TRADEOFFS

AMONG CONSTRUCTION TIME, COST AND QUALITY

Abstract

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.