DIRE DAWA UNIVERSITY

SCHOOL OF CIVIL ENGINEERING AND ARCHITECTURE

CONSTRUCTION TECHNOLOGY AND MANAGEMENT CHAIR

TIME-COST RELATIONSHIP ON PUBLIC BUILDING PROJECTS

(THE CASE OF DIRE DAWA CITY)

BY
ADINAN IDRIS
BEZA KIDANE
MESFIN HAILU
MIKIYAS TASEW
DEJEN G. HEWOT
EBRAHIM MEKONNEN

ADVISOR: YOHANNES H.

JUNE, 2022
DIRE DAWA
 DECLARATION
We hereby, declare this final Thesis report is the results of our work except as cited in the reference;
and compiled according to the Thesis report guideline given.

Name of the student: Adnan Idris Signature: _______ Date: __________

Name of the student: Beza Kidane Signature: _______ Date: __________

Name of the student: Mesfin Hailu Signature: _______ Date: __________

Name of the student: Mikiyas Tasew Signature: _______ Date: __________

Name of the student: Dejen G/hewot Signature: _______ Date: __________

Name of the student: Ebrahim Mekonnen Signature: _______ Date: __________

This final internship report has been submitted for examination with my approval as university
advisor.

Advisor Name : _________________ Signature: _______ Date: __________

…………………….

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 ACKNOWLEDGEMENTS

First of all, we would like to thank God for everything he has done for us and for the courage and
strength he gave us. We are also thankful to our advisor YOHANNES H. for his support and
guidance throughout our thesis.

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 EXECUTIVE SUMMARY
This research work has tried to test the time – cost relationship of road projects by using the
hypothesized empirical and graphical models developed for the concept. Based on the Empirical
Bromilow’s Model, the duration of Ethiopian Federal Road Construction Projects has been modeled
by a time - cost formula expressed in the form of T = KCB, where T is the actual construction time
in calendar days, C is the final cost of contract in Ethiopia Birr, K is a constant characteristic of time
performance, and B is a constant indicative of the sensitivity of time performance to cost level. This
thesis applied the relationship to 16 public building projects in Dire Dawa city.

Analysis using linear regression technique was performed between project duration (i.e., time), and
project cost, the analysis results indicated that the above principle is valid for the projects. In
addition, the research has developed a cost prediction model for the projects. T = 891.730.1023,
671.090.1305, and 1,377.040.1359 for Contracted Cost and Contracted, Actual Cost and Actual Time,
and Adjusted Actual Cost and Actual Time respectively

Key Words: Construction Management; Time - Cost relationship; Bromilow’s Principle

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 Contents
ACKNOWLEDGEMENTS ............................................................................................................... ii
EXECUTIVE SUMMARY .............................................................................................................. iii
List Of Tables .................................................................................................................................. vii
List of Figures .................................................................................................................................. vii
ACRONYMS .................................................................................................................................. viii
CHAPTER ONE ................................................................................................................................ 1
1. INTRODUCTION ...................................................................................................................... 1
1.1. Background of the study ..................................................................................................... 1
1.2. Statement of problem .......................................................................................................... 2
1.3. Research Questions ............................................................................................................. 3
1.4. Objectives of the Study ....................................................................................................... 4
1.4.1. General Objective ........................................................................................................ 4
1.4.2. Specific objectives ....................................................................................................... 4
1.5. Scope of the study ............................................................................................................... 4
1.5.1. Theoretical Scope......................................................................................................... 4
1.5.2. Geographical scope ...................................................................................................... 4
1.5.3. Sectoral scope .............................................................................................................. 4
1.5.4. Project stage Scope ...................................................................................................... 4
1.5.5. Variables scope ............................................................................................................ 5
1.6. Significance of the Study .................................................................................................... 5
CHAPTER TWO ............................................................................................................................... 6
2. LITERATURE REVIEW ........................................................................................................... 6
2.1. Theoretical Review ............................................................................................................. 6
2.1.1. Project Planning ........................................................................................................... 6
2.1.2. Factors Affecting Construction Duration................................................................... 10
2.1.3. Duration Estimation Modeling for Construction Projects ......................................... 13
2.1.4. Bromilow’s Time - Cost Model ................................................................................. 13
2.1.5. Effect of time on cost data of projects ....................................................................... 14
2.1.6. Adjustment for Inflation ............................................................................................ 15
2.2 Empirical Review .............................................................................................................. 16

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CHAPTER THREE ......................................................................................................................... 18
3. Research Methodology ............................................................................................................. 18
3.1. Study area and period ........................................................................................................ 18
3.2. Research Design ................................................................................................................ 18
3.3. Research Approach ........................................................................................................... 18
3.4. Data Type and Data Source ............................................................................................... 18
3.4.1. Secondary sources ...................................................................................................... 18
3.5. Data Collection Method .................................................................................................... 19
3.6. Target population .............................................................................................................. 19
3.7. Sampling Techniques ........................................................................................................ 19
3.8. Materials ............................................................................................................................ 19
3.9. Model analysis................................................................................................................... 19
3.10. Validation of BTC Model .............................................................................................. 20
CHAPTER FOUR ............................................................................................................................ 21
4. Data Presentation and Analysis ................................................................................................ 21
4.1. Data Summary ................................................................................................................... 21
4.2 Exploratory Analysis of Data.......................................................................................... 22
4.2.1 Correlation Test ............................................................................................................... 22
4.2.2 Analysis of Project Actual Cost and Time ...................................................................... 23
4.2.2.1 Actual Cost for Projects ................................................................................................ 23
4.2.2.2 Actual Time ............................................................................................................... 25
4.2.2.3 Correlation Analysis for Actual Cost and Time ........................................................ 26
4.2.2.4 Correlation analysis of unadjusted Actual cost /time ................................................ 26
4.2.2.5 Correlation analysis of Adjusted Actual Cost and Time ........................................... 27
4.2.2.6 Correlation analysis of Adjusted Contracted Cost and Actual Time ......................... 27
4.3 Regression Modeling ....................................................................................................... 27
4.3.1 Regression Analysis of Contracted Cost and Contracted Time ................................. 29
4.3.2 Regression Analysis for Actual Cost and Actual Time ............................................. 30
4.3.3 Regression Analysis for Adjusted Actual Cost and Actual Time .............................. 31
4.4 Checking the validity of Bromilow’s principle ............................................................. 34
4.2. Summary ........................................................................................................................... 37
CHAPTER FIVE ............................................................................................................................. 38

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5. Conclusion, and Recommendations ......................................................................................... 38
5.1. Conclusion......................................................................................................................... 38
5.2. Recommendations ............................................................................................................. 38
5.2.1. Recommendation for Future research ........................................................................ 38
References ........................................................................................................................................ 40

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 List Of Tables
Table 1 1 1 Ethiopian Inflation Data................................................................................................ 16
Table 1.2 1 Yeong time - cost relationship of building projects in both Australia and Malaysia ... 17
Figure 4.1 1 Scatter Plot for Linear Regression Analysis of Ln (CC) and Ln (CT) ....................... 29
Table 4.2 1 Correlation coefficients of Contracted time/cost .......................................................... 22
Table 4.3 1 Correlation coefficients of Actual Time/Cost ............................................................... 22
Table 4.4 1 Actual cost of projects .................................................................................................. 23
Table 4.5 1 CPI data of Ethiopian Construction Industry ................................................................ 24
Table 4.6 1 Summary of Adjusted Contract and Actual Cost.......................................................... 24
Table 4.7 1 Summary of time variation from selected projects ....................................................... 25
Table 4.8 1 Correlation coefficients of Unadjusted cost/ time ........................................................ 26
Table 4.9 1 Correlation coefficients of Adjusted cost/ time ............................................................ 27
Table 4.10 1 Correlation coefficients of Adjusted cost /time .......................................................... 27
Table 4.11 1 Transformed into ln function of AC, AC adj& AT ...................................................... 28
Table 4.12 1 Actual and Estimated AT for Contracted time and cost ............................................. 32
Table 4.13 1 Estimated time-cost relationship (Actual Cost) .......................................................... 33
Table 4.14 1 Estimated time-cost relationship (Adjusted Actual Cost)........................................... 33
Table 4.15 1Predicted and Actual Duration of Regression Analysis of Contracted Cost and
Contracted Time............................................................................................................................... 35
Table 4.16 1 Predicted and Actual Duration of Regression Analysis for Actual Cost and Actual
Time ................................................................................................................................................. 35
Table 4.17 1 Predicted and Actual Duration of Regression Analysis for Adjusted Cost and Time 36

