACp,i, ESp,i (i = t – (T –
1,…,t), three groups of normal distribution random numbers EVp,R, ACp,R, ESp,R are
generated with their own parameters of μ and σ2 respectively.
3 Regard EVp,R and ACp,R as the input nodes, ESp,R as the output node, with the help of
∧ ∧
ANN to forecast ES p ,t +1 and then to obtain SPI c ,t +1 as the performance index of
future unfinished part of the project.
4 Employ formula (3) to (6) to make interval estimation and point estimation of the
project total duration standing at period t.
5 t = t + 1, loop Step (2) to (5) until the project is actually finished.
3.1 ANN forecasting procedure
Although traditional models outperform in terms of accurately describing the
phenomenon of long-term trends (Sallehuddin et al., 2009; Zou et al., 2007; Kayacan et
al., 2010; Yao et al., 2003), they require a large amount of observations to construct the
model. Unlike these forecasting requirements, forecasting within a project has much
fewer data, including the number of variables and observations. At the very beginning of
the project, we have only two to three month data and less than six indicators;
furthermore, related literatures suggest that detailed project analysis is a burdensome
activity. Thus, some widely used model like time series model and classic statistic
method do not match this type of forecasting.
In this paper, we employ two input nodes – one hidden layer – one output node
architecture ANN to forecast ESp,t+1. Training a network is an essential factor for the
success of the neural networks (Satish Kumar, 2006). Among the several learning
algorithms available, back-propagation is the most popular and most widely implemented
learning algorithm of all neural networks paradigms. In this paper, the algorithm of
back-propagation is employed and in the following experiment.
In order to construct the training set, based on the Assumption 2, we generate 1,000
normal distribution random numbers for the periodic EVp,t+1, ACp,t+1 and ESp,t+1
respectively. Each randomly selected corresponding ternary terms as a pattern (Satish
Kumar, 2006), then we have got 1,000 patterns as the training set. The 1,000 ternary
terms cover as much as possible combinations of periodic EV, AC and ES, which is a
simulation to actual performance situation. According to the cross validation theory, we
randomly select the learning set, the validate set and the test set from the training set,
where EVp,t+1, ACp,t+1 are the input nodes, ESp,t+1 is the output node, via pattern training
mode, after learning and validation, the test set is filled in the well-trained ANN, then the
∧ ∧
forecasting value ES p ,t +1 is obtained and so does SPI c ,t +1 .
∧
In view of the random nature of our training set, for each forecasting value ES p ,t +1 ,
we repeat the above forecasting process 100 times, and calculate its average value as our
∧
final forecasting value ES p ,t +1 . Since our ANN is not designed for the specific project,
the number of nodes in the hidden layer is not necessarily designed in details. We
6. Hybrid artificial neural network and statistical model 407
uniformly set it to 20. A real-life project data from Fabricom Airport system
(Vandevoorde and Vanhoucke, 2006) is employed as the experiment data, the brief
information of which is listed in Table 1. The whole model is programmed with
Matlab 7.11.
Table 2 The brief project data of Fabricom Airport system
AT 1 2 3 4 5 6 7
PV 3023 5508 7828 10098 12158 13951 14205
EV 928 1904 2467 3414 4472 7152 7476
AC 1606 2766 4324 6138 7888 9835 10135
8 9 10 11 12 13 14
PV 15933 17902 19967 22208 24286 26331 26658
EV 9272 11441 13302 14699 15985 16753 17077
AC 13217 14755 16656 18768 20897 23364 23664
15 16 17 18 19 20 21
PV 28647 30989 33040 34909 36709 38016 38140
EV 20318 23061 26588 28681 30135 31487 32526
AC 26651 28437 30408 32012 34000 35554 37111
22 23 24 25 26
PV 38140 38140 38140 38140 38140
EV 33504 34513 36489 37630 38140
AC 38468 39798 41155 42600 43983
For the consideration of S-curve and the scarcity nature of samples of available
cumulative ESc,i(i = 1, 2,…,t), we also employ the Grey Verhulst rolling model (Kayacan
et al., 2010) to forecast ESc,t+1, the rolling cycle is also set to 3 (which is equal to T of our
method). However, the relative error percentage is larger than that of ANN method. The
forecasting results of two frameworks are listed below for comparison, where the actual
value is the actual cumulative parameters ESc,t+1 in each period.
