a critical review of prioritization models for pavement ... · this will help in evaluating the...

2nd International Conference on Emerging Trends in Engineering & Technology, April12, 13, 2013

College of Engineering, Teerthanker Mahaveer University.

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A Critical Review of Prioritization Models for Pavement

Maintenance Management Decisions

Yogesh U.Shah1, Dr. S.S. Jain

2, Dr. M.K. Jain

3, Dr. Devesh Tiwari

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A primary purpose of a pavement management system (PMS) is to provide information so that roadway

improvements can be priority ranked. Ideally, prioritization is a consistent and justifiable process. It should involve

minimizing life cycle costs subject to minimum levels of serviceability and budget constraints. Prioritization is a

complicated process that requires sound engineering judgment and a good understanding of local conditions.

Current fiscal crises and rising roadway improvement costs have made prioritization decisions more important than

ever. Priority analysis is a systematic process that determines the best ranking list of candidate sections for

maintenance based on specific criteria such as pavement condition, traffic level, pavement functions, etc. Various

methods are used for priority analysis ranging from simple listing based on engineering judgment to true

optimization based on mathematical formulations.

This paper examines theoretical and pragmatic problems surrounding the prioritization process. This study

report a detailed review of various prioritization techniques and models developed for flexible pavements at global

level. This will help in evaluating the usefulness of the various models in some particular condition having the

similar prioritization parameters. A discussion on the limitations of the different models is also given in this study.

Keywords: Pavement management system, prioritization models.

1. Introduction

Pavements are the important component of the inland

transport system. It‟s a challenging job for engineers

and scientists to augment the performance of roads to

meet the needs of growing urban communities. It is very

important to maintain the existing pavement network in

its serviceable condition within the available resources.

And this can be achieved by adopting appropriate

maintenance strategy for the road network under

consideration. Managing the pavements is a systematic

approach, which includes different activities like

pavement performance evaluation, determination of

maintenance and rehabilitation (M&R) requirements,

optimization of resources and prioritization of pavement

sections for timely and resource effectively maintenance.

These activities collectively create the pavement

management system (PMS).

Priority ranking, as used in PMS, is a process used

to rank the pavement sections in an order of urgency for

maintenance and repair. The prioritization process is the

main step of PMS, before the decision maker‟s takes

final decision on execution of maintenance program.

1. Research Scholar, Centre for Transportation Systems

(CTRANS), Indian Institute of Technology Roorkee. Email:

[email protected]

2. Professor & Coordinator of Transportation Engg. Group,

Civil Engg. Dept., IIT Roorkee.

3. Assistant Professor, Dept. of Hydrology, IIT Roorkee.

4. Principal Scientist, Pavement Evaluation Division, Central

Road Research Institute of Technology (CRRI), New Delhi.

The quality of priority-setting is directly influencing the

effectiveness of available resources which are, in most

cases, the primary judgment of the decision maker

(Sharaf & Mandeel 1998). The priority ranking process

depends on various factors like pavement condition,

traffic volume, environmental effects, desired

performance standards, and budgetary constraints. Since

maintenance actions affect the scheduling of work and

allocation of resources, proper selection of such actions

(priorities) is crucial to the most efficient use of limited

resources. In the present study an effort has been made

to broadly classify various approaches/methods for

prioritization of pavement maintenance and the

applications of these models made by different

researchers at global level. A discussion on the

limitations of the different models is also given in this

study.

2. Prioritization Methods / Approaches

Priority setting techniques as used in the PMS cover a

wide spectrum of methods and approaches ranging from

simple priority lists based on engineering judgment to

complex network optimization models as shown in

Table 1 (Haas et al. 1994). These prioritization methods

can be further divided as: (i) Ranking Methods (ii)

Optimization Methods (iii) Artificial Intelligence

Techniques (iv) Analytical Hierarchy Process Method.

mailto:[email protected]



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Table 1. Different classes of priority programming

method

S.

N.

Class of Method Advantages and

Disadvantages

1 Simple subjective

ranking of projects

based on judgment,

overall condition

index, or decreasing

first cost

Quick, simple; subject to

bias and inconsistency;

may be far from optimal

2 Ranking based on

parameters, such as

serviceability or

distress; can be

weighted by traffic

Simple and easy to use;

may be far from optimal,

particularly if traffic

weighting not used

3 Ranking based on

condition analysis

and traffic, with

economic analysis

Reasonably simple; may

be closer to optimal

4 Annual optimization

by mathematical

programming model

for year-by-year basis

over analysis period

Less simple; may be

close to optimal; effect of

timing not considered

5 Near optimization

using heuristics

including benefit-cost

ratio and marginal

cost effectiveness

Reasonably simple;

suitable for

microcomputer

environment; close to

optimal results

6 Comprehensive

optimization by

mathematical

programming model

taking into account

the effects of M,R&R

timing

Most complex and

computationally

demanding; can give

optimal program

(maximization of

benefits)

(Source: Haas et al. 1994)

2.1 Ranking Methods

2.1.1 Composite Index Ranking Method

The ranking of pavement sections for maintenance is

done on the basis of the priority index calculated by

combining different pavement indices. These indices are

estimated by considering parameters like pavement

distresses, riding quality, traffic conditions, economic

analysis, functional class, accident details, geometric

deficiencies, structural capacity, skid resistance,

pavement age, engineering judgement, etc.

The prioritization program should not only be based

on current pavement condition, for making it efficient

future pavement condition should also be considered.

As generally the treatments are applied at least one year

after the condition surveys are carried out, giving the

time to require for relative prioritization and organizing

for funds.

There are different approaches to develop a priority

combined index for pavement maintenance. These

approaches include unique sum approach, utility theory,

Delphi method, factorial rating method, and fuzzy set

theory. The application of few methods is discussed in

following sections.

2.1.2 Economic –based Methods

The prioritization methods based on economic analysis

can be of two types: (i) using optimal benefit/cost ratio

(ii) using incremental benefit/cost ratio. In the first

method, prioritization process uses the optimal M&R

recommendations and corresponding benefit/cost ratios

(or effectiveness/cost (E/C) ratio) for each pavement

section of the network produced from the dynamic

programming. The higher the E/C ratio of a section, the

higher the priority of that section for repair. The

available budget is allocated to the pavement sections as

per the priority list till the budget is completely

exhausted.

