TRADEOFFS affects the other two parameters. Typically

TRADEOFFS
AMONG CONSTRUCTION TIME, COST AND QUALITY

Abstract

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Construction time, cost
and quality are the driving factors for feasibility of any civil engineering
project. They are interdependent on each other wherein increase or decrease of
either parameter proportionately affects the other two parameters. Typically we
don’t have unlimited resources or time to complete the project. This
necessitates the need for finding an optimum balance between these parameters.

In the past, project
managers used to search the optimum balance between construction cost and time,
totally ignoring quality. Since, quality has a direct impact on both cost and
time, the results provided by the analyzing tradeoff among only cost and time
could not provide clarity on level of quality associated with the cost. This
two-dimensional approach often resulted in high construction cost or
underutilization of resources. Thus, advanced three-dimensional
time-cost-quality tradeoff is used to find optimum resource utilization plan to
reduce construction time and costs while maximizing quality.

Project bidding is
getting more competitive resulting in very low profit margins. This leaves small
margins of error for construction planners and estimators resulting in
increased pressure to formulate optimum utilization plan. Various techniques
which are used to find optimum balance between cost-time-quality were studied
and a summary report is presented in this paper. An overview of genetic
algorithm is also given in the paper. An example using Genetic Algorithm is
also analyzed to demonstrate how cost and time are minimized while maximizing
the quality.

 

 

Background:

Traditional time/cost
analysis technique is a two dimensional analysis method, which does not
consider quality at all. In time/cost analysis, it is assumed that an equal
magnitude of quality will be maintained throughout the project duration. However,
in reality it is not practically possible to have same level of quality
throughout the project. Moreover, general contractor due to resource and other
constraints had to sub-contract some of the activities to sub-contractors.
Quality of work done by sub-contractors and general contractor can never be
same. 1 Also, emerging innovative contract types in recent times
has entailed the need to minimize construction cost and time while maximizing
the quality. To take an example, department of transportation (DOT) of United
States in various states use the following new highway contracting method 2:

·        
Bidding on cost/time (Herbsman 1995;
El-Rayes 2001)

·        
Incentive/disincentive contract clause
(Jaraiedi et al. 1995)

·        
Nighttime construction (Ellis and Amos
1996; El-Rayes and Hyari 2002, 2004)

·        
Warranty contracting (Anderson and Russel
2001; ENR 2002)

·        
Multi-parameter contracts (Anderson and
Russel 2001)

Impact of contracting
methods on decision making in construction is illustrated in Fig. 1. This
necessitated the need to find optimal or near optimal resource utilization
plans that incorporate quality in time/cost analysis to minimize the construction
cost & duration and at the same time maximize the quality. This three
dimensional approach allows project managers to assess the impact of various
resource utilization plans on project performance.

 

 

Fig.
1 Impact of contracting methods 2

Time-cost-quality is an
advanced three dimensional optimization approach which helps the project
managers in taking key project decisions. It also enables the project managers
to quantify the quality in construction. The model for optimization in
time-cost-quality tradeoff is developed in three main phases which are
explained in detail in later sections of the paper. 2

·        
Model formulation,

·        
Quantifying construction quality, and

·        
Model implementation.

A brief overview of the
various methods for analyzing time-cost tradeoff are also discussed in the
paper, however emphasis has been laid on use of Genetic Algorithms for solving
Time-Cost-Quality Tradeoff problems.

 

Time-Cost
Tradeoff Techniques

Concept of time-cost
tradeoff started gaining popularity in early 1960s with the introduction of
Heuristic methods. Since, then various techniques have been developed to solve
and find optimum solution for the problems of time-cost tradeoff. A succinct overview
of various methods of solving the only time-cost tradeoff problems is compiled
in Table 1.

Table
1.
Time-Cost Tradeoff Analysis Techniques 4

Techniques for Time-Cost Tradeoff
Analysis

Heuristic Methods

Mathematical Programming Model

Genetic Algorithms

Descriptions:
Simple
rules of thumb

 
Linear
programming; integer programming; or dynamic programming

 
Optimization
search procedures that mimic natural evolution and reproduction

Advantages:
–         
Easy to understand
–         
Provide good solutions.
–         
Used for large-size projects

 
–         
May provide optimal solutions

 
–         
Robust search algorithm
–         
Can use discrete relationship between time and cost
–         
Applicable to large problems

Drawbacks:
–         
Lack mathematical rigor
–         
Do not guarantee optimal solutions
–         
Mostly assume linear, rather than discrete,
relationship between time and cost

 
–         
Difficult to formulate
–         
The gradient-descent approach often terminates in
local minimum.
–         
Applies to small problems only.
–         
Mostly assume linear, rather than discrete,
relationship between time and cost

 
–         
Random search is time consuming.
–         
Cannot tell when or if an optimal solution is
obtained.