The forecasting details are described as follows:
Set T = 3
At the very beginning of the forecasting, suppose only three month is performed, i.e.,
current time t = 3, so we have three true values for EVc,i, ACc,i, ESc,i (i = 1, 2, 3)
respectively, that is also mean we have got EVp,i, ACp,i, ESp,i (i = 1, 2, 3). Based on these
true values, we generate random numbers and training set according to the above
∧ ∧
framework, then forecast ES p ,t +1 just one step further, i.e., ES p ,4 , so the forecasting
∧ ∧
value ESc ,4 = ES p ,4 + ESc ,3 is naturally obtained. The comparative error percentage is
calculated by
∧
error % = ESc,t +1− ESc ,t +1 / ESc ,t +1 *100 (8)
7. 408 Y. Li and L. Liu
Table 3 ES forecasting results of two models
GM(1,1) Verhurlst model ANN model
Actual value
AT ∧ ∧
(ESc,t+1) Error (%) Error (%)
ESc ,t +1 ESc ,t +1
4 1.1573 0.86 26 1.09 6.12
5 1.5831 1.87 18.27 1.45 8.63
6 2.7086 2.06 23.77 1.90 29.82
7 2.8483 7.12 149.93 3.23 13.58
8 3.6361 2.84 21.85 3.33 8.46
9 4.6519 5.52 18.65 4.15 10.87
10 5.6380 5.94 5.44 5.21 7.54
11 7.2859 6.49 10.94 6.25 14.28
12 8.0264 10.30 28.36 8.03 0.008
13 8.4165 8.24 2.06 8.77 4.14
14 8.5810 8.59 0.1 9.12 6.32
15 10.1566 8.64 14.94 9.27 8.74
16 11.4105 11.51 0.88 10.93 4.20
17 13.7859 12.30 10.81 12.22 11.39
18 15.0145 18.62 24.01 14.71 2.04
19 15.6354 15.49 0.91 15.96 2.08
20 16.2428 15.90 2.11 16.57 2.03
21 16.7494 16.83 0.50 17.16 2.43
22 17.2483 17.16 0.50 17.65 2.35
23 17.7881 17.74 0.28 18.13 1.90
24 18.8778 18.37 2.67 18.64 1.25
25 19.7047 20.89 6.01 19.75 0.23
26 21 20.30 3.33 20.56 2.10
RMSE 1.41 0.57
MSE 2.0 0.32
MAPE(%) 16.19 6.55
MAD 0.89 0.45
In the next forecasting process t = 4, we use the nearest T (= 3) true values of EVc,i, ACc,i,
∧
ESc,i (i = 2, 3, 4) to forecast ESc ,5 . The process is performed until the project is finished.
We list the detail forecasting values of every forecasting period guided by two
forecasting frameworks based on the experiment project data in Table 3. To evaluate the
two forecasting metrics, four statistical test indexes [formula (9) to (12)] are carried out:
root mean square error (RMSE), mean square error (MSE), mean absolute percentage
error (MAPE), mean absolute deviation (MAD). In all the four aspects of basic
forecasting performance indexes, the designed ANN model outperforms the GM(1,1)
8. Hybrid artificial neural network and statistical model 409
Verhurlst rolling model. Hence, in the first stage of forecasting, we employ ANN instead
of GM(1,1) Verhurlst rolling model.
