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Procedía - Social and Behavioral Sciences 54 (2012) 956 - 965

EWGT 2012

15th meeting of the EURO Working Group on Transportation

New optimization model for road network maintenance

management

Susana Menesesa, Adelino Ferreira^*

aTechnology and Management High School of Oliveira do Hospital, Coimbra Polytecnic Institute, Oliveira do Hospital, Portugal bDepartment of Civil Engineering, University of Coimbra, Coimbra, Portugal

Abstract

This paper presents a Multi-Objective Decision-Aid Tool (MODAT) tested with data from the Estradas de Portugal's Pavement Management System (PMS). Nowadays, the PMS used by the main Portuguese concessionaire (Estradas de Portugal, S.A.) uses a deterministic section-linked optimization model with the objective of minimizing the total expected discounted costs over the planning time-span while keeping the road pavements within given quality standards. The MODAT considers three different possible goals: minimization of agency costs (maintenance and rehabilitation costs); minimization of user costs; and maximization of the residual value of pavements. This new approach allows PMS to become interactive decision-aid tools, capable of providing road administrations with answers to "what-if' questions in short periods of time. The MODAT also uses the deterministic pavement performance model used in the AASHTO flexible pavement design method that allows closing of the gap between project and network management. The application of the MODAT is illustrated with a case study involving the main road network of Castelo Branco, a district of Portugal.

© 2012 Published by ElsevierLtd.Selectionand/or peer-review underresponsibilityoftheProgramCommittee Keywords: road assets; pavement management system; pavement performance models; optimization model; maintenance & rehabilitation.

1. Introduction

One of the main components of a Pavement Management System (PMS) is the methodology used to select the best maintenance and rehabilitation (M&R) strategy taking into account the expected evolution of pavement quality. This methodology, realized in a Decision-Aid Tool, may be based on prioritization (ranking) models

* Corresponding author. Tel.: +351-239797101; fax: +351-239797123. E-mail address: adelino@dec.uc.pt

1877-0428 © 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Program Committee doi:10.1016/j.sbspro.2012.09.811

(Wong et al., 2003; Kulkarni et al., 2004) or optimization models (Abaza, 2006; Madanat et al., 2006; Ferreira et al, 2009).

Recently, researchers have concluded that maintenance planning and programming requires optimization analysis involving multi-objective considerations (Fwa et al, 2000; Flintsch and Chen, 2004; Kaliszewski, 2004; Wu and Flintsch, 2009). However, traditionally single-objective optimization techniques have been employed by pavement researchers and practitioners because of the complexity involved in multi-objective analysis. Other researchers concluded that it is possible to develop a Multi-objective Decision-Aid Tool, incorporating into the same optimization model several objectives, for example one for minimization of maintenance costs and another for maximization of the residual value of pavements using the concepts of Pareto optimal solution set and rank-based fitness evaluation (Deb, 2008; Mansouri, 2005; Iniestra and Gutiérrez, 2009).

Nomenclature

ACrst agency cost for applying operation r to road section 5 in year t

Bt budget for year t

Co total cracked pavement area in year 0 (m2/100m2)

Ce structural coefficient of layer n

Cd Cn drainage coefficient of layer n

C cost of the last rehabilitation action applied in pavement section 5

d discount rate

Do total disintegrated area (with potholes and ravelling) in year 0 (m2/100m2)

Hn thickness of layer n (mm)

IRI o pavement longitudinal roughness in year 0 (mm/km)

Mr subgrade resilient modulus (pounds per square inch)

Nmax, maximum number of M&R operations that may occur in road section 5 over the planning time-span

W8o number of 80 kN equivalent single axle load applications estimated for a selected design period and

design lane

Pao pavement patching in year 0 (m2/100m2)

PSIt Present Serviceability Index in year t

PSIs,r Present Serviceability Index value after the application of a rehabilitation action in pavement section 5

R number of alternative M&R operations

Ro mean rut in year 0 (mm)

RVs,T+l residual value for the pavement of section 5

S number of road sections

So combined standard error of the traffic prediction and performance prediction

SNt structural number of a road pavement in year t (AASHTO, 1993)

T number of years in the planning time-span

tc annual average growth rate of heavy traffic

TMDAp annual average daily heavy traffic in the year of construction or the last rehabilitation, in one direction

and per lane

UCst user cost for road section 5 in year t

VOCt vehicle operation costs in year t (€/km-vehicle)