 

Genetic algorithm is
discussed in detail in this paper.

Genetic
Algorithm

Genetic algorithm (GA) is
one of the optimization model besides linear programming, integer programming,
and dynamic programming developed using a variety of methods. 2
The basic principles of genetic algorithm are inspired by the mechanism of
natural selections wherein stronger individual will most likely emerge as the
winner in a competitive ambient. In other words it is the survival of the
fittest. Genetic algorithm presumes that a potential solution of a problem is
an individual and can be represented by a set of parameters (Resat Selbas,
Onder Kizilkan, and Marcus Reppich 2005). These parameters are deemed as the
genes of a chromosome and thus can be structured by a string of values in
binary form. 3 Fitness value in genetic algorithms is a positive
value which is used to indicate the strength of a chromosome which in turn is
associated with the objective function of the problem.

Genetic algorithms can be
used in conjunction with neural nets and fuzzy logic to solve more convoluted
problems. A typical cycle of a genetic algorithm consists of 4 stages (Resat
Selbas, Onder Kizilkan, and Marcus Reppich 2005). Each cycle of genetic
algorithm generates a new set of possible solutions for a given problem.

·        
Creation of population of strings,

·        
Evaluation of each string,

·        
Selection of best string,

·        
Genetic manipulation to create population
of strings.

These four stages are
presented in a flow diagram in Fig. 2.

Fig.
2 The cycle of GA 3

During the very first
stage of analysis, initial strings having the properties of potential solution,
are created to start the search process. The various elements of the problem
set are then encoded into bit-strings, which are typically called chromosomes
or strings. The fitness of these strings (i.e. performance relative to each
other), is then analyzed with the help of some functions which represents the limitation
of the problem. Chromosomes having higher fitness survives the process and are
then chosen for further genetic manipulation process. This selection process is
mainly responsible to ascertain and select the fittest chromosome. After
selecting fittest population strings, the genetic manipulation process is
carried out in two steps.

First step of the
manipulation process involves, the crossover operation that again combines the
genes of each two selected chromosomes to produce a crossover chromosome. In
order to achieve this objective, various types of crossover operators can be
used to perform manipulation process. After this operation, randomly select the
crossover points of any two strings for the next step of the genetic
manipulation process. The second step of the process is known as mutation. In
this step genes at randomly selected positions of the strings are modified. The
mutated chromosomes generated by the mutation process are the next population strings
to be analyzed. This cycle of evolving chromosomes using mutation is then repeated
again and again until a predetermined termination criterion is accomplished. Termination
criteria can be accomplished using any one of the three conditions:

·        
Fixing the total number of computational
cycles,

·        
By providing the permissible variation in
fitness factor of individuals chromosomes of different generations, and

·        
Defining a pre-defined value of strength
of chromosome or fitness factor.

By the end of the
process, the generated pool of mutated chromosomes will merge and the final
chromosome will emerge as the optimal solution to the problem.

Model
Formulation

In this stage, a robust
optimization model supporting the advanced three dimensional time-cost-quality
tradeoff is formulated. This can be done in two steps. 2

·        
Establishing major decision variables, and

·        
Objective Optimization.

Decision Variables

This is first step
towards developing an optimization model and the accuracy of results largely
depends on how accurately various decision variables are incorporated. For any
given construction activity, there are lot of factors which may have direct and
indirect impact on project time, cost and quality. In this step, for each construction
activity all variables having an impact on project cost, time and quality are
ascertained. After determining all possible variables, all variables are
combined into a single decision variable known as the resource utilization.

Variables impacting
project time, cost and quality typically includes: 1) construction method (m),
it is an indication of different types of methods and or material that can be
utilized on the project; 2) crew formation (f), it represents the optimum crew
size and configuration needed to execute various activities of the project; and
3) crew overtime policy (p), it represents the overtime hours and work shifts
available at disposal during various phases of the project. 2 These
three decision variables are then combined into a single decision variable
(resource utilization) and is shown in Fig. 3. Optimum crew sizes and reduction
in production due to overtime can either be derived from past project
experience or taken from RS Means.