The second methodology is a heruistic method for

budget optimization. In this mehtod all feasible M&R

alternatives of a section are identified and the

coressponding inflated initial cost, present-worth costs,

and weighted benefits are obtained. This information is

then used in the program to produce optimal M&R

recommendations for each pavement section, including

initial cost and type of treatment. The budget

optimization also gives the total network-weighted

benefits corresponding to optimal M&R

recommendations (Butt et al. 1994).

2.2 Optimization Methods

Priority programming by optimization is conceptually

different from others methods. It combines the function

of priority programming, program formulation, and

project scheduling into one operation which gives the

optimum schedule of projects through precise analytical

techniques such as linear and dynamic programming.

Generally, these method uses maintenance cost

minimisation or maintenance benefits maximization to

generate the optimal maintenance plans.

2.3 Artificial Intelligence Techniques

Artificial intelligence techniques include fuzzy

mathematical programming, ANNs, and evolutionary

computing (including genetic algorithms). These

techniques are particularly appropriate for pavement

management because the information may be uncertain

and incomplete. The data may involve combinations of

objective measurements, subjective rating, and expert



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inputs, such as those data used to create M, R&R

decision criteria and policy tables. Artificial neural

networks and fuzzy systems have been used for needs

analysis as alternatives to the traditional priority ranking

tools, such as decision trees.

2.4 Analytical Hierarchy Process Method

Analytical hierarchy process (AHP) is one of the multi

criteria decision making methods (MCDM) used to

scale and quantify measurements. AHP theory was

developed by Saaty in 1970. Fig. 1 shows a typical

schematic hierarchy of prioritization process. The first

step is the formation of the problem components

(hierarchy); the second phase of the AHP is the

evaluation which is based on the concept of paired

comparisons. The parameters considered at each level

of hierarchy are compared in relative terms as their

importance or contribution to a given criterion. This

process of comparison yields a relative scale of

measurements of priorities or weights of the elements.

These relative weights sum to unity. For project-level

evaluations where a few sections are to be considered

simultaneously, AHP is an effective method for

analysis.

Fig. 1 Typical hierarchy structure for prioritization

3. Studies on Pavement Maintenance

Prioritization

3.1 Based on Subjective Ranking

Fwa and Chan (1993) illustrated the feasibility of using

neural network models for priority assessment of

highway pavement maintenance needs. A simple back-

propagation neural network with three different priority

setting schemes viz. a linear function relating priority

ratings to pavement conditions, a nonlinear function,

and subjective priority assessments obtained from a

pavement engineer, was tested using general purpose

micro-computer based neural network software known

as Neural Works. The validation analysis was carried

out for all three schemes as described below:

Chen et al. (1993) developed a prioritization procedure

as a part of an Urban Roadway Management System

(URMS) at network level. The procedure combined two

matrices and an equation for computing priority index

(PIX). PIX was taken as a function of PCI, pavement

age, mixed traffic and street class. The process is shown

in Fig. 2.

(Source: Chen et al. 1993)

Fig. 2 Priority index procedure used in URMS

Sharaf (1993) compared three methods for priority

ranking. In the first model the priority index was

estimated as follows:

(1)

The traffic levels were classified as less than 2500

vehicle per day (vpd), between 2500-10,000 vpd, and

more than 10,000 vpd and the corresponding traffic

factors were selected as 1.0, 0.5 and 0.1 respectively.

The defect factor (values between 0.1 to 1.0) was

assigned on the basis of the distress type and required

treatment (lower values for major treatments). The

sections were then ranked in descending order after

calculating the section priority index, and converted to a

cost list by using appropriate maintenance treatment

unit cost. The second model was a modification of the

first, where the pavement sections were arranged

according to road type (i.e. desert or agricultural roads)

and traffic level into four classes. Also in this model the

budget shares were reserved for different maintenance

treatments. In the third model, the distribution of budget

among all the sections was done on the basis of

optimization method.

Jain et al. (1996) selected four sections of flexible

pavement on NH-21 & NH-22 in state of Himachal



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Pradesh and eight sections in state of U.P. on NH-2,

SH-45 & MDR-121 for maintenance prioritization.

Various field studies like measurement of surface

deflection, roughness, rut depth, cracks & cracking

patterns, pot holes and axle load studies were performed

on all pavement sections. Based on the collected data

M&R investment strategy for design life of 5 years was

suggested. Priority fixation for M&R was done based on

following factors:

i. Importance of road (i.e. road type and commercial

traffic);

ii. Characteristic deflection (Dcs) value;

iii. Road condition based on roughness, cracks, rutting

and potholes;

iv. Investment needs for maintenance and

rehabilitation.

Suma et al. (2000) developed a simplified ranking

methodology based on distresses to prioritise the

pavements for maintenance management. Data

pertaining to pavement distress viz., cracking and

patching along with their severity levels, unevenness

(roughness), and pavement condition ratings were

collected and weightages were assigned to each type of

distress based on the severity level and extent and

deduct value curves were developed. Pavement

Condition Indices were then determined and the

pavement sections were ranked for maintenance.

Agarwal et al. (2004) presented a rational approach

using AHP for prioritization of highway sections for

maintenance on the basis of present highway condition,

future highway condition and the highway importance.

The functional condition of highway sections was

evaluated considering the (i) safety (ii) efficiency of

traffic operation and (iii) riding comfort. The relative

weights of these factors have been conceived from the

expert opinion of field engineers which were analysed

using AHP. For evaluation of structural condition a

simple and cost effective statistical model based on

Long Term Pavement Performance (LTPP) database of

US Department of Transportation was developed. The

highway importance is assessed considering the (i)

highway class (ii) importance to community and (iii)

political importance. The relative weights of these

factors have also been conceived from the expert

opinion of field engineers and using the AHP. A total of

15 factors are considered and identified by thicker

borderline of the text boxes in Fig.3. The developed

approach was employed for prioritizing the sections for

maintenance in a small highway network.