List of Figures
Figure 1.1 1 Factors affecting construction project duration. .......................................................... 12
Figure 4.1 1 Scatter Plot for Linear Regression Analysis of Ln (CC) and Ln (CT) ....................... 29
Figure 4.2 1 Linear Regressions of Ln (AC) and Ln (AT) ............................................................ 31
Figure 4.3 1 Scatter Plot for Linear Regression Analysis of Ln (AC Adj) and Ln (AT) .................. 31

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 ACRONYMS
AC Actual cost

ADDSS Activity Duration Decision Support System

AT Actual Time

BTC Bromilow’s Time-Cost Model

BCDC Building Construction Duration Calculator

BCIS Building Cost Information Service

CC Contracted cost

CPI Construction price index

CPM Critical Path Method

DC Domestic Contractor

IC International Contractor

MAPE Mean Absolute Percentage Error

MLR Multiple Linear Regressions

PE Percentage Error

PERT Program Evaluation and Review Technique

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 CHAPTER ONE

1. INTRODUCTION

1.1. Background of the study

The primary purpose of construction project management is to complete the project on time, within
the budget and in accordance with the given technical requirements (Pewdum et al., 2009 as cited in
De Marco and Narbaev, 2013). Adequate prediction of construction time is of great importance in
contract administration because predicted project duration and cost form the basis for budgeting,
planning, monitoring and even litigation purposes.

In order to reduce overruns and delays, project managers should use effective tools and techniques
to monitor project status during the construction stage (Fleming and Koppelman, 2006 as cited in
Abdul-Rahman et al., 2011). Effective control of project progress is very important for later
successful delivery of construction project (Turkan et al., 2013).

This trend seems to be in its edge in Ethiopia as most off projects are found to be delayed relative
their planned time. Stakeholders in the construction industry make use of the traditional way of
project control. This method seems to inaccurate and limit the view that stakeholders have to the
indicators to be involved in decision making. (Researchers, 2022)

The traditional way involves comparing the planned and realized values, which does not always
have to be an accurate project performance indicator. If the project takes place according to the
schedule, it does not have to mean that the project costs are within the planned budget. In order to
establish a comprehensive project performance control, all volume, time and cost indicators need to
be integrated and calculated as interdependent sizes (Katić and Duspara, 2014).

In order to reduce overruns and delays, project managers should use effective tools and techniques
to monitor project status during the construction stage (Fleming and Koppelman, 2006 as cited in
Abdul-Rahman et al., 2011). Effective control of project progress is very important for later
successful delivery of construction project (Hegazy, 2002 as cited in Turkan et al., 2013). No matter
how good a project design is, if there is no regular and timely control during project execution, it is
impossible to evaluate project progress and effectiveness of the plan (Cleland and Ireland, 2007 as

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cited in De Marco and Narbaev, 2013). Feedback enables project managers to identify issues in early
stage and make the necessary adjustments, which is crucial to later project success.

Construction projects make use of common planning and controlling tools,; similar as Bar charts,
Critical Path Method (CPM), and Program Evaluation and Review Technique (PERT). The
disadvantage associated with these techniques is that they require preparation of fully detailed
construction projects and periods to implement. To ensure effectiveness using these techniques
require experiences and knowledge in planning and implementation. Different models lately
becoming available to overcome such lengthy processes associated with techniques. These models
allow prediction of construction duration on the basis of reliability and practical ways. These models
help contractors to use project characteristics briefed in the tender documents to estimate the time to
be taken in completing overall construction works.(ELVAN ODABAŞI, 2009)

Construction duration models arestatistical data based and represent the true picture which shows
the reliability of these models. There exist different types of models similar as Bromilow’s Time-
Cost Model (BTC), Building Cost Information Service (BCIS) Model also called the Building
Construction Duration Calculator (BCDC), the Simple Linear Regression (SLR) Analysis and the
Multiple Linear Regression (MLR).

This study will make use of Bromilow’s Time-Cost Model (BTC) in computation of construction
project duration for selected construction projects in Dire Dawa city. The researchers used chose
BTC model due to predictive accuracy of time-cost models was slightly better than parametric
models and it is the pioneer of duration estimation model in order to verify the presence of time and
cost relationship in the selected construction projects in Dire Dawa city.

Accordingly, the main purpose of this paper is to to develop time-cost model which can be used in
predicting construction project duration in construction building projects of Dire Dawa City. In
doing so, the study uses literature review as source in making analysis of the purpose of the study.

1.2. Statement of problem

Werkukoshe, K.N. Jha, (2016), studies investigating the causes of construction delay in Ethiopia,
showed that in Ethiopia only 8.55% projects have been finished to the original targeted completed
date. This is a huge indication that vast majority of projects in our country prone to delay and cost

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overruns. One of the major reasons for such delays is failing to have effective cost and time
estimation methods.

If projects didn’t complete in pre-specified period bring losses on the project contractors due to
escalated costs and penalties. Clients will also be part of such losses as their objectives of finishing
projects in the shortest possible couldn’t be met. Therefore, just as keeping a project within budget
and quality is important, so is the accurate estimation of construction duration for the successful
completion of a project. (ELVAN ODABAŞI, 2009)

Successful estimation criterion of project duration is an important for both the contractor and the
client. It enables the client in making financial, cash and material flow prior to the commencement
of the project in making appropriate funds to undertake the project. On the other side, the contractor
will be able to predict the construction accurately and performing construction tasks on time will be
helpful in having better advantages over the market. Consequently, the contractor will be in the
position to make appropriate decisions and less susceptible to delays.

Most construction projects in Ethiopia involve common planning and controlling tools like Bar
charts, Critical Path Method (CPM), and Program Evaluation and Review Technique (PERT). These
tools believed to have drawbacks as they involve complex procedures like preparation of fully
detailed construction project aspects and the period to implement each activity. Such a task requires
planner’s experience and knowledge and complex planning process. But the application of
estimation model for estimating construction project duration grants reliable and practical way of
estimation. Stakeholders will able to use projects characteristics in illustrated in tender documents
to estimate the actual time and cost it takes to complete the construction project.

The study will make use of BTC time cost relationship model which the pioneer model and will
allow to identify the time cost relationship presence in th projects understudy and develop the best
possible time cost estimation model accordingly.

1.3. Research Questions

• To identify the presence of a time - cost relationship for building projects in Dire Dawa City.
• To check the applicability of Brimelow’s time-cost relationship principle for Dire Dawa
Administration public building projects.
• To compute construction project duration -cost using BTC time model.

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 • To give a recommendation for project duration on estimation depending developed model

1.4. Objectives of the Study

1.4.1. General Objective
The main objective of this study will be to develop time-cost model which can be used in predicting
construction project duration in construction building projects of Dire Dawa City.

1.4.2. Specific objectives

• To check the applicability of Bromilow’s time-cost relationship principle for Dire Dawa
Administration public building projects.
• To compute construction project duration -cost using BTC time model.
• To give a recommendation for project duration on estimation depending developed model

1.5. Scope of the study

1.5.1. Theoretical Scope
Theoretically, the study will develop a model on the basis of time-cost relationship which will be
helpful for the stakeholders in estimating construction project duration. In doing so, the study will
identify the factors that should be considered in development of the model

1.5.2. Geographical scope

The study will be undertaken in Dire Dawa city. Construction projects in Dire Dawa city will be
targets of the study in assessing their past experience of project cost and duration estimation. Project
managers, contractors, consultants, and financial managers and other officials who have direct
relationship with the subject matter will be participants of the study.

1.5.3. Sectoral scope

There are various building projects being undertaken in Dire Dawa city from different sectors and
purpose. This study will be conducted on public building projects.

1.5.4. Project stage Scope

This study will mainly focus on projects those are fully completed or projects those have > 85%
completion status.

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 1.5.5. Variables scope
It is obvious that there are various variables which may affect project duration but in this study the
researchers will only consider project cost variable as a factor that hinder on time completion of
public building projects.

1.6. Significance of the Study

The increasing expansion of technology together with the development of multiple processes made
construction industry to become dynamic. Uncertainties are also becoming the common feature of
the construction industry due to its dynamic nature. The more complex the construction process
become more variables impact the effective completion of the construction building projects. In this
regard effective completion of this paper will be expected to deliver the following significant
benefits;

• Primarily, the study will help stakeholders in Dire Dawa city to be introduced to the adoption
of time-cost relationship model and the benefits associated.
• The study will motivate stakeholders’ in terms of having effective construction duration
estimation model and deployment of this model.
• It helps project managers to identify the accuracy that this model could deliver to their
project.
• The study will help contractors in minimizing and if possible in avoiding or may be deal with
delays in the projects.
• The researchers will be significantly benefit in acquiring further concepts related
construction project duration estimation which will be useful input for future career.
• The study could be used as a reference for those with intention of making further studies on
the subject matter.