Xrst equal to 1 if operation r is applied to section 5 in year t, and is equal to 0 otherwise

Yt time since the pavement's construction or its last rehabilitation (years)

Zr standard normal deviate

PSIst pavement condition for section 5 in year t

PSI warning level for the pavement condition

a average heavy traffic damage factor or simply truck factor

APSIt difference between the initial value of the present serviceability index (PSI0) and the value of the present

serviceability index in year t (PSIt)

>Fa agency cost functions

Tp pavement condition functions

fr residual value functions

lit user cost functions

Q feasible operations sets

2. Proposed Multi-Objective Decision-Aid Tool

The Multi-Objective Decision-Aid Tool (MODAT) is constituted by the following components: the objectives of the analysis; the data and the models about the road pavements; the constraints that the system must guarantee; and the results. Several objectives can be considered in the analysis, including the minimization of agency costs (maintenance and rehabilitation costs), the minimization of user costs, the maximization of the residual value of pavements at the end of the planning time-span, etc. The results of the application of the MODAT to a road network are constituted by the M&R plan, the costs report, and the structural and functional quality report. The optimization model is formulated as follows:

Objective functions

R S T 1

Min AC £ £ — X ACrSt X Xrst

r=l s=1 t=l V1 + a) (1)

Min UC = YZ TT-ÂT x UCst

S=1 t=1 v + a) (2)

Max RV=X irroF * RV~i (3)

_s=1 v ;_(3)

Constraints

PSIst - ^p(PSIso^Xisi,...,Xist,...,xrîi,...,xrîîX s - 1,...,S; t - 1,...,T

PSIst >PSls, s = 1,...S; t = 1,...,T

Xrst e Q{PSIst), r = 1,...R; s = 1,...S; t = 1,...T (6)

^ Xrst = 1, s = 1,...,S; t = 1,...T

r=1 (7)

ACrst = Wa(PSIst,Xrst), r = 1,...R;s = 1,...S;t = 1,...T (8)

UCst = Wu{PSIst), s = 1,...,S;t = 1,...T (9)

RVs,T+1 = ^r{PSIsJ+i), s = 1,...S (1o)

£ Z ACrst X Xrst ^ Bt, t = r=l S=1 (11)

^^Xrst < N max s, V S = 1,...,S (12)

r=2 t=1

Pavement condition functions

PSI0 = 5 x e-0000065:IR » _ 0.000535 x r02 _ 0.21 x (C0 + D0 + Pa0f5 (13)

PSIt = PSI 0- (4.2-1.5)x10

(logu^yZR*So-9.36<log10(SN+1 )+0.2-2.32<log10(MR)+8.07><|

(1 + tc)Yt - 1 W^ = 365xTMDAp --xa

'80t ^-i-Ly-L^^-p ■

SNt =2 Hn x Cen x Cd (15)

User cost function

VOCt = 1.20487 - 0.49116 x PSIt + 0.05458 x PSIt2

Residual value of pavements function

c PSIst+1 -1.5 RVS T+1 = c x-

S,T +1 s,r PSIsr-1.5

3. Results of the Application of MODAT

The MODAT was tested with data from the Estradas de Portugal's PMS (Picado-Santos and Ferreira, 2008; Ferreira et al, 2009) for planning the maintenance and rehabilitation of the road network considering two objectives, the minimization of agency costs and the minimization of user costs. The Estradas de Portugal road network has a total length of 13836.0 km. The MODAT was applied only to the road network of one of the eighteen districts of Portugal, the district of Castelo Branco. This road network has a total length of 589.9 km and the corresponding network model has 32 road sections.

Figure 1 represents the Pareto optimal set of solutions (Das, 1999) in the objective space by varying the weight values while Figure 2 represents the optimal set of normalized solutions. The point with black color represents the "Knee point" and was obtained considering the following weight values: (wAC, wUC, wRV) = (0.04, 0.96, 0.00); and it corresponds to the following objective values (AC, UC, RV) = (€62.8x106, €1508.8x106, €31.3x106). The range of values for the two objective functions are (ACmin, ACmax) = (€44.2x106, €206.0x106), and (UCmm, UCmax) = (€1424.2x106, €2529.3x106).