(Source: Agarwal et al. 2004)

Fig. 3 Decomposition of the maintenance priority problem into a hierarchy

Chandran et al. (2007) formulated the prioritization

technique of low-volume pavement sections for

maintenance using fuzzy logic. Eight pavement sections

each of 500m length with different deterioration levels

Overall Highway Condition

Maintenance Priority

Overall Highway Importance

Percentage Highway

Condition

Future Highway

Condition

Present functional

Condition (PFC)

Present Structural

Condition (PSC) 6

Hwy Class

(HC) 13

Imp. To Community

(IC) 14

Political

Imp. (PI) 15

Future functional

Condition (FFC)

Future Structural

Condition (FSC) 12

Present Fatigue

Cracking

Present Fatigue

Cracking

Present

Traffic

Safety (PTS) 1

Present Efficiency

of traffic

Operation (PTO) 2

Present

Riding

Quality

Present

Fractured

Surface (PFS) 3

Present

Distorted

Surface

(PDTS) 4

Present

Disintegrated

Surface (PDIS) 3

Future

Traffic

Safety (PTS) 7

Future Efficiency

of traffic

Operation (PTO) 8

Future

Riding

Quality

Future

Fractured

Surface (PFS)

9

Future

Distorted

Surface

(PDTS) 3

Future

Disintegrated

Surface

(PDIS) 11

Future Fatigue

Cracking

Future Fatigue

Cracking



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were selected in the Trivandrum and Kollam Districts in

Kerala State. Fuzzy condition indices (FCI) were used

to prioritize the pavement sections by suitable fuzzy

ranking methods. Fuzzy membership functions were

formulated for severity, extent, and relative importance

of each distress with respect to maintenance. The

common index aggregating above parameters in form of

fuzzy condition index (FCI) was computed using

following expression:

(2)

Where wki = subjective weight of distress k at severity

level i, Aki = subjectively assessed extent of distress k at

severity level i, and Si = subjective assessment of

severity level i.

Fuzzy condition indices were developed for each

pavement section by using MATLAB software. The

FCI so obtained for various sections are shown in Fig. 4.

The ranking based on PCI values were also compared

with FCI ranking.

(Source: Chandran et al. 2007)

Fig. 4 Fuzzy condition indices for various sections

Sandra et al. (2007) proposed a Fuzzy Multi Criteria

Decision Making (FMCDM) approach for prioritizing a

pavement stretches. An expert opinion survey was

conducted to quantify the influence of various distresses

with respect to their extent and severity on the

functional condition of the pavement. For collecting

pavement condition data, four different stretches

dominated by different types of functional failures have

been chosen in the state of Rajasthan, for a total length

of 25km, representing different functional classes of

highways viz. National Highways (NH), State Highways

(SH) and Major District Roads (MDR).

Priority Index (PI) for all the pavement stretches was

computed from the fuzzy preference relation matrix

using the following mathematical form:

– (3)

Where, eij = real number indicates the degree of

preference between the respective ith and j

th pavement

stretches. It has been calculated using positive (Sij+) and

negative areas (Sij−) of difference between two fuzzy

values ( ). The eij was calculated using following

equation and Fig. 5.

(4)

Where, ( = Total area of ( )

(Source: Sandra et al. 2007)

Fig. 5 Computation of

The road link which had highest Priority Index (PI) was

given top priority and vice versa. A code was developed

in MATLAB in order to calculate the PI for the present

study.

Zhang (2004) presented an Analytic Hierarchy Process

(AHP) based quantitative approach to the prioritization

of data requirements for pavement management. Using

the Weighted Sum technique, the importance and

frequency of usage of data items were combined to

yield their comprehensive ranking score. The overall

methodology is illustrated in Fig. 6. The process of

establishing the hierarchy to prioritize pavement data

collection using AHP is illustrated in Fig. 7.

Farhan & Fwa (2009) made an attempt to explore the

use of an analytic hierarchy process (AHP) for the

prioritization of pavement maintenance activities. Three

forms of AHP were examined, namely, the distributive-

mode relative AHP, the ideal-mode relative AHP, and

the absolute AHP. For analysis purpose, three road

functional classes, three distress types and three levels

of distress severity were considered which gave 27

possible combinations of maintenance treatments. The

hierarchy structure used for the AHP analysis is as

shown in Fig. 8. The study concluded that the absolute

AHP was suitable for the pavement maintenance

prioritization process, on the basis of its ability to

provide priority assessments for pavement maintenance

activities in good agreement with the priority

assessments obtained by the direct assessment method

and its operational advantage in evaluating a large

number of maintenance activities.



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(Source: Zhang 2004)

Fig. 6 Overall process of the methodology

Moazami et al. (2010) generated AHP and Fuzzy logic

modelling for prioritization of pavement rehabilitation.

The developed models were executed for 131 sections

of urban streets of district No. 6 of Tehran municipality.

The modelling was done in two steps, in the first step

analytical hierarchy process was employed to compute

the relative weights of parameters. The pairwise

comparison between the following criteria and sub-

criteria as given in Table 2 was done by considering

ideas of about 200 PMS experts. Finally, with rating

approach in Expert Choice software prioritization was

done.

In the next step, fuzzy logic modelling was used to

obtain satisfactory precision. The three fuzzy sets were

defined and following Gaussian membership function

were used for demonstration of being high, medium and

low fuzzy sets.

(5)

where, μ(X) = Value of Membership of Variable X to

Fuzzy Set, G = Mean of Gaussian Function , σ =

Gaussian Function Bell Radius. The Singleton Fuzzifier,

a product inference engine was used to calculate the

priorities of the sections using fuzzy logic. The analysis

was done using the fuzzy toolbox of MATLAB 7.0

software and coded M-files.

It was concluded that, in AHP pairwise

comparison between criteria and sub-criteria is arbitrary,

while gauss mean and sigma matrixes constitutions are

based on reality. Also it was shown that AHP method

cannot differentiate between two almost identical

sections. Consequently, fuzzy logic programming was

considered as the best choice in the study.

(Source: Zhang 2004)

Fig. 7 Application of AHP to prioritizing pavement

data collection

3.2 Based on Composite Condition Index

Karan (1981) described the pavement management

implementation project for Prince Edward Island (PEI),

Canada covering a road network of 500km. It included

the field inventory, identification of needs for pavement

improvements, evaluating the rehabilitation alternatives,

priority analysis and budget analysis. The Condition

Index (CI) was computed considering the severity of 10

different distresses on road sections. The overall

Serviceability Index (SI) was calculated for all road

sections using following expression:

SI = a (RCI) + b (SAR) (6)