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 CHAPTER TWO

2. LITERATURE REVIEW
2.1. Theoretical Review
2.1.1. Project Planning
Construction project time performance has long been identified, together with cost, quality and
safety as one of the four main critical success factors in any construction project (Johansen and
Wilson (2006)). The initial planning framework of a project, including contractor commitment to
the overall construction timescale, is set during the preconstruction ‘first planning’ period. Adequate
preconstruction planning is therefore recognized as essential to limit potential for later construction
delays and cost overruns. However, many recent industry initiatives while recognizing the need for
accurate planning at the strategic level have resulted in much focus upon improving site-based
construction planning (Johansen and Wilson (2006)). This, of course is after the contractor has
irretrievably committed to a contractually binding construction project timescale. The production of
feasible preconstruction and project master plans is essential to achieve later success during the
construction phase and any failure in producing this can affect both the client’s and contractor’s
success and negate or neutralize any successful onsite planning.

This is critically important in Ethiopia construction industry because, the Government of Ethiopia
waived the use of completion time and allowed low evaluated cost award system for tender
evaluation in 1993 (Wubishet (2004)). Accordingly, Section 1 presents subject to the Ministry's
approval, the consultant shall estimate a reasonable time for the completion and announce the same
on invitation to bid and the estimated time for completion should satisfy the interest and schedule of
the client. This simply meant that time planning for bid and subsequent construction process were
decided ahead of time or at the preplanning period (Wubishet (2004)).

There is an increasing need for prediction of construction time at planning and bid preparation stages
for including realistic project duration in the bid package. It represents a problem of continual
concern and interest to both researchers and contractors. It is also important for the studies related
to estimating, scheduling, and management of construction works taught both at the graduate and
undergraduate levels in the schools of construction science.

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Construction planning is aimed at making effective use of space, people, materials, plant,
information, access, energy, time and money in order to achieve the set project objectives and is
made up of four main parts: (1) programming and scheduling; (2) method statements; (3)
organizational systems; and (4) site set-up and layout (Gidado, 2004 cited by Johansen and Wilson
(2006)). These four parts are interdependent both with one another and also with the environment
surrounding the project, while the planning strategies proposed are ‘refined’ by considering the
financial and physical constraints imposed with the aim being to implement reliable cost, time,
quality and safety plans.

The term ‘first planning’ as applied in this study describes the initial construction planning which
takes place during the preconstruction phase of a project. Depending upon the specific procurement
methodology employed, this may take the form of informal strategic planning advice, direct
negotiation or competitive bid tendering and also encompasses the development of the project master
construction program. Preconstruction planning efficiency has been identified as of crucial
importance in the successful delivery of any project (Dvir et al., 2003; Gidado, 2004; Waly and
Thabet, 2002 cited by Johansen and Wilson (2006)).

During preconstruction, planners add value by attempting to ensure that planning is based on a robust
understanding of the methods, time and space required to carry out tasks while also identifying and
communicating the potential risks involved (Kelsey et al., 2001 cited by Johansen and Wilson
(2006)). Their output can be highly influential in demonstrating the contractor’s competence when
tendering for projects not awarded purely on financial criteria (Winch and Kelsey, 2005 cited by
Johansen and Wilson (2006)) and set the initial planning framework for later development. An
additional concern for first planning is the quality of the planning of design work and its input into
the master plan. The levels of concern over this depend, in part, on the procurement method and
whether the problem is viewed from the client’s or the contractor’s point of view. It could be
considered that the contractor is less concerned with this in traditionally tendered projects where
design is meant to be substantially complete before they are involved in the project.

For the contractor, plans are used for cost estimating and cash flow forecasting of the project at the
tendering stage (Odeyinka and Lowe, 2001 cited by Johansen and Wilson (2006)) and if the agreed
project duration is too short then time-based tender items priced in accordance with the periods
shown in the programme may be undervalued and result in consequential financial loss (Laptali et

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al., 1997 cited by Johansen and Wilson (2006)) and/or liquidated damages arising on late completion
(Farrow, 1984 cited by Johansen and Wilson (2006)).Pre – contract determination of the construction
duration is essential for proper cash flow forecasting by both the contractor and the client. From the
contractor’s point of view, it facilitates optimal resource allocation, financial planning, profitability
and efficiency of capital flow within a predetermined time limit. An enhanced certainty of the time
frame also assists the client’s own financial planning and contractor selection.

There is a divergence of research opinion as to the efficacy of detailed front-end construction

planning (first planning) and its use for strategic or tactical purposes. Johansen and Wilson (2006),
considered the challenge of delivering the construction stage and the relationship between first
planning and successful project delivery. They viewed the contrasting perspectives of office- and
site-based staff upon the accuracy of project timescales together with their dissimilar methods of
program development and preferred first planning detail level. They concluded that there is a
divergence in both literature sources and industry practices and is mainly caused by the differing
approaches of those who produce first plans and those who deliver the project. Unless there is
mechanism to amend this difference, construction planning will resume being inefficient.

A review of the literature suggests that there are a number of issues that affect the worth and
usefulness of first planning. During the preconstruction stage, planning decisions are made at the
macro-level and are mainly concerned with design review, site investigation, selection of the
construction sequence and procurement of the major elements required for the execution of the work.
It is considered essential to create preconstruction and project master plans that are feasible as their
overall reliability and achievability is deemed a prerequisite for later success during the construction
phase (Miyagawa, 1997 cited by Johansen and Wilson (2006)). Ballard (2000b) cited by Johansen
and Wilson (2006) termed this process ‘front end’ planning. However, Ballard (2000a) cited by
Johansen and Wilson (2006) also suggested that the traditional way of using this front-end planning
in construction can be considered the ultimate source of ‘schedule push’ in many projects. This
‘pushing’ of the plan is seen as a key factor in the perceived lack of success in achieving project
time certainty and time to complete.

Laufer and Tucker (1988) cited by Johansen and Wilson (2006) also concluded that detailed planning
of activities to be carried out far into the future adds production and monitoring cost, hinders a clear
overview of the project and is generally futile owing to uncertainties which cannot be quantified and

8
they recommended that first planning be at the lowest level of detail possible. Ballard (2000b) agreed
that the main purpose of ‘front end’ planning is to demonstrate the feasibility of the overall project
duration and does not require a high level of detail, while Ballard and Howell (2003) cited by
Johansen and Wilson (2006) highlight the potential waste and early obsolescence in proceeding with
early detailed planning. These views contrast with Gidado (2004), who recommended that more
detailed planning is required to improve preconstruction planning efficiency.

Burrows et al. (2004) cited by Johansen and Wilson (2006) reported that the 2003 national key
performance indicators (KPIs) demonstrated that the industry’s ability to predict the time a building
will take to construct is significantly worse than its ability to predict how much it may cost, with
some 25% of projects experiencing increased costs over the construction period, but with nearly
40% overrunning their originally contracted timescale. In practice, the ability to estimate the
completion time is often considered a matter of individual intuition, and its reliability really depends
on the skill and experience of the planning engineer. Despite the use of planning and programming
methodologies in the feasibility study phase, a reliable estimate of the duration of a construction
project is rarely easily formulated at the outset.

Research by Johansen and Wilson (2006) confirmed that many contractors view their own plans as
likely to be unachievable. Kelsey et al. (2001) suggested that systematic review of completed
projects to improve planning are in fact rare; claiming planners tend not to refer to past job records
as they are either non-existent or considered inaccurate and that those who could potentially
contribute most to this process have the least motivation to expose their own errors. Johansen and
Porter (2003) cited by Johansen and Wilson (2006) highlighted the need for improved subcontractor
planning competence, their increased input and closer involvement in the planning process and the
availability and distribution of accurate subcontract trade performance output and resource data.

Winch (2002) cited by Johansen and Wilson (2006) proposed that overall project Programme
methodology is often effectively formed during the tender or preconstruction period and quickly
becomes enshrined within the master construction Programme; therefore, subsequent programs
developed to actually manage the project are constrained by decisions often made in haste during
preconstruction

One other area of interest is the use of predictive models to assist planning. Johansen and Wilson
(2006) stated that the potential use of predictive models to estimate project duration was not initially

9
familiar to the industry professionals and indicated that the model is either in its extreme infancy
(although, as the Nedo study was published some 18 years ago, this appears unlikely) or
alternatively, has perhaps lacked sufficient publicity and exposure to many industry professionals to
date.