n
1
RMSE =
n ∑ (observed − predicted )
t =1
t t
2
(9)
n
1
MSE =
n ∑ (observed − predicted )
t t
2
(10)
t =1
n
observedt − predictedt 100
MAPE = ∑ observedt
×
n
(11)
t =1
n
observedt − predictedt
MAD = ∑t =1
n
(12)
3.2 Statistical estimation for total duration
In Stage 2, for each period, we make use of the latest one step further forecasting value
∧ ∧
ESc ,t +1 to calculate the schedule performance index SPI c,t +1 as the SPI of future
unfinished part, which is our Assumption 1. The benefit of doing this lies in:
Firstly, the classic IEACt method regards the current SPIc,t as the SPI of future undone
part. In essence, this is a kind of simple averaging process because the current
SPIc,t = ESc,t/t, that is to say, SPIc,t is the average performance ability of all t periods
∧
already finished. In comparison, SPI c,t +1 is a kind of fitting value by fitting the average
performance ability of the nearest T periods, which can better express the current
performance status of the project, which is an extension to SPIc,t as we employ random
number simulation method to construct a scene that can simulate the performance ability
trends (the trends are calculated by fitting many different ternary ties of EV, AC, ES,
which can cover more possible actual situations close to actual performance).
∧
Secondly, standing at the current period, due to the extra forecasting SPI c ,t +1 , the
sample number n in the formula increases compared to the classic based on n true
samples; besides, low error percentage forecasting could bring an effect that if we had
known the true value of the next period, according to the experiments provided by Lipke
et al. (2008), which proves that the logarithm of periodic indexes of SPI or CPI
approximates to a normal distribution and would become more and more stable after 30%
percent of the project. The above explanation enables our one step further forecasting to
produce an analogical effect as if we stood at the next period to forecast the total
duration, which has more possibilities to perform a comparatively better result in both
aspects of interval estimation and point estimation.
Based on the above explanations, we draw the result of total duration forecasting both
in our hybrid method and the classic IEACt method from the 4th period to the 26th,
including both interval and point estimation. The details for each forecasting round are
listed in Table 4, and shown in Figure 1.
10. Hybrid artificial neural network and statistical model 411
4 Tests
From Figure 1, we could easily observe that the interval estimation of our hybrid method
is better than the classic IEACt, as to the effect of two methods are similar in the aspect of
point estimation, paired t-test is carried out on forecasting accuracy (error%) to test the
hypotheses. The aim of this test is to check whether the means of forecasting values
obtained from our hybrid method are different from those of classic IEACt. Therefore, the
following hypotheses are proposed:
H01 There is no difference between the means of the classic IEACt and the proposed
hybrid method (μ1 = μ2).
H11 There is a difference between the means of the classic IEACt method and the
proposed hybrid method (μ1 > μ2 or μ1 < μ2).
H02 The means of IEACt lower boundary and that of the proposed hybrid method are
equal (IEACt_lower = Hybrid_lower).
H12 The means of IEACt lower boundary and that of the proposed hybrid method are
not equal (IEACt_lower > Hybrid_lower or IEACt_lower < Hybrid_lower).
H03 The means of IEACt upper boundary and that of the proposed hybrid method are
equal (IEACt_upper = Hybrid_upper).
H13 The means of IEACt upper boundary and that of the proposed hybrid method are
not equal (IEACt_upper > Hybrid_upper or IEACt_upper < Hybrid_upper).
From the test results, the 2-tailed Sig (μ1 ≠ μ2) is 2.8727460171483986E-4, the
corresponding H01 single-tailed Sig (μ1 > μ2) is 1.4363730085741993E-4, under 95%
confidence level the test is significance, so we reject the null hypothesis H01.
Then, we test the interval estimation accuracy of two models, we compare the upper
and lower boundaries of two models respectively, the results are combined in Table 4.