Efficient and Cost

Effective Pavement

Management

Aiding in

Policy

Decisions

Structural

Adequacy

Enhancement

Serviceability

Enhancement

Safety

Improvement

Pavement Management User

Needs

Identification of Core Pavement

Management

Activities to be Conducted

Grouping of Similar Core

Pavement Management

Activities

Use f Analytic Hierarchy Process

Priorities of Group of Core

Pavement Management

Activities

Identification of Core

Pavement of

Management Activities

for Each

Pavement Life - Stage

Grouping of

Similar Activities

Use of AHP to

Arrive at Priorities

of Activity Groups

Use of Delphi

Process to Arrive at

Consensus of opinion

about Priorities of

Activity Groups

Final Priorities of

Activity Groups

Adjusted Priorities of

Activities

Use of Weighted Sum Technique

to combine Frequency of Usage

of Data Items and Their

Importance

Comprehensive

Ranking of Data Items

Scoring of

Activities in

Each Activity

Group Based

on Levels of

Importance

Identification

of Major

Categories of

Pavement

Data Items

Frequency

Analysis of

Major

Categories of

data Items

for Identified

Activities

The Average

Score of Each

Activity

Multiplied with

Respective

Activity group

Priority



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where, SI = serviceability index (Rating Scale: 0-10, 0 –

totally unacceptable pavement, 10 - perfectly smooth

and strong pavement), RCI = Riding Comfort Index

(Rating Scale: 0 – 10, 0 - worst riding comfort & 10 –

perfectly smooth pavement), SAR = Structural

adequacy rating (Rating Score: 0 – 10, 0-4.9 indicates

structural adequate pavement, 5-10 indicates structural

inadequate pavement), a, b = weighting factors (a + b =

1.0)

The calculated values of CI, RCI, SAR, SI was given as

an input for development of PMS at network level. One

of the components of PMS was establishing the

pavement improvement priorities. A mathematical-

optimization (linear-programming) model was adopted

to set priorities based on benefit maximization and

budget constraints.

(Source: Farhan & Fwa 2009)

Fig. 8 Hierarchy structure for AHP analysis

Table 2. Criteria and sub-criteria for AHP process Level - 1 Criteria PCI Types of Urban Roads

(Road Width m – both

direction)

Traffic Volume (pcu/hr/

direction)

M & R Cost (USD per red)

Level - 2 Sub-

Criteria

0 – 10 : Failed

10 – 25 : Very Poor

25 – 40 : Poor

40 – 55 : Fair

55 – 70 : Good

70 – 85 : Very Good

85 – 100: Excellent

Local (5.5 - 6.5)

Minor Arterial (5.5 - 21)

Major Arterial (13 - 30)

Low Volume (<433)

Medium Volume (433-2660)

High Volume (2660 – 6200)

Others (> 6200)

Very Low (< 2000)

Low (2000-20000)

Medium (20000-50000)

Omit High (50000-100000)

Very High (>100000)

(Source: Moazami 2010)

Selection of a Pavement Section for Maintenance

Expressway Arterial Access

Pothole Rutting Cracking

High Moderate Low

Objective (Level 1)

Criteria (Level 2)

Sub-Criteria (Level 3)

Alternatives (Level 5)

Sub Sub-Criteria

(Level 4)

Section 1 Expressway

Pothole

High


Pothole

Moderate


Pothole

Low


Rutting

High


Rutting

Moderate


Rutting

Low

Section 7

Expressway

Cracking

High

Section 8

Expressway

Cracking

Moderate

Section 9

Expressway

Cracking

Low

Section 10

Arterial

Pothole

High

Section 11

Arterial

Pothole Moderate

Section 12

Arterial

Pothole Low

Section 13

Arterial

Rutting

High

Section 14

Arterial

Rutting Moderate

Section 15

Arterial

Rutting Low

Section 16

Arterial Cracking

High

Section 17

Arterial Cracking

Moderate

Section 18

Arterial Cracking

Low

Section 19

Access

Pothole

High

Section 20

Access

Pothole

Moderate

Section 21

Access

Pothole

Low

Section 22

Access

Rutting

High

Section 23

Access

Rutting

Moderate

Section 26

Access

Rutting

Low

Section 27

Access Cracking

High

Section 28

Access Cracking

Moderate

Section 29

Access Cracking

Low



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Zhang et al. (1993) developed a comprehensive ranking

index for flexible pavements using Fuzzy sets theory.

The model developed was named as overall

acceptability index (OAI) is given as follows:

(7)

Where W1, W2, W3 & W4 are the weighing factors for

roughness, distress, structural capacity and skid

resistance respectively. The sum of all weighing factors,

Wi = 1.0. The membership functions for each

parameter as developed using nonlinear regression

analysis for a subjective opinion survey about the level

of acceptance for selected pavement attributes and their

relative importance, are given in Table 3.

Table 3. Membership functions and weights for

secondary roads

Attribute Membership

Function R

2 Weight

Roughness

(PSI)

A1 = 1 - exp (-

0.01274*PSI4)

0.970 0.306

Distress

(D)

A2 = exp (-

0.00000185*D2)

0.971 0.244

Structural

Capacity

(SC)

A3 = 1-exp (-

0.207*(CS/50)5)

0.960 0.225

Skid

Resistance

(CF)

A4 = -0.22 +

1.6308*CF 0.979 0.231

(Source: Zhang et al. 1993)

Andres (1994) details the prioritization methodology of

local roadway improvements for the town of Eastharm,

Massachusetts. The system used a composite

performance based index to assess priorities. The index

was formed by first determining an effectiveness ratio.

This is accomplished by dividing “benefits” (areas

under deterioration curves after treatment is assigned)

by the cost per square yard of treatments. This

effectiveness ratio was then weighted by functional

class. This measure of the influence of traffic volume on

priority assessment can be modified by user. The

weighted effectiveness ratio was then used to prioritize

road segments in each category. The prioritization was

done considering different budget scenarios like zero

funding, full funding, moderate budget cut and severe

budget cuts.

Flintsch et al. (1998) presented the formula to prioritize

pavement rehabilitation projects based on expert‟s

opinion. It was used for the 5 yr pavement preservation

program of Arizona Department of Transportation

(ADOT). The preliminary list of candidate projects

were prioritized using a “rate” number computed

according to the following equation:

Rate = Cr + 0.2*Rg + 2*Rut + 0.0015*MC (8)

where; Cr = cracking (%), Rg = roughness (Maysmeter

units), Rut = rutting (in.), and MC = average

maintenance cost for last 3 years (dollars per year).

Pavement experts were instructed to examine carefully

all pavement sections presented in the questionnaire and

to assign a priority rating to each of the sections using a

scale from 1 to 10. A priority of 1 indicated the

pavements most in need of a preservation treatment.