Though planners seem to be polarized against the use of predictive models, contractor’s project
managers are receptive to the model (Johansen and Wilson (2006)). It is surprising that planners are
negative to a concept which uses previous data where they are used to using previous data
themselves.

Thus, having detailed first planning is not that much useful as it is difficult to produce accurate plans
at a time when the uncertainties in project are not clearly identified (Johansen and Wilson (2006)).
And the promotion and use of predictive models shall be encouraged.

2.1.2. Factors Affecting Construction Duration

According to Chan and Kumaraswamy (1995) a range of significant factors influencing the duration
of a construction project are postulated hierarchically as illustrated in Figure 2.1, which is based on
the general international literature, observed common construction practice and survey results. These
factors include both qualitative and quantitative contributors. The construction duration can be
regarded as a function of all these hierarchical factors, that is, construction time = f (all the factors
in the hierarchy of Figure 2.1). The factors shown in Figure 2.1 can be reviewed into three levels
namely: Primary, Secondary and Tertiary levels. Primary factors include construction cost, type of
construction, location, stakeholder’s priorities, productivity, type of contract and post contractual
developments. Looking at for example post contractual developments at the secondary level, factors
like variation, and conflicts will be noticed. Detailing the variation factor even further will result in
the tertiary factors like magnitude, interference level and timing of the variation. Though they did
not identify a conclusive detail, productivity and factors affecting it have been determined as key
factors that can affect duration of construction projects.

Nkado (1995) stated that site productivity, which impliedly affect construction time, is affected by
buildability (which is not clearly defined), management and leadership, knowledge of
subcontractor’s work, the nature of the relationships between the general contractor, subcontractor
and client’s agent and the degree of coordination in design information and the completeness of
project information. Other factors include work space availability, attendance of operatives, learning

10
curve, weather, labour relations, project complexity, foundation condition and effectiveness of
supervision.

Walker (1995) stated that there are four factors that significantly affect construction time
performance. These are: Construction Management Effectiveness, Sophistication of Client and the
Client’s representative in terms of creating and maintain a positive project team relationship with
the construction management and design team, Design team effectiveness in communicating with
construction management and client’s representative teams, and a small number of factors
describing project scope and complexity.
Kumaraswamy and Chan (1995) studied determinants of construction duration by using data from
111 questionnaire responses. The results indicated that the factors affecting construction durations
are the same as has been identified by the trio on Chan et al (1995).
Nkado (1995) also stated that from the system viewpoint, the construction project can be
distinguished from the environment in which the project takes place. Sidwell (1982) cited by

Nkado (1995) opined that the environment describes all external influences on the building process.
Walker (1980) enumerated factors in the environment which can affect the construction time, cost
and quality performance of a project as legal/political, institutional, cultural/sociological,
technological ad economic/competitive. Huges (1989) added to the list aesthetic, financial and
physical factors.

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 Figure 1.1 1 Factors affecting construction project duration.
According to Farzard (1984) the following additional factors reflect the environment of developing
countries, educational, natural resources, industry, religious and demographic factors (Nkado
(1995)). Chan (1999) tried to develop other influencing factors of construction durations.
CitingIreland (1983), Sidwell (1982), and Nkado (1995) Chan (1999) stated that cost or project value
is the most important one and the other factors affecting can be assessed explicitly.

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In summary the factors affecting construction durations are Project Scope (measured by Cost or
Value), Type of Construction, Location, Productivity, Type of contract, Post Contractual
development, Construction Management Team Effectiveness and Environmental Factors.

2.1.3. Duration Estimation Modeling for Construction Projects

A time cost model is useful for all parties associated with the construction industry to predict the
mean time required for the delivery of a project, when the cost of the project is known. It provides
an alternative and logical method for estimating construction time, both by bidders and clients, to
supplement the prevailing practice of estimation predominantly on individual experience. The study
will hopefully generate enough interest to do further research for deriving models for time-cost
relationships of construction projects in other sectors and in construction industries in different
regions. Developing time-cost relationship models for different construction industries will have a
far-reaching effect on both national and international competitive bidding.

According to Kaka and Price (1991), the need for evaluation of performance of building contracts
arose in the late 1960s. In 1967, the Commonwealth Scientific and Industrial Research Organization
undertook a pilot study on the performance of building contracts. This was the first step in a larger
programme of research into the structure of the building industry. The results published in the
Annual Report of the Division of Building Research (1968) showed that the extent of change, as
measured by construction duration, cost, number and value of variations was in fact larger than had
previously been supposed. A fuller investigation, using a larger number of projects, was
subsequently performed. In 1969, Bromilow published the results, and the first relationship between
cost and duration of building contracts appeared.
This research is mainly based on the application of this model for the Dire Dawa Public
BuildingsConstruction Projects, thus a detailed literature review is carried out and summarized as
follows.
2.1.4. Bromilow’s Time - Cost Model
As mentioned above, the idea of a possible relationship between the realization cost and the construction
duration of projects was first proposed and researched by Bromilow [2]. In his study in 1969, Bromilow
examined the time-cost relationship of 328 superstructure projects in Australia. This model was subsequently
updated by Bromilow et al. (1980). The equation describing the relationship can be stated as:

13
 T=KCB

Where: T = duration of construction period from the date of possession of site to substantial completion in
days
C = completed cost of project in millions of Australian dollars adjusted to constant labor and material prices.
K = a constant indicating the general level of time performance per million Australian dollars and
β = a constant describing how the time performance is affected by the size of the construction projects
measured by the cost.
This model indicates that one factor (scope of the project as measured by construction costs in 1972 Australian
dollars) principally determines construction time. This model was a function of the cost C of the project. A
total of 329 building projects with a total value exceeding 270 Million Australian dollars (A$) were analyzed.
These projects were conducted in Australia during the period between June 1964 and June 1967.The
relationship may be summarized (Bromilow, 1974) as:
T = 313 C0.3

Bromilow made use of mathematical models to show the relationship between cost and time, variations, and
preconstruction time. These provided norms for the speed of the building process and the occurrence of
variations. He also analyzed overruns on time and cost, which provided a measure of the accuracy of the
industry’s time and cost prediction. Effect of time on cost data of projects
2.1.5. Effect of time on cost data of projects
Estimates for construction work are produced at a specific point in time and the prices used therein are (unless
other parameters are specifically set) relevant only for that date. This is because prices for items supplied and
work undertaken are continually subject to market forces. These forces arise from two main directions:
Inflation (and potentially and alternatively, ‘deflation’) and the ever-changing relationship between supply
and demand for construction in the market place.

Major Projects Team (2006), the driver for price increases in respect of both of the above is primarily related
to supply capacity relative to demand. In the case of inflation, the effect is at a macro level, generally affecting
the whole economy. In an economist’s term, inflation is often described as ‘too much money is chasing too
few goods’ – demand itself being ineffectual unless the capacity to purchase is also present. In the case of
basic supply and demand, this can have a significant effect on construction prices in various ways.

Major Projects Team (2006), thus estimates and previous costs at completion times need to be properly
adjusted in order to provide meaningful figures. The adjustments are usually carried out to cover for effect of
inflation and change in tender price index. The adjustment for inflation can be carried out by taking the
average inflation rate which is usually based on the change of the consumer price index. According to the

14
practice in UK, the adjustment for change in tender price index is carried out by adjusting the prices by the
tender price index developed and index in each year. However, this has not be practiced in Ethiopia as the
tender price index is not developed by the Central Statistical Authority of the country.
2.1.6. Adjustment for Inflation

Considerations shall be taken for effects of inflation on cost comparisons (Congressional Research Service
(2003)). In Ethiopian Economy where the market is not fully indexed for inflation, the effect of inflation shall
be carefully considered. The inflation rate of Ethiopia is assumed to be high (Index of Economic Freedom,
Ethiopia, (2007)).

Hazlitt (1965) No subject is so much discussed or so little understood as inflation. The definition of Inflation
can be traced as follows: According to the American College Dictionary, the first definition of inflation is
given as follows: "Undue expansion or increase of the currency of a country, esp. by the issuing of paper
money not redeemable in specie."

In recent years, however, the term has come to be used in a radically different sense. Hazlitt 1965, this is
recognized in the second definition given by the American College Dictionary: "A substantial rise of prices
caused by an undue expansion in paper money or bank credit." Now obviously a rise of prices caused by an
expansion of the money supply is not the same thing as the expansion of the money supply itself. A cause or
condition is clearly not identical with one of its consequences. The use of the word "inflation" with these two
quite different meanings leads to endless confusion. Hazlitt (1965) strongly argues that the true cause of
inflation is inflated money at the hand of the consumer or the increase in debt by the government not by the
increase in price. He suggested that the solution for inflation can not be price fixing as inflation is not caused
by increase in price.

