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An executive model for network-level pavement maintenance and rehabilitation planning based on linear integer programming

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  • Although having too many details can complicate the planning process, this study involves the formulating of an executive model having a broad range of parameters aimed at network-level pavement maintenance and rehabilitation planning. Four decomposed indicators are used to evaluate the pavement conditions and eight maintenance and rehabilitation categories are defined using these pavement quality indicators. As such, some restrictions called ''technical constraints" are defined to reduce complexity of solving procedure. Using the condition indicators in the form of normalized values and developing technical constraints in a linear integer programming model has improved network level pavement M&R planning. The effectiveness of the developed model was compared by testing it under with-and-without technical constraints conditions over a 3-year planning period in a 10-section road network. It was found that using technical constraints reduced the runtime in resolving the problem by 91%, changed the work plan by 13%, and resulted in a cost increase of 1.2%. Solving runtime reduction issues can be worthwhile in huge networks or long-term planning durations.

    Mathematics Subject Classification: Primary: 90C05, 90C90; Secondary: 90B50.

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  • Figure 1.  Cost comparisons from different objective functions

    Figure 2.  Overall cost comparison for different objective functions

    Figure 3.  Overall cost comparison in $ ob3 $ with and without technical constraints

    Figure 4.  Results of objective functions with and without technical constraints

    Table 1.  Comparison of applied methodologies in investigated studies

    StudyOptimization MethodLevel of StudyFormulationModel TypeCondition Indicator
    MuObSiObOthersNetPro
    (TF Fwa, et al., 1996)GADetPSI
    (T Fwa, et al., 1998)GARobustPCI
    (Smilowitz & Madanat, 2000)LMDPCondition StateCondition State
    (TF Fwa, et al., 2000)GARobustPCI
    (Ferreira, et al., 2002)GADetPSI, IRI, SN
    (Chen & Flintsch, 2007)LCPAFuzzyPSI, PCI
    (Wu, et al., 2008)GP & AHPDetCondition State
    (Abaza & Ashur, 2009)CLIPDetPCR
    (Wu & Flintsch, 2009)MDPProbCondition State
    (Meneses & Ferreira, 2010)GADetPSI
    (Moazami, et al., 2011)AHPFuzzyPCI
    (Irfan, et al., 2012)MINLPProbIRI
    (Gao & Zhang, 2013)KnapsackDetPCI
    (Medury & Madanat, 2013)LPProbCondition State
    (Mathew & Isaac, 2014)GADetPCI
    (Meneses & Ferreira, 2015)GADetPSI
    (Saha & Ksaibati, 2016)LCCADetPSI
    (Yepes, et al., 2016)GRASPDetPCI
    (Swei, et al., 2016)MINLPDet & ProbPCR
    Current studyMILPDet$ q \dot{x} (qf, qt, qs, qr), qo $
    MuOb - Multi Objective; SiOb - Single Objective; Net - Network; Pro - Project; Det - Deterministic; Prob - Probabilistic
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    Table 2.  List of indices

    Variable IndexDescription
    $ t, (t \in \{1, 2, \dots, T\}) $Period (year)
    $ n, (n \in \{1, 2, \dots, N\}) $No. of Section
    $ m, (m \in \{1, 2, \dots, M\}) $M&R actions category
    $ b, (b \in \{1, 2, \dots, B\}) $Auxiliary index corresponding to condition
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    Table 3.  List of M&R action categories

    ID No.Action CategoryPolicy
    1Localized safety maintenanceTemporary
    2Localized preventive maintenancePreventive
    3Level 1: Global preventive maintenance with the objective of improving thermal distresses
    4Level 2: Global preventive maintenance with the objective of improving skid resistance in addition to the level 1 objective
    5Level 3: Global preventive maintenance with the objective of surface irregularity correction in addition to improving the level 2 objective
    6Surface rehabilitationCorective
    7Deep rehabilitation(rehabilitation and
    8Reconstructionreconstruction
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    Table 4.  Model parameters