The average response for each section was used for the

analysis. The average proposed treatment was computed

by averaging the numeric values corresponding to all

treatments recommended for each section. The average

was rounded and converted back to a treatment

recommendation. The average priority values computed

for each pavement section were used to obtain an

alternative prioritization formula. The following model

was selected to calculate the priority for pavement

sections:

Priority = 4.82 – 0.83A – 0.64B – 0.50C – 0.82D

– 0.81E – 1.11F (9)

Where, Priority = priority value, A = functional

classification code (Inter-state or State route), B =

traffic code, C = maintenance cost code, D = roughness

code, E = cracking code, and F = rutting code.

This model includes all the variables in the rate formula

plus two more: roadway classification and rutting.

A model for selection of maintenance treatment to

pavement sections was also developed as shown below:

Treat = 2.28 + 0.33A + 0.14B + 0.32D + 0.34E + 0.56F

-0.06G – 0.26EF (10)

Where, Treat = type of treatment, A = functional

classification code, B = traffic code, D = roughness

code, E = cracking code, F = rutting code, and G =

structural number code.

The result of the analysis were then implemented in a

computer program that automatically computes the

recommended treatment for each homogeneous

pavement section in the preliminary list of candidate

sections using a default assignation matrix that can be

modified by the user. The program also assigned a

priority value based on the alternative pavement

prioritization formula (priority) and sorts the projects by

priority within each roadway group (roadway

classification, traffic, and region). The sections with the

highest priority within each group are funded until they



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reach the budget recommendation provided by the

network optimization system, increased by a coefficient.

Ramadhan et al. (1999) used Analytical Hierarchy

Process for priority ranking of pavement maintenance.

The priority index (PI) used in this study for pavement

maintenance priority has the following form:

PI = Wj*Fj (11)

Where, PI = Priority index for any section (out of 100);

Wj = Factor “j” weight of importance to priority ranking;

Fj = Factor “j” value (out of 100); and SWj = 1.0.

A questionnaire was prepared in four parts for

collecting the respondent‟s opinion about the weight of

importance of the seven priority factors. The seven

factors considered for priority ranking were road class,

pavement condition, operating traffic, riding quality,

safety condition, maintenance cost and importance to

community. The procedure followed in the preparation

of this questionnaire is detailed in Ramadhan (1997).

The factor weights were computed using the AHP

method by analyzing the data collected. The factor

weights so obtained were further adjusted for the

individual experience factor, in the following manner:

(12)

Where, CWi = corrected overall weight of factor i; wj =

factor weight as estimated by individual j; Ej =

individual experience factor for individual j, i = factor

number (one to seven for priority factors, and one to six

for sub-factors); and j = individual number out of the

total number of individuals n.

The final form of the developed maintenance priority

ranking procedure was given as:

PI = CWi * Fi (13)

where, PI = priority index (out of 100), CW = Corrected

weights, Fi = priority factors.

It was concluded that the developed procedure can

adequately and efficiently rank a huge number of

pavement sections for maintenance.

Bandara and Gunarante (2001) tested a methodology

developed for pavement maintenance prioritization

based on rapid visual condition evaluation using fuzzy

logic, on the major pavement network of Sri Lanka.

Four commonly observed distress types and their

severity levels chosen in this study are given below.

1. Alligator cracking [low severity (AL), medium

severity (AM), high severity (AH)]

2. Potholes [low severity (PL), medium severity (PM),

high severity (PH)]

3. Edge failures [low severity (EL), medium severity

(EM), high severity (EH)]

4. Raveling [low severity (RL), medium severity (RM),

high severity (RH)]

The concept of triangular fuzzy numbers (TFNs) with a

linear membership function as described in the Fig. 9

was used for analysis.

The mathematical equations for the membership

function for TFN that has been adopted are given as

follows:

(14)

(15)

(16)

; (17)

(18)

(Source: Bandara and Gunarante 2001)

Fig. 9 TFN – A

The efficient fuzzy weighted average (EFWA)

algorithm was employed to compute the weighted fuzzy

pavement condition index with slight adjustments to

suit the study. The employed aggregation method can be

expressed as follows:

(19)

Further a ranking index was defined for each pavement

section i using the FCI values and the rating difference

matrix, given as follows:

(20)

Where, = element indicating the degree of

difference between the respective fuzzy condition

ratings of the ith and j

th pavement sections. The ranking

for maintenance as per the current rehabilitation

urgency was done based on these ranking indexes (Ri).

Also a fuzzy pavement condition forecasting model was

developed by incorporating subjective probability

assessments regarding pavement condition deterioration

rates, in the Markov transition process. And the re-

ranking of same sections was done based on ranking

indexes (Ri) for the forecasted pavement condition in

the second year.



10

Reddy and Veeraragavan (2001) proposed a priority

ranking methodology based on overall distress index

model and traffic adjustment factors. A schematic flow

chart of the proposed priority ranking model is as shown

in Fig. 10.

The degree of acceptability on a 0 to 1 scale was

determined, for pavement distresses of different extent

based on the expert opinion survey. The degree of

acceptability and the extent of distress were correlated

to obtain best fit function as the membership functions.

Table 4 shows the mathematical relationships developed

as a member ship functions and the relative weightage

assigned to each of distress based on expert‟s opinion.

Table 4. Mathematical relationships as membership

functions for distress

Performance

Attribute

Membership

Function R2 N S.E.

Relative

Weight-

age

Cracked

Area

AL = Exp

(0.0137 –

0.024 CRA)

0.975 21 0.121 0.30

Area of Pot

holes

AL = Exp

(0.073 –

0.077 PT)

0.982 19 0.102 0.25

Unevenness

AL = 1.157 –

1.088*10-3

UI

0.987 21 0.040 0.25

Patched

Area

AL = Exp

(0.155 –

0.0398 PA)

0.984 20 0.079 0.10

Rut Depth AL = 1.03952

– 0.0351 RD 0.996 21 0.022 0.10

(Source: Reddy and Veeraragavan 2001)

Where, AL = acceptability level (0 to 1), CRA =

cracked area of pavement (%), PT = area of pot holes

(%), UI = unevenness index (cm/km), PA = patched

area of pavement (%), RD = rut depth (mm).