Major Projects Team (2006), the rise in the general level of prices, the essence of inflation, is measured by
using a price index. Ideally, the price index used should be broad based and one in which the individual prices
are weighted to indicate their importance to the economy. Three separate price indexes can be used. The first
two are very broad based and derived from the measurement of the Nation’s gross domestic product (GDP).
They differ in the quantities that are used to weight the prices. The first uses side-by-side year quantities (that
move every year) and is called, the chain weight deflator. The second uses current year quantity weights and
is called the implicit price deflator. The third index is the Consumer Price Index (CPI), which prices a “market
basket” of goods and services purchased by an urban family, a market basket whose individual items are
weighted by how much the urban family spent on them in a base year period currently 1994 -2007.

15
The inflation data for Ethiopia, shown in Table 4 – 6 below, has been obtained from IMF's International
Financial Statistics CD-ROM (International Monetary Fund (2006)) but since the data for the latest two years
were not on IFS, the inflation data for the last two years was taken from the African Economic Outlook (2008)
(forthcoming) Master data file, and interpolated through linear regression the figures for CPI. There is no
reason to believe that the data generated by the process is faulty.
Table 1 1 1 Ethiopian Inflation Data

Year CPI % Year CPI %

1994 7.59 2001 -8.24

1995 10.02 2002 1.65

1996 -5.07 2003 17.76

1997 2.40 2004 3.26

1998 2.58 2005 11.61

1999 7.94 2006 10.10

2000 0.66 2007 17.80

(Source: International Monetary Fund (2006) & African Economic Outlook (2008))

Accordingly, the research cost data collected for both the international and domestic contract and final
amounts have been adjusted to January, 2008.

2.2 Empirical Review

Mensah (2010), in a bid to estimate project duration in Ghana, adopted the Bromilow’s time cost model and
found that it is applicable to donor funded feeder roads projects in Ghana. This prompted the need to ascertain
the suitability of the model to building projects in Ghana.

Kaka and Price (1991) used the time-cost model for both civil and building projects and indicated that the
original model, as introduced by Bromilow (1969), remained unchanged but the coefficient of the equation
changed with the project type.

Ng et al. (2001) found that unit construction periods developed positively over time, when compared to
previous findings in Australia, and they attributed this improvement to increased productivity in construction
projects over time after Bromilow's study.

Kumaraswamy et al. (1995) conducted a study by using the BTC model on the 111 projects in Hong Kong.
They analyzed these projects in the data set under public and private sub-groups. They confirmed the usability
of the model proposed by Bromilow. On the other end Hoffman et al. (2007) focused on the Air Force-

16
financed facility projects and indicated that the BTC model represents the data set to a large extent, and they
suggested that the BTC model can be used in order to determine time-cost relationship.

Bayram (2017) investigated the completion period of the public buildings, consisting health and educational
buildings, in Turkey using both Bromilow’s time-cost (BTC) and Love's Time - Floor (LTF) models. The
researcher concluded that the BTC model is superior to the LTF model, stating that "cost" is a more significant
predictor of duration than number of floors and total floor area.

Odabaşı (2009) examined the construction projects, consisting 7 educational buildings, carried out between
2004 and 2007 at the Middle East Technical University Campus and the factors affecting the construction
time. Odabaşı has suggested that the BTC model can be used in predicting time cost relationship in
construction projects.

Yeong (1994) studied the time - cost relationship of building projects in both Australia and Malaysia. Based
on 67 Australian government projects, 20 Australian private projects and 51 Malaysian government projects,
Yeong’ s study confirmed the Bromilow’ s model at the 0.00 level of significance and that the time-cost
relationships of the various projects could be represented by the following equations.

Table 1.2 1 Yeong time - cost relationship of building projects in both Australia and Malaysia
Project Type Equation
Australian private projects: T = 161C0.367
Australian government projects: T = 287C0.237
All Australian projects: T = 269C0.215
Malaysian (government) projects: T = 518C0.352

As per the knowledge of researchers the only study on time-cost relationship made in Ethiopia has been made
by Abrham (2008) on construction road projects. The study has been made on 33 projects has based on the
two categories International Contractor (IC) and Domestic Contractor (DC) Projects and on the adjusted and
unadjusted cost basis. According to the findings of the study the Bromilow’s principle has been found to
invalid for DC projects, the relationship between contract Time and length has been developed. In addition
the research has developed a cost prediction model for IC projects.

17
 CHAPTER THREE

3. Research Methodology
3.1. Study area and period
The study was be conducted in Dire Dawa city. Selected public construction building projects with
completion rate of 85% or above and projects which has been completed in the last 2 years was be
subject to this study. The study was be conducted from April – June, 2022.

3.2. Research Design

Th study employed explanatory study type to find out the relationship between the relationship
between time and cost. Additionally, the study also made use of descriptive study type as it tries to
describe the relationship by systematically viewing the problem and undoubtedly seeks for the
variations in between the contracted and actual construction time and cost for public building
construction projects in Ethiopia. So, the research adopted both descriptive and explanatory study
types.

3.3. Research Approach

In terms of approach a research can be divided into qualitative and quantitative. Quantitative research
method involves a numeric or statistical approach to the research. Aiming to achieve the objectives
of the study, quantitative method has been employed. Quantitative data was used in computation
BTC model for projects under study as it involves quantifying the relationship of two variables i.e.
time and cost.

3.4. Data Type and Data Source

The study used data from secondary sources.

3.4.1. Secondary sources

Appropriate secondary data examined from respective Projects documents/publication and reports
produced books, literatures, websites (internet) and available source for conducting the research.
Most of all data related to the public building projects under study was obtained from the officials
of respective construction projects, Dire Dawa City Administration Construction Bureau, Urban
Development & Construction Bureau of Dire Dawa Administration, and Construction Projects
Regulatory Authority Bureau.

18
 3.5. Data Collection Method
The method of data collection is by collecting the secondary data. The number of full data 16 projects
during the period from 2011-2014. The collected data involves commencement date, budget plan
(agreed contract amount), agreed contract duration, completion status, actual amount, and actual
duration.

3.6. Target population

This research has selected 16 projects as a subject for the study on time-cost relationship model
development. The researchers will allow all projects to be part of the study as it is small number to
take sample size from.

3.7. Sampling Techniques

By taking in to consideration the focus given on the subject matter the researchers chose purposive
sampling technique to allow participation of project which are completed in the last two years and
have completion rate of 85% or above to better fit model computation.

3.8. Materials
Data of 16 projects under study will be analyzed. Data of actual durations will be used in this study.
Their data such as: durations (contract duration, actual duration, and effective duration), contract
cost, detailed cost, reason of delay, etc.

Two types of durations have been identified in this study, which are:

1. Contract Duration which is the duration given by the client, here contract duration included all
the days as working days.
2. Actual Duration was the time taken from start to finish, actual duration includes the duration
extensions but not nonworking days (nonworking season)
Data for the contract and actual durations was obtained and that for variation duration was calculated
to be used in the models for comparing the results.

Detailed costs have been used in the models. The researchers have adoptedconsumer price index of
Ethiopia as specific construction price index is unavailable by the authorities.

3.9. Model analysis

For statistical verification of the time-cost relationship, the equation has been rewritten in the natural
logarithmic form for calculating using Microsoft Excel.

19
 Ln (T) = Ln (K) + B*Ln (C)
Where,
Y = Ln (T)
x = Ln (C)
α0 = Ln (K) and
α1 = B;
Simple linear regression equation is provided by double log form to convert the nonlinear model to
linear model.

3.10. Validation of BTC Model

The mean absolute percentage error (MAPE) method was used to find the closeness of fit to the
model.

To evaluate the closeness of fit of the model, Percentage Error (PE) for the comparison of actual
durations and predicted durations is defined as follows:

𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 – 𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛

PE = 𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛

The validity of the model will be tested by comparing the actual values with predicted values. The
mean absolute percentage error (MAPE) method was used to test the reliability of the model, using
the following equation;

1 (𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛)𝑖 – (𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛)𝑖

MAPE = 𝑛 ∑𝑛𝑖=1 (𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛)𝑖

20
 CHAPTER FOUR

4. Data Presentation and Analysis

4.1. Data Summary
The study was made on 16 public building projects in Dire Dawa city. Summary of the basic data
for the projects is detailed in the table below.