Fig.
3 Time-cost-quality tradeoff optimization model 2

Consider an example of
concrete paving activity for a highway project. Variables having an impact on
optimum resource utilization includes: 1) Construction material (compressive
strength of concrete being 31 MPa or 34 MPa); 2) crew formations (crew A
consisting of one paving machine, one grader and one foreman, one cement
finisher, two equipment operator & three laborer forming labor force, or
crew B having same labor composition, however having larger and more powerful
equipment); 3) overtime of 0 to 4 hours per day. 2 Various
possible combinations of these three variables are used to calculate different
resource utilization alternatives and are represented in Table 2. Each and
every resource utilization option has expected daily production rate, quality
performance, crew type considered and associated cost rate. On the same basis,
for all remaining activities of the project a set of practically feasible
resource utilization plan is formulated.

Table
2.
Feasible Resource Utilization Options for Concrete Paving 2

Resource Utilization Option
n

Resource Composition

Performance

Material (MPa)

Crew

Overtime
(h)

Cost
($ / m2)

Productivity
(m2 / day)

Quality
(%)

1

31

A

0

32.44

2,090

90

2

31

B

0

37.36

2,510

90

3

34

A

0

33.54

2,090

96

4

34

B

0

38.57

2,510

96

5

31

A

4

38.86

2,613

88

6

31

B

4

44.71

3,135

88

7

34

A

4

33.65

2,613

94

8

34

B

4

46.28

3,135

94

 

Selecting an optimal
resource utilization option, from the result obtained using decision variables
is very challenging. Various possible combinations of decision creates
significantly high number of solutions in which each and every single solution
represents a possible resource utilization option for delivering the project.
To get a rough idea, a small project having 21 activities and 6 possible
resource utilization option for each activity creates a 621 (i.e.
approximately 21 quadrillion) possible solutions. Among 21 quadrillion possible
solutions, there will be only a handful of solutions attaining the multiple
project objectives.

Optimization
Objectives

For preparing a robust
model, it is very important to quantify and measure the influence of resource
utilization decisions on time, cost and quality parameters of a project. To
meet this objective, following three equations are incorporated for evaluating
the project performance with respect to construction time, quality and cost.

Minimizing Project Time =
                                                                        (1)

Where,  is the duration of an activity (i) on the critical
path of the project using resource utilization (n).

Minimize project cost =                                        (2)

Where,  is the material cost of an activity (i) using
resource utilization (n),

 is the duration of an activity (i) using
resource utilization (n),

 is the daily cost rate of activity (i) of
resource utilization (n) in $ / day, and

 is the sub-contractor lump sum cost for
resource utilization (n) in activity i, if any.

Equation for maximizing project
quality is discussed in the next section (i.e. Quantifying Construction
Quality) of the paper.

 

 

Quantifying
Construction Quality

Resource utilization has
an indirect impact on the quality of a construction activity, thus eventually
on the entire project. It is very hard to estimate and quantify the impact of a
given resource utilization option (n) on quality of an activity than its impact
on construction cost & duration. 2 This is primarily because
of the two reasons.

·        
Complications in calculating and
quantifying effect of each resource utilization option on the quality of an
activity under consideration, and

·        
Summing up the quality performance at an activity
level to project level.

This is illustrated using
an example. Consider the case of resource utilization options for concrete
paving shown in Table 1. For fourth resource utilization option (n = 4) calculating
the production rate and expected cost 2,510 m2/day and $ 38.57 /m2
respectively is quiet easy and less challenging when compared to calculating overall
quality as 96%.

In order to overcome
these two challenges, a new objective function was incorporated for optimizing construction
quality.

Maximize project quality
=                                          (3)

Where,  is the performance of quality indicator (k) in
activity (i) using resource utilization (n),

 is the weight of quality
indicator k compared to other indicators in activity (i), and

 is the weight of activity
(i) compared to other activities in the project.

For quantifying the
construction quality in equation 3, a new and pragmatic approach is used.

 

Measuring
Quality Performance

Quality objective
function incorporated in the project quality measurement equation Eq. (3)
enables the consideration of quality indicators. Pragmatic and easy quantification
of performance of each quality indicator is a must. These indicators have been
derived after a thorough research and some of these indicators are listed below
in Table 3.