    VariableDescriptionDomain
    $ \mu $A large value (close to infinity)$ (\mu \to \infty ) $
    $\epsilon$A small value (close to zero)$ (\epsilon \to 0) $
    $va_{n, t}$Pavement financial value of section $ n $ at the year $ t $ while is in the best condition$va_{n, t} \in [0, \infty) $
    $ drop\dot{x}_{n, t} $Condition drops from $ t=1 $ to the target year of $ t $ if no M&R action is performed$drop\dot{x}_{n, t} \in [0, 1] $
    $ drop v\dot{x}_{n, m, t, b} $Condition drops from the year of performing M&R action $ (m) $on a pavement section$ (n) $ with condition index $ b $ to the target year of $ t $$ drop v\dot{x}_{n, m, t, b} \in [0, 1]$
    $ inq\dot{x}_n $Initial condition$ inq \dot{x}_n \in [0, 1] $
    $ im\dot{x}_m $Condition improvement$ im \dot{x}_m \in [0, 1] $
    $ crl\dot{x}_n $Lower threshold of condition$ crl\dot{x}_n \in[0, 1] $
    $ crlo_{n, s} $Lower threshold of overall condition$ crlo_{n, s} \in [0, 1] $
    $ crh\dot{x}_n $Upper threshold of condition$crh\dot{x}_n \in[0, 1] $
    $ crho_n $Upper threshold of overall condition$ crho_n \in [0, 1] $
    $ bu_t $Allocated budget$ bu_t \in [0, \infty) $
    $ co_{n, m, t} $M&R action cost (operating cost) $co_{, m, t} \in [0, \infty) $
    $ crq_n $Critical condition in the vehicle operation cost (VOC) vs overall condition curve$ crq_n \in [0, 1] $
    $ cuc_{n, t} $VOC at the critical condition$ cuc_{n, t} \in [0, \infty) $
    $cub_{n, t}$VOC at the worst condition (0)$cub_{n, t}\in [0, \infty) $
    $ cug_{n, t} $VOC at the best condition (1)$cug_{n, t}\in [0, \infty) $
    $ ce_{n, m, t} $Delay cost due to performing M&R actions$ ce_{n, m, t}\in [0, \infty) $
    $ k\dot{x} $Coefficient of $ \dot{x} $ condition in overall condition equation$ k\dot{x}\in[0, 1] $
    cDeterioration constant in overall condition equation$ c\in[0, 1] $
    $ \dot{x} $ can be replaced by $ f, t, s $ or $ r $ which respectively related to Fatigue, Thermal distress, Skid or Roughness.
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    Table 5.  Variables

    VariableDescriptionDomain
    $ x_{n, m, t} $Binary variable for M&R action $ m $, section $ n $ and year $ t $ in the M&R work planning$ x_{n, m, t} \in \{0, 1\} $
    $ q \dot{x}_{n, t} $Condition indicator$ q \dot{x}_{n, t} \in [0, 1] $
    $ w \dot{x}_{n, t, b} $Auxiliary variable of condition$ w \dot{x}_{n, t, b} \in [0.5 -10 \epsilon , 1]$
    $ kw \dot{x}_{n, t, b} $Binary variable determining whether (1) or not (0) auxiliary variable of condition is in index $ b $$ kw \dot{x}_{n, t, b} \in \{0, 1\} $
    $ cubq_{n, t} $Binary variable determining whether (1) or not (0) the condition is in the poor zone in the VOC vs overall condition curve$ cubq_{n, t} \in \{0, 1\} $
    $ cuqg_{n, t} $Binary variable determining whether (1) or not (0) the condition is in the good zone in the VOC vs overall condition curve$ cuqg_{n, t} \in \{0, 1\} $
    $ cb_{n, t} $Auxiliary variable for the effect of poor condition on the VOC$ cb_{n, t} \in [0, 1] $
    $ cg_{n, t} $Auxiliary variable for the effect of good condition on the VOC$cg_{n, t} \in [0, 1] $
    $ qo_{n, t} $Overall condition indicator$ qo_{n, t} \in [0, 1] $
    $ k_{n, m, t} $Intensity of distress variable$ k_{n, m, t} \in [0, 1] $
    $ z_{n, m, t} $Auxiliary variable for intensity of distress$ z_{n, m, t} \in [0, 1] $
    $ da \dot{x}_{n, t} $Condition drop$ da \dot{x}_{n, t} \in [0, 1] $
    $ dd \dot{x}_{n, t} $Auxiliary variable for condition drop$ dd \dot{x}_{n, t} \in [0, 1] $
    $ d \dot{x}_{n, m, t, t^{'}} $Condition drop at $ t^{'} $ once M&R action was performed at $ t $$ {d \dot{x}_{n, m, t, t^{'}} } \in [0, 1] $
    $ \dot{x} $ can be replaced by $ f, t, s $ or $ r $ which respectively related to Fatigue, Thermal distress, Skid or Roughness.
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    Table 6.  Types of influential costs used in this study

    IDCost
    $ ce $Delay cost due to performing M&R actions
    $ co $Operating cost
    $ cu $Vehicle Operation cost
    $ va $Consumed pavement financial value compared to the highest pavement value
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    Table 7.  Limits of condition indicators for ignoring M&R action

    m12345678
    $ qo $ $ crl< $ $ <crl $ * $ <crl $ $ <crl $ $ <crl $--$ **crh< $
    $ qf $-$ <crl$$ <crl$$<crl$$<crl$---
    $ qt $--$ crh< $-----
    $ qs $---$ crh< $----
    $ qr $----$ crh< $---
    * The $ <crl $ indicates the lower threshold value for a condition indicator in which performing M&R action over sections with values of less than that is not justified.
    ** The $crh < $ indicates the upper threshold value for a condition indicator in which performing M&R action over sections with values greater than that is not justified.
    - No limitations on performing M&R action.
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    Table 8.  M&R actions assignment results