Table 4.1 1 Data List of Projects

Object Commen Contracted Actual Contracted Actual cost Time Cost

cement time time cost Overrun Overrun
date (%) (%)
1 2008 E.C 525 745 15,554,012.92 22445163.42 70.5% 69.3%
2 2009 E.C 720 1500 206,556,488.53 244758868.4 48.0% 84.4%
3 2008 E.C 480 900 12,321,785.01 20034358.36 53.3% 61.5%
4 2009 E.C 365 925 10,162,368.56 18391020.54 39.5% 55.3%
5 2008 E.C 480 880 12,327,201.75 16432735.1 54.5% 75.0%
6 2009 E.C 420 940 35,407,923 47903182.5 44.7% 73.9%
7 2008 E.C. 420 910 14,508,973.70 20123949.82 46.2% 72.1%
8 2009 E.C. 480 700 15,478,774.24 17996858.33 68.6% 86.0%
9 2008 E.C. 720 1920 163,515,745.41 281320061.9 37.5% 58.1%
10 2010 E.C. 420 1420 143,000,000 165000000 29.6% 86.7%
11 2010 E.C. 420 1000 36,000,000 47410772 42.0% 75.9%
12 2008 E.C. 540 1840 57,413,677.20 103208419.6 29.3% 55.6%
13 2009 E.C 420 620 10,199,138.15 12803580.17 67.7% 79.7%
14 2009 E.C. 285 789 197,131,013.10 243,583,989.57 36.1% 80.9%
15 2009 E.C. 370 898 381,611,333.10 482,156,093.60 41.2% 79.1%
16 2009 E.C. 440 988 542,295,166.40 628,332,681.33 44.5% 86.3%

Source: Own Data, 2022

21
 4.2 Exploratory Analysis of Data

4.2.1 Correlation Test

The researchers conducted correlation test to identify the dependent and independent variable of the
two identified variables i.e. time and cost. In this regard, the result for Pearson correlation for time
and cost has been displayed as follows;

Table 4.2 1 Correlation coefficients of Contracted time/cost

Variables
Variables Contracted Time/Cost
Time Cost
Time 1 -0.01627
Cost -0.01627 1
Source: Own Data, 2022

Table 4.3 1 Correlation coefficients of Actual Time/Cost

Variables
Variables Actual Time/Cost
Time Cost
Time 1 0.5906
Cost 0.5906 1
Source: Own Data, 2022

Based on the results from Pearson correlation of the above table, the researcher only used the result
from the actual time and cost as the relationship between time and cost has been significant and
positive. From this, it is possible to take cost as independent variable as there exists a better
correlation among time – cost for selected 16 projects in Dire Dawa city.

22
4.2.2 Analysis of Project Actual Cost and Time

4.2.2.1 Actual Cost for Projects

Table 4.4 1 Actual cost of projects

Project Contracted Cost (ETB) Actual cost % of Actual Cost

code/No.

1 15,554,012.92 22445163.42 69.3%

2 206,556,488.53 244758868.4 84.4%

3 12,321,785.01 20034358.36 61.5%

4 10,162,368.56 18391020.54 55.3%

5 12,327,201.75 16432735.1 75.0%

6 35,407,923 47903182.5 73.9%

7 14,508,973.70 20123949.82 72.1%

8 15,478,774.24 17996858.33 86.0%

9 163,515,745.41 281320061.9 58.1%

10 143,000,000 165000000 86.7%

11 36,000,000 47410772 75.9%

12 57,413,677.20 103208419.6 55.6%

13 10,199,138.15 12803580.17 79.7%

14 197,131,013.10 243,583,989.57 80.9%

15 381,611,333.10 482,156,093.60 79.1%

16 542,295,166.40 628,332,681.33 86.3%

Source: Own Data, 2022

The costs listed above have to adjust to have more accurate estimation of inflation caused by lengthy
of duration. In doing so, researchers used CPI (Customer Price Index) value, the cost of both

23
contracted cost or actual cost and variation cost or actual variation cost were adjusted for inflation.
The researchers used CPI for the national construction industry.

𝐂𝐏𝐈𝟏 + 𝐂𝐏𝐈𝟐
Adjusted real cost = Actual cost *𝟏 + 𝐂𝐏𝐈𝟐

Where, CPI1 =refers to the index value at the contract date, and
CPI2= refers to the date at which the project costs are to be examined.
Table 4.5 1 CPI data of Ethiopian Construction Industry
Year CPI% Year CPI%

2004 3.256 2008 44.391

2005 12.944 2009 8.468

2006 12.31 2010 8.136

2007 17.238 2011 32.014

2012 23.378 2013 7.464

Spruce: https://fred.stlouisfed.org/series/FPCPITOTLZGETH
Table 4.6 1 Summary of Adjusted Contract and Actual Cost
(2013
at
Comm. Year

Percentage of
Adjusted cost
contract year

contract cost

actual cost
Adjusted

Adjusted
Current
Project

(E.C.)

E.C)
CPI

CPI
No.

1 2008 44.391 7.464 123613142.1 178379508.2 69.3%

2 2009 8.468 7.464 647453859.3 767199689.8 84.4%

3 2008 6.628 7.464 97925504.42 159220003.2 61.5%

4 2009 8.468 7.464 31854069.51 57646880.57 55.3%

5 2008 44.391 7.464 97968553.14 130596652.4 75.0%

6 2009 8.468 7.464 110986571.1 150153116 73.9%

7 2008 44.391 7.464 115307852.5 159932017.6 72.1%

24
 8 2009 8.468 7.464 48518408.64 56411374.26 86.0%

9 2008 44.391 7.464 1299516412 2235748225 58.1%

10 2010 8.136 7.464 441874598.1 509855305.5 86.7%

11 2010 8.136 7.464 111241157.6 146500809.9 75.9%

12 2008 44.391 7.464 456286430.6 820233151 55.6%

13 2009 8.468 7.464 31969324.24 40132979.86 79.7%

14 2009 8.468 7.464 617909590.4 763517017.7 80.9%

15 2009 8.468 7.464 1196165427 1511324218 79.1%

16 2009 8.468 7.464 1699830883 1969516534 86.3%

Source: Own Data, 2022

4.2.2.2 Actual Time

Summary of data related to project duration including contracted time, Actual time, and the
percentage AT has been organized in the following table.

Table 4.7 1 Summary of time variation from selected projects

Project No. Contracted Time Actual Time Time Variation % of Actual Time

1 525 745 220 70.5%

2 720 1500 780 48.0%
3 480 900 420 53.3%
4 365 925 560 39.5%
5 480 880 400 54.5%
6 420 940 520 44.7%
7 420 910 490 46.2%
8 480 700 220 68.6%
9 720 1920 1200 37.5%
10 420 1420 1000 29.6%

25
 11 420 1000 580 42.0%
12 540 1840 1300 29.3%
13 420 620 200 67.7%
14 285 789 504 36.1%
15 370 898 528 41.2%
16 440 988 548 44.5%
Source: Own Data, 2022

4.2.2.3 Correlation Analysis for Actual Cost and Time

The Pearson relationship coefficient(r) is utilized to test on the off chance that a straight relationship
exists between two factors. The relationship coefficient could be a f actual degree of the affiliation
between two numerical factors (Zikmund, 2003). The esteem of “r” ranges from +1.0 to -1.0, where
positive “r” esteem shows a coordinate relationship and a negative ‘r” esteem speaks to a reverse
relationship between two factors. When “r=0” it infers that there's no relationship between the two
factors. When “r=+1” it implies that there's ideal coordinate relationship between the variables.
When “r=-1” it infers that there's a culminate negative/inverse relationship between the factors.
When “r” is in between 0.10-0.29, it infers that variables have powerless connections and when “r”
esteem is in between 0.3-0.49, it infers that the variables have direct relationship. When “r” esteem
gets to be more significant or breaks even with to 0.5 it demonstrates the relationship is solid. The
relationship between cost and time were tried by employing a relationship analysis.

4.2.2.4 Correlation analysis of unadjusted Actual cost /time

Table 4.8 1 Correlation coefficients of Unadjusted cost/ time
Variables
Variables Time/Cost
Time Cost
Actual Time 1 0.5277
Actual Cost 0.5277 1
Source: Own Data, 2022

As it can be seen above, there is positive and significant relationship between actual variation in cost
and actual variation in time which is justified by the r = 0.5277.

26
 4.2.2.5 Correlation analysis of Adjusted Actual Cost and Time
Again here, the correlation analysis result shows very strong association between adjusted cost
variation and actual time variation registering a value of r = 0.5327.