The surface condition for pavement sections was

assessed in form of acceptability and relative weightage,

defined in terms of Pavement Distress Index (PDI) as

PDI = [1 - (ALi * wi) / wi] 100 (21)

Where, ALi = Acceptability level of any distress, i, wi =

weightage of distress i. Based on above equation, PDI

values have been assigned as 0 to very good pavement

and 100 to completely deteriorated pavement. Further

the prioritization factors (F) based on functional class

and average daily traffic were also considered as given

in Table 5. These factors were used to adjust the PDI

values in order to assign greater priority to the higher

functional class roadways and also to roadways with

higher traffic levels within a given functional class. The

Priority Index (PI) for a pavement section was

computed as:

PI = F x PDI = F x [1 - (ALi * wi) / wi] 100 (22)

Where, PDI = Pavement Distress Index, F =

Prioritization factor based on functional class and

average daily traffic.

Using this priority index, different maintenance

strategies were assigned to pavement sections. Also, the

developed model identified the availability of budget

and compared with the total cost required for

strengthening. It was concluded that the Priority

Ranking Model (PRM) so developed provides a

consistent, reliable and facile method of evaluating

pavements at network level.

Table 5. Prioritization factors based on functional

class and average daily

Functional Class

Average Daily Traffic

Prioritization

Factor (F) Level

No. of

Commercial

Vehicles

Expressway/

National Highway

(NH)

High >5000 1.00

Medium 3000 – 5000 0.90

Low < 3000 0.80

State Highway

(SH)

High > 3000 0.80

Medium 1500 – 3000 0.75

Low <1500 0.70

Other Roads (OR) High >1500 0.75

Medium 500 – 1500 0.70

Low < 500 0.60


Cafiso et al. (2002) provided a Multicriteria analysis

(MCA) framework for pavement maintenance

management. An AHP method of MCA was

implemented to compute the ranking values (RV) for

the maintenance alternatives. The overall computational

procedure for implementation MCA within HDM-4 to

compute the ranking vector is as shown in Fig. 11. The

HDM-4 was used to produce outputs that can be used as

attributes for each road section and investment

alternative (i.e., the average IRI values in Figure: Part b).

The above procedure produced a matrix of

“Multicriteria ranking numbers” for every year (or the

whole analysis period), and for all road sections

included in the study. The alternative with highest RV

was selected in case of unconstrained budget. When

there is budget constraint, as is always the case in

practice, this need to be considered by applying further

analysis of prioritization or optimization.

Narasimha (2003) defined a procedure prioritizing roads

in a network for periodic maintenance based on the

subjective rating technique as per the guidelines of

Asphalt Institute (AI), USA. The field surveys on

various categories of roads (SH, MDR & ODR) were

conducted and data regarding the present serviceability

conditions were collected for about 22 km of road

length from a total of 160.334 km under study area, in



11

Tamil Nadu. The pavement condition survey was

carried out, by identifying and evaluating thirteen types

of distresses as defined by AI and then the pavement

condition rating (PCR) of each stretch of road was

computed. The distresses considered with their rating

score were: Transverse crack (Rating : 0-5),

Longitudinal crack (Rating : 0-5), Alligator crack

(Rating : 0-10), Shrinkage crack (Rating : 0-5), Rutting

(Rating: 0-5), Corrugations (Rating :0-5), Ravelling

(Rating: 0-5), Shoving (Rating: 0-5), Potholes and

Patching (Rating: 0-10), Excess bitumen (Rating: 0-10),

Polished aggregate (rating: 0-10), Deficient drainage

(Rating: 0-10), Riding quality (Rating : 0-10). For all

rating scores lowest value indicated good pavement

condition and highest value indicate worst pavement

condition.


Fig.10 Schematic flow of priority ranking model

Finally, the PCI value was calculated using the charts

given in AI and the prioritization of maintenance for

road sections was done.

Kumar (2004) developed a methodology for priority

ranking of highway pavements for maintenance of

certain roads in Thiruvananthapuram city based on

composite criteria. The approach included the opinions

from the users in first step and opinions from the

experts in the second step. The questionnaire for user

opinion survey consisted two parts one with trip

information and second with pavement condition.

Average response of each user was found out using

Excel Macro Programming. Analysis of Variance

technique was used to decide that minimum sample size

should be 30 so that there is no variation between users.

From the user opinion different pavement section

was ranked for priority maintenance.

In next step functional evaluation of pavement sections

was done and following parameters were analyzed:

(i) Visual rating was done and sections were rated on

a scale of 0 – 5. The riding quality assessment was done

by driving the vehicle at uniform speed of 30kmph and

a subjective rating scale of 0-5 was adopted.

(ii) Crack measurement was done and crack index was

computed based on width of crack.

(23)

where, C1 = area of cracks with width 1mm or less, C2

= area of cracks with width 1 to 3 mm, C3 = area of

crack with width greater than 3 mm, w = pavement

width in m.

The Crack Index (CI) for each km was computed

by assigning weightages to the different severity levels.

Crack Index = (Crack Percentage x WF) x 100 (24)

Where, WF = weightage factor = 0.5 for low severity

level = 0.75 for medium severity level = 1.0 for high

severity level.

(iii) The number of small, medium and large potholes

per km of roads was recorded and the percentage of

potholes was compute as:

(25)

where, S = number of small potholes, M = number of

medium potholes, L = number of large potholes, W =

pavement width in m.

Then percentage of potholes were converted to Pothole

Index (PI) is calculated by assigning weightages to the

different severity levels. The PI is calculated as:

Start

Total No. Of Pavements

Pavement Condition Information

Cracked Area, Raveled Area

Patched Area, Pothole Area

Put Depth, Unevenness Index

Determination of acceptability

levels

Determination of PDI

Membership

Functions

Weightage of

Distresses

Budget

Priority Index

PI = PDI F

Functioned class

Traffic Volume

Prioritization Factor „F‟

PI > 2.5

10 < Pi < 25

Assign Strategy – I

PI Priority

>50 1

45 – 50 2

20 – 45 3

35 – 40 4

30 – 35 5

25 – 30 6

Assign Strategy –

II

PI Priority

20 – 25 1

15 – 20 2

10 – 15 3

Assign Strategy –

III

PI Priority

5 – 10 1

< 5 2

Total Cost of Improvements

Cost Budget

Allocated Budget to All

Pavements for

Improvements

Allocate Budget According to

Priority Index & Priority List

Outputs of Priority model & listing of overlay strategies as per

Budgets



12

Pothole Index = (% of pothole x WF) x 100 (26)

Where, WF = weightage factor = 0.5 for low severity

level = 0.75 for medium severity level = 1.0 for high

severity level.