From Figures 1 and 2 it can be concluded that, when varying the two weights through a grid of values from 0 to 1 with a fixed increment step, as for example 0.05, the two objective values were not transformed maintaining the same fixed range. Therefore, each weight value not only indicates the importance of an objective, but also compensates, to some extent, for differences in objective function magnitudes.

o ■fS

tn o o

(D tl>

Tä ,o

2400 2200 2000 1800 1600 1400 1200 1000

0 50 100 150 200

Total M&R costs over 20 years (x10A6 €) Fig. 1. Pareto optimal set of solutions

■fS tn o o

0,6 ' I

0,5 0,4 0,3 0,2 0,1 0,0

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 Normalized total M&R costs over 20 years

Fig. 2. Pareto optimal set of normalized solutions

In multi-objective problems there is no perfect method to select one "optimal" solution from the Pareto optimal set of solutions. The final best-compromise solution is always up to the decision maker. For that purpose, four different M&R solutions of the Pareto frontier were considered for comparison:

a) Solution I: Multi-objective optimization approach (corrective-preventive) considering the "Knee point" (wAC = 0.04, wUC = 0.96, wRV = 0.00);

b) Solution II: Multi-objective optimization approach (corrective-preventive) considering the following weights (wAC = 1.00, wUC = 0.00, wRV = 0.00);

c) Solution III: Multi-objective optimization approach (corrective-preventive) considering the following weights (wAC = 0.00, wUC = 1.00, wRV = 0.00);

d) Solution IV: Multi-objective optimization approach (corrective-preventive) considering the following weights (wAC = 0.50, wUC = 0.50, wRV = 0.00).

The costs and normalized costs during the entire planning time-span for these four Pareto optimal solutions are summarized in Figures 3 and 4, respectively. Figure 4 shows that, as expected, solution I ("Knee point") is t he Pareto optimal solution with less normalized value of M&R costs plus user costs. Considering the non-normalized value of M&R costs plus user costs (Figure 3), one can verify that this optimal solution continues to have the least value but this is not necessary to happen. In Meneses and Ferreira (2010), considering a municipal road network with low quality pavements and reduced values of traffic volume, it happened the opposite. Figure 4 also shows that solution I ("Knee point") is the Pareto optimal solution with less total normalized costs, computed by adding M&R normalized costs and user normalized costs and deducting the residual normalized value. Figure 5 represents the predicted PSI average value over the years of the planning time span for all the road network pavements and for each solution.

■ Solution I (Knee point) Solution II Solution III Solution IV

* 2.000

£ 1.500

Ü 1.000

M&R costs User costs M&R Residual value Total costs

costs+user costs

Fig. 3. Costs throughout the planning time-span of 20 years

Fig. 4. Normalized costs throughout the planning time-span of 20 years

......Solution I —o— Solution II x Solution III —û— Solution IV

Fig. 5. PSI average value for all the road network pavements

By analyzing this figure it can be seen that solution III, i.e., the solution of the multi-objective optimization approach (corrective-preventive) considering the weights (wAC = 0.00, wUC = 1.00, wRV = 0.00), corresponds to the largest average PSI values as expected because this solution corresponds to the minimization of user costs. Solution I ("Knee point") is the second best solution in terms of average PSI values also as expected because corresponds to a high weight value for user costs and a small weight value for agency costs (wAC = 0.04, wUC = 0.96, wRV = 0.00).

In addition to these summarized results, the MODAT provides extensive information about the M&R strategy to be implemented for each road section. To analyze these road section-linked results, four road sections were chosen with different attributes in the present year. Table 1 illustrates the attributes of these four road sections including their present PSI value.

Table 2 presents the M&R operations to be applied in the four road sections considering the four M&R solutions of the Pareto frontier. Figure 6 represents the predicted evolution of the PSI value over the years for pavement section 05001 of a national road as a consequence of the execution of the M&R plan. For this pavement section, which is in good quality condition (with a PSI value of 3.81), if solution I of MODAT is adopted, the same M&R operation 2 (non-structural maintenance) would be applied in years 2016 and 2024. If solution II or solution IV of MODAT is adopted no M&R operation will be needed in all the planning time-span. If solution III of MODAT is adopted the recommended M&R operations are very different. The MODAT recommends the application of four M&R operation 5 (major rehabilitation) in years 2016, 2020, 2024 and 2028, with a constant interval of 4 years. In this solution the M&R operations are more and heavier because this solution corresponds to the minimization of user costs which means that the pavement quality must be always high. An identical analysis could be made for any other pavement section. For example, for pavement section 05004 of another national road, which has a PSI value of 2.75, if solution I of MODAT is adopted the M&R operation 4 (medium rehabilitation) would be applied in year 2012 and M&R operation 2 (non-structural maintenance) would be applied in years 2019 and 2026 (Table 2 and Figure 7). If solution II or solution IV of MODAT is adopted only one M&R operation is recommended, which is M&R operation 3 (minor rehabilitation) applied in year 2012. Again, if solution III is adopted the recommended M&R operations are more and heavier as appended for pavement section 05001. In this case the MODAT recommends the application of four M&R operations 5 (major rehabilitation) in years 2012, 2016, 2020, and 2024.