Table 4.9 1 Correlation coefficients of Adjusted cost/ time

Variables
Variables Time/Cost
Actual Time Adjusted Actual Cost
Actual Time 1 0.5327
Adjusted Actual Cost 0.5327 1
Source: Own Data, 2022

4.2.2.6 Correlation analysis of Adjusted Contracted Cost and Actual Time

Table 4.10 1 Correlation coefficients of Adjusted cost /time
Variables
Variables Variation in Time/Cost
Actual Time Adjusted Contracted Cost
Actual Time 1 0.9403
Adjusted Contracted Cost 0.9403 1
Variations
Source: Own Data, 2022

The correlation table above yield a value of r = 0.9403. The same result i.e. positive and significant
relationship is obtained from correlation of variables for both adjusted and unadjusted Actual cost
and Actual time. These results indicate that there is a possibility to develop a model as there is a
positive relationship between time (construction duration) and cost (construction cost) of public
building projects in Dire Dawa city.

4.3 Regression Modeling

The researcher chose to utilize linear regression analysis to test existing relationship between
variables. The regression model is prepared from 16 public building projects as it has been identified
earlier. Additional time incurred by the projects under study has been used as Y-axis or dependent
variable whereas additional cost variation of these projects taken as X-axis or independent variable.

27
As it has been discussed in the above sections, first time-cost relationship model was developed by
Bromilow’s (1974) and later 1980 updated by Bromilow’s, et al. This model was expressed as;

T = KCß,

Which is non-linear form, and needs to convert into a linear in double–log form?

Ln (T) = Ln (K) + ß*Ln (C)

Where,
Y = Ln (T), x = Ln (C), α0 = Ln (K) and α1 = ß;
Then, Y = α0+α1*x
A simple linear regression technique was used to analyze the data. For the purpose of statistical
analysis of the data, Bromilow’s model was rewritten in the natural logarithmic form as shown in
the above equation.

Where, ln T = the natural logarithm of Time, ln C = the natural logarithm of Cost, ln K = the natural
logarithm of K, and ß = the coefficient of ln C.

Table 4.11 1 Transformed into ln function of AC, AC adj& AT

object Commencement Actual cost Adjusted Actual Ln of AC Ln of

date actual cost time AC Adj

1 2008 E.C 22445163.42 178379508.2 745 16.9265857 18.999

2 2009 E.C 244758868.4 767199689.8 1500 19.3157841 20.458

3 2008 E.C 20034358.36 159220003.2 900 16.8129593 18.886

4 2009 E.C 18391020.54 57646880.57 925 16.7273731 17.870

5 2008 E.C 16432735.1 130596652.4 880 16.6147859 18.688

6 2009 E.C 47903182.5 150153116 940 17.6846925 18.827

7 2008 E.C. 20123949.82 159932017.6 910 16.8174212 18.890

8 2009 E.C. 17996858.33 56411374.26 700 16.7057078 17.848

28
 9 2008 E.C. 281320061.9 2235748225 1920 19.4550036 21.528

10 2010 E.C. 165000000 509855305.5 1420 18.921456 20.050

11 2010 E.C. 47410772 146500809.9 1000 17.67436 18.803

12 2008 E.C. 103208419.6 820233151 1840 18.452261 20.525

13 2009 E.C 12803580.17 40132979.86 620 16.3652354 17.508

14 2009 E.C. 243,583,989.57 763517017.7 789 19.310972 20.453

15 2009 E.C. 482,156,093.60 1511324218 898 19.993778 21.136

16 2009 E.C. 628,332,681.33 1969516534 988 20.25858 21.401

Source: Own Data, 2022

The transformed result from the above table is used to compute linear regression model for both
adjusted and unadjusted costs.

4.3.1 Regression Analysis of Contracted Cost and Contracted Time

Figure 4.1 1 Scatter Plot for Linear Regression Analysis of Ln (CC) and Ln (CT)

Linear Regression of Ln (CC) and Ln (CT)

7
6
5
4
Ln (CT)

3 y = 0.1023x + 4.8437
R² = 0.1181
2
1
0
0 2 4 6 8 10 12 14 16 18
Ln (CC)

Source: Own Data, 2022

The scatter plot from the above figure shows that y-intercept or α1=4.8473 and the slope (α0) =
0.1023 and substituting these results in to an equation of natural logarithm;

29
Y = α0+α1*x, Then Y = 0.1023x + 4.8473, this equation equals the previous equation which is: Ln
T = ln K + ß ln C
Y = Ln (T), x = Ln (C), α0 = Ln (K) and α1 = ß;
Ln (K) = 4.8473, α1= 0.1023
Inverse of Ln (K) needs to be found and exponential function is used to represent the model in the
normal form.
K = e4.8473= 127.39weeks, or 127.39*7 days = 891.73days

T = KCß, form this, the equation the model for time-cost; T = 891.730.1023

4.3.2 Regression Analysis for Actual Cost and Actual Time

The scatter plot below shows that y-intercept or α1=4.0493 and the slope (α0) = 0.1191and
substituting these results in to an equation of natural logarithm;

Y = α0+α1*x, Then Y =0.1305x + 4.563, this equation equals the previous equation which is: Ln T
= ln K + ß ln C
Y = Ln (T), x = Ln (C), α0 = Ln (K) and α1 = ß;
Ln (K) = 4.563, α1= 0.1305
Inverse of Ln (K) needs to be found and exponential function is used to represent the model in the
normal form.
K = e4.563= 95.87weeks, or 95.87*7 days = 671.09days

T = KCß, form this, the equation the model for time-cost; T = 671.090.1305
Figure 4.2 1 Scatter Plot for Linear Regression Analysis of Ln (AC) and Ln (AT)

30
 Figure 4.2 1 Linear Regressions of Ln (AC) and Ln (AT)

Linear Regression of Ln (AC) and Ln (AT)

7.800
7.600
7.400
7.200 y = 0.1305x + 4.563
Axis Title

R² = 0.2879
7.000
6.800
6.600
6.400
6.200
0 5 10 15 20 25
Axis Title

Source: Own Data, 2022

4.3.3 Regression Analysis for Adjusted Actual Cost and Actual Time
Figure 4.3 1 Scatter Plot for Linear Regression Analysis of Ln (ACAdj) and Ln (AT)

Linear Regression of Ln (ACAdj) and Ln (AT)

8
7
6
5
4 y = 0.1359x + 5.2818
3 R² = 0.1618
2
1
0
0 2 4 6 8 10 12 14 16 18

Source: Own Data, 2022

Y = 0.1359x + 5.2818, this equation equals the previous equation which is: Ln T = ln K + ß ln C
Y = Ln (T), x = Ln (C), α0 = Ln (K) and α1 = ß;
Ln (K) = 5.2818, α1= 0.1359

31
Inverse of Ln (K) needs to be found and exponential function is used to represent the model in the
normal form.
K = e5.2818= 196.72weeks, or 196.72*7 days = 1,377.04days

T = KCß, form this, the equation the model for time-cost; T = 1,377.040.1359
Based on the results above, the researchers deduce the following interpretations

T = 891.730.1023, T = 671.090.1305, and T= 1,377.040.1359are the results for linear regression of

contracted cost, actual cost and adjusted cost respectively. The results imply that increment in actual
or contract cost causes construction time increment. The researchers found that public building
projects under study contract cost of one million require extra 891.73 days, actual cost of one million
takes 671.09 additional time, and on the other end adjusted cost of one million takes 1377.04 days
of extra actual time. This model fits in every project under study as it allows to predict extra time
required to complete the project having known the actual cost of construction project. Additionally,
the model facilitates suitable options and logical ways in estimating construction duration by
stakeholders.
Table 4.12 1 Actual and Estimated AT for Contracted time and cost

project Contracted Cß K Estimated AT in days

No. cost in millions or C (KCB)

1 15.55 1.3240 891.73 1,180.65

2 206.56 1.7251 891.73 1,538.32
3 12.32 1.2929 891.73 1,152.36
4 10.16 1.1278 891.73 1,005.69
5 12.327 1.2929 891.73 1,152.36
6 35.4 1.2948 891.73 1,154.05
7 14.5 1.3146 891.73 1,172.26
8 15.478 1.3234 891.73 1,180.11
9 163.5 1.6843 891.73 1,501.94
10 143 1.6614 891.73 1,481.52
11 36 1.4428 891.73 1,286.58
12 57.413 1.5133 891.73 1,349.45
13 10.2 1.2681 891.73 1,130.8

32
 14 197.13 1.7169 891.73 1,531.01
15 381.6 1.8369 891.73 1,638.01
16 542.295 1.5047 891.73 1,341.78
Source: Own Data, 2022