Table
3.
Quality Indicators

Construction
activity

 
Possible construction quality indicator
 

Concrete
pavement

W/C
ratio, consolidation/density, air content, thickness, compressive strength,
flexural strength, ride quality

Bituminous
pavement

Compaction
density, asphalt content, gradation, surface smoothness, thickness, aggregate
quality, void ratio, skid resistance

Bridge
deck

Consolidation/density,
rebar cover, W/C ratio, density, curing, air content, strength

Structural
concrete

Consolidation/density,
rebar cover, W/C ratio, density, curing, air content, strength

Base
course

Aggregate
quality, drainage, gradation, thickness, compaction/density, moisture content

Embankment

Compaction/density,
moisture content, material quality, uniformity, drainage

Note: W/C = Water /
Concrete

Quality indicators
mentioned in the Table 3 are easy to measure and quantify. Like compressive
strength of concrete can be easily determined using standard compressive
strength test. Same is applicable for other parameters like rebar cover, air
content etc. It should always be kept in mind that the selected quality
indicators are typically in different measurement units. It is therefore, very important
to convert it into a unified system of measurement to maintain consistency and to
be used in calculation.

A simple weighted
approach is used for summing the individual quality indicators of an activity
to calculate the overall project quality. In order to do so, two different
types of weights are calculated for each activity being evaluated: (1) Weight
of activity (wti); and (2) weight of quality indicator k(wti,k).
wti represents the vitality of quality of a particular activity with
respect to the overall quality of the project and k(wti,k) represents
the relative importance of this indicator to others.

Model
Implementation

Genetic algorithm model
is executed in three stages:

·        
Generation of initial set of possible solutions
(S),

·        
Fitness evaluation, and

·        
Population generation phase.

An elaborate overview of the
computational procedure involved in these three stages is explained in the
following sections of the paper. Fig. 4 illustrates the various steps involved
in analyzing the optimization problem using genetic algorithm.

Phase
1: Initialization

In this phase,
optimization process is commenced by following two major steps.

1.     
Carefully study and select the project and
genetic algorithm parameters needed to start the search process. Various project
parameters needed to start algorithm include:

a.       Project
size,

b.      Activity
precedence information, and

c.       Available
resource utilization option.

Fig.
4 Genetic algorithm model implementation 2

Genetic
algorithm parameters needed for this phase includes:

a.       String
size,

b.      Number
of generations,

c.       Population
size,

d.      Mutation
rate, and

e.       Crossover
rate.

After
inserting the project and GA parameters, depending upon string size the number
of generations (G), population size (S), mutation and crossover rates are determined.

2.     
After inserting the input parameters,
random solutions are generated (s =1 to S) for the initial population P1
in the first generation (g = 1). In the next two phases of the analysis, initial
set of possible solutions are evolved to generate set of optimal utilization option
for each activity of the project.

Phase
2: Fitness Functions Evaluation

In this phase of the
analysis, cost, time and quality of each possible generated solution is
evaluated to ascertain the fitness of the solution. As genetic algorithm method
is based on the survival of the fittest, the fitness level of each and every
solution determines the chances of its survival and reproduction in following
generations. For each solution three predetermined fitness functions are identified.

·        
Calculate project duration consisting of total
duration of all the activities on critical path.

·        
Calculate project cost comprising of
labor, material and equipment cost.

·        
Calculate project quality.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

References

1 Incorporating Quality
Considerations into Project Time/Cost Analysis and Decision Making

http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1715645

2 Time-Cost-Quality
Trade-Off Analysis for Highway Construction

https://ascelibrary.org/doi/pdf/10.1061/%28ASCE%290733-9364%282005%29131%3A4%28477%29

3 A New Design Approach
for Shell and Tube Heat Exchangers Using Genetic Algorithms from Economic Point
of View

https://ac.els-cdn.com/S0255270105001790/1-s2.0-S0255270105001790-main.pdf?_tid=6e3c27e8-de91-11e7-af7a-00000aacb360=1513010374_1ed60315f3c160e79ad1ddd14c7ec9cb

4 Tarek Hegazy (1999). “Optimization
of construction time-cost trade-off analysis using genetic algorithms.” Canadian
Journal of Civil Engineering, 26(6): 685-697.