From the test results, the 2-tailed Sig (IEACt_lower ≠ Hybrid_lower) of two models’
lower boundaries is 0.0013633818441228292, hence the corresponding H02 single-tailed
Sig (IEACt_lower < Hybrid_lower is 0.0006816909220614146, under 95% confidence
level the test is significance, so we reject the null hypothesis H02.
Similarly, the 2-tailed Sig (IEACt_upper ≠ Hybrid_upper) of two models’ upper
boundaries is 2.7602225137402837E-4, so the corresponding H03 single-tailed Sig
(IEACt_upper > Hybrid_upper) is 1.38011125687014185E-4, under 95% confidence
level the test is significance, so we reject the null hypothesis H03.
To observe the test results, it is found that our hybrid model outperforms the
traditional IEACt in both aspects of the means of point estimation and interval estimation,
especially for the interval estimation, in the former part of the project, our model could
achieve much more accurate interval estimation than IEACt does.
11. 412 Y. Li and L. Liu
Table 5 Paired t-test results of two model means
Paired differences
95% confidence
Std. Sig.
Std. interval of the t df
Mean error (2-tailed)
deviation difference
mean
Lower Upper
Pair 1 IEAC(t) – 1.936870 2.158306 .450038 1.003548 2.870191 4.304 22 0.000
Hybrid_forecast
Table 6 Paired t-test results of two model boundary means
Paired differences
95% confidence interval Sig.
Std. Std. error t df
Mean of the difference (2-tailed)
deviation mean
Lower Upper
Pair 1 IEAC_lo – –1.480217 1.937407 .403977 –2.318015 –.642420 –3.664 22 .001
Hybrid_lo
Pair 2 IEAC_up – 2.403217 2.667834 .556282 1.249559 3.556875 4.320 22 .000
Hybrid_up
5 Conclusions
In this paper, we propose a new hybrid model for project total duration forecasting With
the help of random number simulation and ANN non-linear fitting ability to simulate the
actual possible project performance combinations of EV, AC and ES, so as to better
forecast the performance factor SPI one step further to improve the traditional IEACt (in
which the latest SPI is regarded as PF of future unfinished part), then replace that of the
classic IEACt to forecast the total duration of the project. Forecasting results and tests
show that our hybrid method outperforms the classic IEACt in the both aspects of point
estimation and interval estimation. Of course, to make a proper T is not an easy task,
different projects due to their different changing trends of performance factor, T is
different; however, our model provides a new idea to better estimate the future
(especially the next one period) project performance index of SPI especially in the
beginning of a project when the true performance status indexes are scarce, which is also
the blind period of a project, because when the project approximates to an end, its
performance status is almost clear, and the forecasting for the total duration becomes less
significant. So our model provides a more effective SPI estimation method for the future
undone part of a project in its beginning period.
Of course our model is far from perfect, since it is build on a hypothesis that the three
main metrics: EV, AC, ES of the next one period fall in the range of normal random
numbers generated by their respective nearest T number of finished periods’ ones, if the
above three metrics change too sharply against their nearest T ones respectively, the
model may not perform well. From Figure 1, we could observe that the advantages of our
method are mainly highlighted in the former and middle part of the whole project, as to
12. Hybrid artificial neural network and statistical model 413
the final part, its prominent effect sharply decreases. This is because the normal random
numbers are a kind of simulation of possible actual combinations of performance status,
which is especially effective when the true performance indexes are scarce, with the
increase of true indexes this simulation becomes weaken; besides, when a project
approximates to its latter part, SPI tends to stabilisation, random numbers may disturb
this trend, under this circumstance, the traditional IEACt based on the average of all
history data could hit the bull’s-eye more easily.
Future work could further extend some research on the final part of the project, since
there are sufficient number of the performance indicators, we could employ a hybrid
method of time-series and EVM to have a try.
Acknowledgements
The research is supported by the National Natural Science Foundation of China under
Grant No. 90924020 and the PhD Program Foundation of Education Ministry of China
under Contract No. 200800060005.
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