Table 4.13 1 Estimated time-cost relationship (Actual Cost)

Project Actual Cß K Estimated AT in days

No. cost in millions or C (KCB)

1 22.44 1.5007 671.09 1,007.1

2 244.75 2.0272 671.09 1,360.43
3 20.034 1.4787 671.09 992.34
4 18.39 1.4622 671.09 981.26
5 16.43 1.4409 671.09 966.97
6 47.9 1.6568 671.09 1,111.86
7 20.12 1.4795 671.09 992.87
8 17.99 1.4580 671.09 978.44
9 281.32 2.0874 671.09 1,400.83
10 165 1.9470 671.09 1,306.61
11 47.41 1.6546 671.09 1,110.38
12 103.2 1.8314 671.09 1,229.03
13 12.8 1.3947 671.09 935.96
14 243.58 2.0485 671.09 1,374.72
15 482.15 2.2395 671.09 1,502.90
16 628.33 2.3182 671.09 1,555.72
Source: Own Data, 2022

Table 4.14 1 Estimated time-cost relationship (Adjusted Actual Cost)

Project Actual Cß K Estimated AT in days

No. cost in millions or C (KCB)

1 178.37 2.0228 1,377.04 2785.47

2 767.19 2.4663 1,377.04 3396.19
3 159.22 1.9918 1,377.04 2742.78

33
 4 57.64 1.7349 1,377.04 2389.02
5 130.6 1.9389 1,377.04 2669.94
6 150.15 1.9760 1,377.04 2721.03
7 159.93 1.9930 1,377.04 2744.44
8 564.11 2.3654 1,377.04 3257.25
9 2235.74 2.8522 1,377.04 3927.59
10 509.855 2.3331 1,377.04 3212.77
11 146.5 1.96941 1,377.04 2711.9
12 820.23 2.4888 1,377.04 3427.17
13 40.13 1.6516 1,377.04 2274.31
14 763.51 2.4647 1,377.04 3393.99
15 1511.32 2.7044 1,377.04 3724.06
16 1969.51 2.8035 1,377.04 3860.53
Source: Own Data, 2022

4.4 Checking the validity of Bromilow’s principle

The mean absolute percentage error (MAPE) method was used to find the closeness of fit to the
models.

Percentage Error (PE) for the comparison of actual durations and predicted durations is defined as
predicted duration – actual duration
follows: PE =
actual duration

The mean absolute percentage error (MAPE) method was used to test the reliability of the model,
using the following equation;

1 (𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛)𝑖 – (𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛)𝑖

MAPE = ∑𝑛𝑖=1
𝑛 (𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛)𝑖

34
 Table 4.15 1Predicted and Actual Duration of Regression Analysis of Contracted Cost and
Contracted Time

Project Estimated Actual Duration PE IPEI

No. AT in days in days
(KCB)
1 1,180.65 745 0.58 0.58
2 1,538.32 1500 0.025 0.025
3 1,152.36 900 0.2804 0.2804
4 1,005.69 925 0.087 0.087
5 1,152.36 880 0.3095 0.3095
6 1,154.05 940 0.227 0.227
7 1,172.26 910 0.288 0.288
8 1,180.11 700 0.685 0.685
9 1,501.94 1920 -0.217 0.217
10 1,481.52 1420 0.7475 0.7475
11 1,286.58 1000 0.8665 0.8665
12 1,349.45 1840 0.4399 0.4399
13 1,130.8 620 1.1464 1.1464
14 1,531.01 789 1.5792 1.5792
15 1,638.01 898 1.4120 1.4120
16 1,341.78 988 0.9127 0.9127
MAPE 0.038*100 = 38%
Source: Own Data, 2022

Table 4.16 1 Predicted and Actual Duration of Regression Analysis for Actual Cost and Actual
Time

Project Estimated Actual Duration PE IPEI

No. TV in days in days
(KCB)
1 1,180.65 745 0.3518 0.3518
2 1,538.32 1500 -0.093 0.093
3 1,152.36 900 0.1026 0.1026
4 1,005.69 925 0.0608 0.0608

35
 5 1,152.36 880 0.0988 0.0988
6 1,154.05 940 0.1828 0.1828
7 1,172.26 910 0.0910 0.0910
8 1,180.11 700 0.3977 0.3977
9 1,501.94 1920 -0.2704 0.2704
10 1,481.52 1420 0.6243 0.6243
11 1,286.58 1000 0.6904 0.6904
12 1,349.45 1840 0.3744 0.3744
13 1,130.8 620 0.8321 0.8321
14 1,531.01 789 1.3811 1.3811
15 1,638.01 898 1.2615 1.2615
16 1,341.78 988 1.12927 1.12927
MAPE 0.031*100 = 31%
Source: Own Data, 2022

Table 4.17 1 Predicted and Actual Duration of Regression Analysis for Adjusted Cost and Time

Project Estimated AC Actual Duration PE IPEI

No. in days (KCB) in days

1 2785.47 745 2.738 2.738

2 3396.19 1500 1.264 1.264
3 2742.78 900 2.047 2.047
4 2389.02 925 1.582 1.582
5 2669.94 880 2.034 2.034
6 2721.03 940 1.8947 1.8947
7 2744.44 910 2.015 2.015
8 3257.25 700 3.653 3.653
9 3927.59 1920 1.045 1.045
10 3212.77 1420 1.966 1.966
11 2711.9 1000 2.2919 2.2919
12 3427.17 1840 1.569 1.569
13 2274.31 620 2.99 2.99
14 3393.99 789 3.94 3.94

36
 15 3724.06 898 3.735 3.735
16 3860.53 988 3.462 3.462
MAPE 0.1493*100 =14.93%
Source: Own Data, 2022
The result for the mean absolute percentage error (MAPE) showed less than 50% for all estimated
durations and Predicted and Actual Duration of Regression Analysis for Adjusted Cost and Time
registered 14.9% value of MAPE which shows closest fit of the prediction.

4.2. Summary
The application of the BTC Model showed that a relationship existed between the cost and the
duration of construction for the sixteen buildings studied and was represented by the equation,

T = 891.730.1023 ………………………. Contracted Cost and Contracted Time

T = 671.090.1305……………………………………………. Actual Cost and Actual Time

T= 1,377.040.1359……………………………. Adjusted Actual Cost and Actual Time

MAPE value for the models

38 ……………………………………. Contracted Cost and Contracted Time
31……………………………………. Actual Cost and Actual Time

14.93……………………………………………… Adjusted Actual Cost and Actual Time

Having this in mind, it is possible to declare that BTC Model is applicable in public building projects in
Dire Dawa city.

37
 CHAPTER FIVE

5. Conclusion, and Recommendations

5.1. Conclusion
The main objective of this study was to develop models that will be used to predict the construction
duration to compare the duration given by contract stage in a reliable and practical way by using
time and cost as a variable.

Basically, the regression model included only cost as a variable as time or duration has been given
by Bromilow (BTC Model). Linear Regression Analysis was conducted between contracted, actual, and
adjusted time and cost. From that it was possible to find the equation for all linear regression cost types and
T = 891.730.1023, 671.090.1305, and 1,377.040.1359 for Contracted Cost and Contracted, Actual Cost and
Actual Time, and Adjusted Actual Cost and Actual Time respectively. In doing so, the researchers
considered only actual costs rather than variation costs which may involve multiple regression
model.

Additionally, the mean absolute percentage error (MAPE) has been used to check the validity of the
model and it has been proved that the model closest fit of eth prediction and Generally, the general
and specific objectives of the paper has been achieved as a model has been developed and checked
for validity if it applicable in building projects under study.

5.2. Recommendations
• Government authorities shall utilize the developed models to predict project Time and Cost and apply
the formulas developed for first planning of their respective building projects.
• Such models need continuous update with additional project data.
• Use completion time as one criterion for bid evaluation
• Consultants need to apply the formulas developed for feasibility and other studies.
• Contractors need to use the models developed to predict time and also cost during bidding stages.
5.2.1. Recommendation for Future research
• Other factors other than cost affecting duration of building projects shall be studied in order
to provide a comprehensive model.

38
• In this study, data for only sixteen public building projects were used to form the models.
However, more case study buildings with the same type of project will provide results that
are more reliable.
• Most of the researchers studied their modeling approach by supposing the effect of cost on
duration, although, this conception was found to be incorrect for all cases. It is necessary to
study the effect of duration on cost in order to rectify this error.
• Models need to be developed using multiple regression to have better correlation of factors.

39
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