(iv) Roughness value in terms of Unevenness Index

(UI) was calculated indirectly by using the mean of ride

rating values termed as Present Serviceability Rating

(PSR). The following model developed at Bangalore

University was adopted:

PSR = -1.9326 loge (UI) + 14.3765 (27)

Based on above functional evaluation indices second

questionnaire was prepared and expert opinions were

taken for fixing priority for maintenance. Finally the

priority obtained from user and experts were compared.

(Source: Cafiso et al. 2002)

Fig. 11 AHP procedure for computing ranking vector

Pantha et al. (2010) developed a Geographic

Information Systems (GIS)-based highway maintenance

prioritization model for major link of 53.2 km to the

capital city of Kathmandu, Nepal. The highway sections

were prioritized considering the pavement and roadside

slope stability condition. Using the bivariate statistical

method (Information Value Method) also know as

statistical index method, the weight value for a

parameter class affecting the landslide and pavement

condition were calculated. Finally an integrated

maintenance priority index (MPI) was computed by

adding pavement maintenance prioritization index and

roadside slope maintenance prioritization index after

multiplying by weighted value of each component, as

given in following expression.

(28)

where, PMPI is the pavement maintenance prioritization

index, RMPI is the roadside slope maintenance

prioritization index, Wp is the weight given to pavement

maintenance and Wr is the weight given to roadside

slope maintenance. The selection of maintenance

sections were done based on these calculated MPI.

Khademi et al. (2010) presented a combined

Conference-Delphi-analytic hierarchy process (AHP)

model employed to prioritize the low-class roads in

Gilan, Iran. The main three objectives defined for this

study was determining the high-priority low-class roads

for maintenance (MA), improvement (IM), and

upgrading (UP).



13

Each part of the designed Conference-Delphi-AHP

decision-making model function interdependently

through a series of systematic steps was as shown in the

Fig. 12.

(Source: Khademi et al. 2010)

Fig. 12 Frame work of the study

The first step included the creation of data bank for road

network in Arc View, GIS software. Then, three

categories for the prioritization were formed by the

classifying algorithm as shown in Figure 33 for three

objectives viz. MA, IM & UP. And all the sections of

low-class road network are tested by the algorithm and

placed in these three categories. Next step included to

finalize the decision criteria and list of decision makers

to participate in AHP. This was done by conducting

conference and Delphi Survey. The AHP hierarchies

decided to make the decisions for MA, IM & UP were

as shown in Fig. 14.

Lastly, the final weight of alternative number n was

calculated by the following equation with regard to all

of the criteria in the hierarchy:

(29)

where io=number of the criteria in Level 1; ji=number of

the criteria in Level 2 whose parent criterion is the ith

criterion in Level 1; and kji=number of criteria in Level

4 whose parent criteria are the jth criterion in Level 3

and the ith criterion in Level 2.

(A-1)

Network Survey

(A-2)

GIS Data Bank

(A-3)

Classifying algorithm

(Alternative Specification)

Decision Alternative Sets (that the

alternative in each set should be

Prioritized) with respect to its

related objective (MA, IP ,or UP))

(C)

Computer Program for:

1-Aggregation of the Views

2-Conversiion of the Pair –wise

Comparisons to the Vector of Wights

3-Calculation of the inconsistencies

GIS Based Routes & Sub-Routs

Data bank

(B-1)

Apply the Conference Group Decision Making Techniques to:

i) Fix the Problem Goal and Objectives.

ii) Construct the Pre- Final hierarchies (the Decision Criteria

Specification)

iii) Select the Group of experts who should be participated in

the AHP session

iv) receive the approval of the algorithm which specify the

alternative s (Step a -3)

(B-2)

Finalizing the hierarchies through the Delphi Survey

(D)AHP

(D-1)

Determine the Criteria Weights

(D-2)

For each decision alternatives set, perform the alternative

Prioritization with respect to its objective (MA, or IP, or UP)

Determine the routes & sub-routes weights

with respect to the objectives, MA,IM and

UP (route & sub-route) prioritization) Based

on the weights derived from step (C-2)

(F)

Negotiation



14

(Source: Khademi et al. 2010)

Fig. 14 Three AHP hierarchies for three objectives

Kaysi et al. (2010) prioritized the National Road

sections based on a multi-criteria analysis (MCA)

approach, the linear additive model, which evaluates

each scheme on a set of criteria derived from the

various national goals and objectives of the Saudi

authorities.

The framework designed and implemented to set the

priorities was explained by flow-chart as show in Fig.

15. To set the priority an exhaustive set of criteria‟s

been decided. The selected criteria were grouped into 5

main criteria (Group Criteria) reflecting the broad

objectives of the key players: A- Road Network

Development; B- Socio-Economic Development; C-

Economic Efficiency; D- Serving Hajj and Umrah; and

D- Other Criteria including Security, Safety, and

Environment. Each main criterion was then divided into

primary criteria, some of which were divided further

into secondary criteria, thus resulting in a three level

hierarchy as given in Fig. 16.

In the next step the relative weights of each criterion

were derived using AHP method by developing the

questionnaire. The following Linear Additive model

was used to calculate the overall value score of a

proposed road scheme by adding its weighted score on a

set of criteria:

(30)

where Si is the total value score of scheme i; wj is the

relative weight of criterion j; Sij is the value score of

scheme i on criterion j; and n is the total number of

criteria. The schemes were then divided into two groups

based on the road category: primary and secondary

roads. The schemes were then ranked based on the

calculated total scores. The sensitivity analysis was also

carried out to evaluate the robustness of the Saudi

Arabian Road Prioritization (SARP) model.



15

(Source: Kaysi et al. 2010)

Fig.15 The prioritization process

3.3 Based on Economic Analysis

Livneh and Craus (1990) suggested an economic-based

model for prioritizing the maintenance of pavement

sections. The model had a following mathematical form:

(31)

Where P% = the first year rate of return, SN = structural

number = 5 - 0.04DR, where DR is a distress grade (0-

100), PSI = serviceability grade (0-5), AADT = annual

average daily traffic, and k = numeric constant.

The first year rate of return was estimated for a

given rehabilitation investment, that is the agency and

road user‟s costs (before and after upgrading), and the

benefits gained from investment in the maintenance and

rehabilitation work. The governing factor of this model

was AADT.