Susana Meneses and Adelino Ferreira /Procedia - Social and Behavioral Sciences 54 (2012) 956 - 965 Table 1. Attributes of road sections

Attributes Road section

Section ID 05012 05003 05004 05001

Road class EN IC IC IP

Pavement type Flexible Flexible Flexible Flexible

District Castelo Branco Castelo Branco Castelo Branco Castelo Branco

Length (m) 21455 14635 19439 1931

Width (m) 5.9 8.6 8.8 9.4

Sub-grade_CBR (%) 5 4 10 6

Structural number 2.11 4.40 3.25 5.20

Age of_pavements (years) 0 10 10 4

Annual average daily traffic 756 5838 5838 4331

Annual average daily heavy traffic 150 800 800 300

Annual growth average tax 3 4 4 3

Truck factor 2.0 4.5 4.5 3.0

PSIo 1.79 2.15 2.75 3.81

Table 2. M&R operations to be applied in road sections

Section PSLï 22222222222222222222 aeuRMi * ^-»u oooooooooooooooooooo

I—'I—'I—'I—'I—'I—'I—'I—'2 2 2 2 2 2 2 2 2 2 U)

Solution I - Knee point ( wAC =0.04, WUC =0.96)

05012 05003 05004 05001 1.79 5 2.15 1 2.75 4 3.81 1 1 3 1 1 1 1 1 1 1 1 1 2 1111111 1112 111 112 1111 1111111 1 1 1 2 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1

Solution II ( WAC =1.00, WUC =0.00)

05012 05003 05004 05001 1.79 5 2.15 1 2.75 3 3.81 1 1 1 1 1 1 1 1 1 1 1 1 1 1111111 2 11113 1 1111111 1111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Solution III ( WAC =0.00, WUC =1.00)

05012 05003 05004 05001 1.79 5 2.15 1 2.75 5 3.81 1 1 5 1 1 1 1 1 1 5 1 5 5 1115 111 15 1115 1 1115 111 1115 111 5 1 5 5 1 1 1 1 1 5 1 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1

Solution IV ( WAC =0.50, WUC =0.50)

05012 05003 05004 05001 1.79 5 2.15 1 2.75 3 3.81 1 1 1 1 1 1 3 1 1 1 1 1 1 1111111 1111111 1111111 1111111 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

KEY (M&R actions):

1 - Do nothing; 2 - Non structural maintenance; 3 - Minor rehabilitation; 4 - Medium rehabilitation; 5 - Major rehabilitation

Fig. 6. Evolution of PSI for pavement section 05001 of a national road

Fig. 7. Evolution of PSI for pavement section 05004 of a national road

4. Conclusions

In the implementation of an optimum solution recommended by the MODAT, a field review must be conducted to identify continuous road sections with the same or identical M&R interventions with the goal of aggregating them into the same road project. It is further recommended that the MODAT is applied as often as necessary (annually or bi-annually) to obtain revised optimum M&R plans that would incorporate the impact of any recent changes that might have taken place in the pavement network. The MODAT constitutes a new useful tool to help the road engineers in their task of maintenance and rehabilitation of pavements. This new approach

allows PMS to become interactive decision-aid tools, capable of providing road administrations with answers to "what-if' questions in short periods of time.

In the near future, our research in the pavement management field will follow two main directions. First, the MODAT will be applied considering also other objectives, beyond the two existent ones, as for example the maximization of the residual value of pavements or the maximization of the road network quality. Second, pavement performance models will be developed using pavement performance data available in some road network databases and will be incorporated into MODAT for future applications to road networks.

Acknowledgements

The authors are grateful to the Portuguese Foundation of Science and Technology for the financial support provided to this study through Grant PTDC/ECM/112775/2009 - MODAT - Multi-Objective Decision-Aid Tool for Highway Asset Management, financed by the European Community Fund FEDER.

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