Data

Collection Objective of

Key Player

GIS Database

Existing Roads

Railway Lines

Airports/Seaports

Regions

Cities

Industrial Area

Agriculture Areas

Topography

Proposed Roads

Mot

Proposed

Road

Schemes

Study

Team

Cost Estimation

Model

Road network Traffic

Model

Study

Team

Budget for Primary

Roads Schemes per

Phase

Criteria

Measurement

s

Set of

Criteria

Scoring

Guidelines

Scores Per

Schemes and

Criteria Co

nsu

ltation

Application

of AHP

Relative Weights of

Criteria

Linear

Additive Model

Total Score Per

Scheme

Ranking of

Primary Road

Schemes at a

national Level

Ranking of

Secondary Road

Schemes by

region

Choice of Primary&

Secondary Data Schemes

to be implemented during

phase

Any More

Phase?

Regional

Budget

for Phase

End of

Prioritization

Process

Repeat process for next

phase

Yes No



16

(Source: Kaysi et al. 2010)

Fig. 16 The hierarchy of the set of criteria

Sharaf & Mandeel (1998) analyzed three techniques for

priority setting. The first technique was a simple ranking

based on four ranking measures viz.: (i) lowest life cycle

cost; (ii) worst condition first; (iii) highest traffic and (iv)

highest benefit/cost ratio. The second technique was a

combined ranking technique based on relative weights

assigned to the above mentioned four ranking measures.

Finally, the third technique was a linear programming

optimization model which considers both time (current

and future) and space (entire network). A comparison

between the three techniques in terms of network

condition over time and in terms of budget deficit over

time was presented. The results indicated a considerable

difference in future network performance under the three

techniques with the optimization technique produced the

best results.

Veeraragavan (2000) presented a methodology of

prioritizing the highway sections for maintenance based

on the current structural and functional condition of the

pavement and the traffic intensity. An economic analysis

was done to evaluate the benefit/cost ratio and net

present value. Based on the highest value of the

economic criteria, the pavement sections were selected

for treatment and the highway sections were ranked on

priority for maintenance.

Roy et. al. (2003) evaluated the uses of HDM-4 as a

versatile tool to study the economic viability of

alternative road projects and to prepare road investment

programmes for the selected sections of State highways

of Kerala. The M&R strategies were selected for

sections based on IRR and B/C values.

Aggarwal et. al. (2004) prioritized the yearly M&R

works for the National Highways based on the

decreasing NPV/Cost ratio. The „Project Analysis‟

component of HDM 4 was used for doing the analysis

PRIORITIZATION OF PRIMARY AND SECONDARY ROADS

Transport

Network

(A) 0.26/0.26

Socio Economic

Development

(A) 0.26/0.26

Economic

Feasibility

(C) 0.09/0.09

Hajj &

Umrah

(D) 0.12/0.12

Other

(E)

0.06/0.06

Traffic Demand

Supply

(A) 0.77/0.200

Connectivity

(A)

0.77/0.200

Connectivity (A)

0.77/0.200

Connectivity

(A) 0.77/0.200

Connectivity (A)

0.77/0.200

Connectivity

(A)

0.77/0.200

Time service

(C1) 0.09/0.09

Traffic Volume during Hajj

(D1) 0.26/0.031

National;

Security (E1)

0.16/0.011

Saving in VOC

(C2) 0.27/0.024

LOS Deterioration during Hajj

(No Subject)

Safety

(E2)

0.62/0.037

Traffic Volume during Umrah

(D3) 0.17/0.020

Environment

(E3)

0.12/0.007

Relative Cost

(C3) 0.30/0.027

LOS Deterioration

During (no project)

(D) 0.12/0.12

Political

Commitment

(E4)

0.08/0.005

Traffic demand

(A1-1) 0.30/0.060

Level of service Deterioration

(no Project)

(A1-2) 0.32/0.064

Extra Capacity

(A1-3) 0.18/0.036

Service Freight

Movement

(A1-4) 0.20/0.040

Multi Model Connectivity

(A2-1) 0.22/0.013

Connecting within National road

Network (A2-2)

0.62/0.037

International Connectivity

(A2-3) 0.18/0.036

Manufacturing

(B2-1) 0.41/0.057

Agriculture

(B2-2) 0.32/0.064

Tourism

(B2-3) 0.18/0.036

Miring

(A2-4) 0.20/0.040

Other Services

(B2-4) 0.15/0.021

Manufacturing

(B3-1) 0.29/0.027

Agriculture

(B3-2) 0.10/0.009

Tourism

(B3-3) 0.13/0.012

Miring

(B3-4) 0.22/0.032

Economic Cities

(B3-4) 0.26/0.024

Weight within Segment /

Relative Weight

Crit

eri

a G

rou

ps

Prim

ary C

rit

eri

a

Seco

nd

ary

Crit

eria



17

and computing the NPV/cost ratio for different

pavement sections of NH under study. A section with

higher NPV/Cost ratio was considered first for

maintenance.

Singh and Sreenivasulu (2005) used programme analysis

of HDM-4 for prioritizing the maintenance of road

sections, under different budget scenarios. The

NPV/Cost ratios were determined for all candidate

sections and were prioritized accordingly.

Parida et al. (2011) & Shah et al. (2012) compared the

two methods for priority ranking of urban road

maintenance, viz. (a) ranking based on subjective rating

and (b) ranking based on economic indicator. The

subjective ranking was done using maintenance priority

index (MPI) which was a function of road condition

index, traffic volume factor, special factor and drainage

factor. The second ranking method was based on

economic indicator in which NPV/Cost ratio was

calculated for each pavement section using the HDM-4

software.

4. Discussion and Conclusions

The main aim of this paper was to build knowledge

about the pavement maintenance prioritization methods

and to present the research studies developed in this area

by different researchers at global level.

It can be concluded that the selection of prioritization

method is a case specific and not applicable everywhere.

The selection of pavement sections on the bases of fund

constraints, may lead to road condition deterioration for

other sections not in priority list. At the same time,

prioritization based on optimization is able to maintain

or even improve road conditions of the overall network.

Also it has been observed that:

- The complexity is added to the calculations as we

move on from simple engineering judgment based to

complex network optimization models, as a

prioritization method.

- Ranking based methods requires less data collection,

than other methods, where data like future traffic

projection, future funding, forecast of effects and

durability of maintenance and pavement deterioration

models need to be studied.

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a critical review of prioritization models for pavement ... · this will help in evaluating the...

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