    $ n $
    (section)
    $ ob1 $$ ob2 $$ ob3 $
    $ t=1 $$ t=2 $$ t=3$$ t=1 $$ t=2 $$ t=3 $$ t=1 $$ t=2$$ t=3 $
    1Noting62NotingNotingNotingNoting62
    2556NotingNotingNotingNoting62
    36626NotingNoting64Noting
    462262Noting62Noting
    5Noting666NotingNoting6NotingNoting
    6522, 552Noting522
    76566NotingNoting62Noting
    8Noting62, 562Noting62Noting
    942, 462, 42Noting2, 42Noting
    10252NotingNotingNotingNotingNoting2
     | Show Table
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    Table 9.  Percentage of allocation to the available budget in each year

    $ t $ (year)Budget Utilization (%)Budget ($1000)
    $ob1 $ $ob2$ $ob3 $
    199.9499.9799.972518
    299.746.8580.682946
    399.9903.373450
    Total99.8930.5056.218914
     | Show Table
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    Table 10.  With and without technical constraints comparison of M&R action assignments

    $ n $$ ob3 $$ ob3 $ Without
    $ t=1 $$ t=2 $$ t=3 $$ t=1 $$ t=2 $$ t=3 $
    1Noting62Noting62
    2Noting62Noting62
    364Noting64Noting
    462Noting62Noting
    56NotingNoting6NotingNoting
    65222, 522
    762Noting46Noting
    862Noting62Noting
    92, 42Noting2, 42Noting
    10NotingNoting2Noting52
     | Show Table
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    Table 11.  With and without technical constraints runtime comparisons

    Objective Function$ ob1 $$ ob2 $$ ob3 $$ ob3 $ Without
    Solution Time (min)4619108
     | Show Table
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  •   K. A. Abaza  and  S. A. Ashur , Optimum microscopic pavement management model using constrained integer linear programming, International Journal of Pavement Engineering, 10 (2009) , 149-160. 
      C. Chen  and  G. Flintsch , Fuzzy logic pavement maintenance and rehabilitation triggering approach for probabilistic life-cycle cost analysis, Transportation Research Record: Journal of the Transportation Research Board, 1990 (2007) , 80-91. 
      A. Ferreira , L. Picado-Santos  and  A. Antunes , A segment-linked optimization model for deterministic pavement management systems, International Journal of Pavement Engineering, 3 (2002) , 95-105. 
      T. F. Fwa , W. T. Chan  and  C. Y. Tan , Genetic-algorithm programming of road maintenance and rehabilitation, Journal of Transportation Engineering, 122 (1996) , 246-253. 
      T. Fwa , W. Chan  and  K. Hoque , Analysis of pavement management activities programming by genetic algorithms, Transportation Research Record: Journal of the Transportation Research Board, 1643 (1998) , 1-6. 
      T. F. Fwa , W. T. Chan  and  K. Z. Hoque , Multiobjective optimization for pavement maintenance programming, Journal of Transportation Engineering, 126 (2000) , 367-374. 
      L. Gao  and  Z. Zhang , Management of pavement maintenance, rehabilitation, and reconstruction through network partition, Transportation Research Record: Journal of the Transportation Research Board, 2366 (2013) , 59-63. 
      G. Chiandussi , M. Codegone , S. Ferrero  and  F. E. Varesio , Comparison of multi-objective optimization methodologies for engineering applications, Computers & Mathematics with Applications, 63 (2012) , 912-942.  doi: 10.1016/j.camwa.2011.11.057.
      M. Irfan , M. B. Khurshid , Q. Bai , S. Labi  and  T. L. Morin , Establishing optimal project-level strategies for pavement maintenance and rehabilitation-a framework and case study, Engineering Optimization, 44 (2012) , 565-589. 
      J. Mallela and S. Sadavisam, Work Zone Road User Costs: Concepts and Applications, US Department of Transportation, Federal Highway Administration, 2011.
      A. Manik , K. Gopalakrishnan , A. Singh  and  S. Yan , Neural networks surrogate models for simulating payment risk in pavement construction, Journal of Civil Engineering and Management, 14 (2008) , 235-240. 
      B. S. Mathew  and  K. P. Isaac , Optimisation of maintenance strategy for rural road network using genetic algorithm, International Journal of Pavement Engineering, 15 (2014) , 352-360. 
      A. Medury and S. Madanat, Simultaneous network optimization approach for pavement management systems, Journal of Infrastructure Systems, 20 (2013), 04014010.
      S. Meneses  and  A. Ferreira , Multi-objective decision-aid tool for pavement management systems, Proceedings of the 12th World Conference on Transport Research, (2010) , 1-11. 
      S. Meneses  and  A. Ferreira , Flexible pavement maintenance programming considering the minimisation of maintenance and rehabilitation costs and the maximisation of the residual value of pavements, International Journal of Pavement Engineering, 16 (2015) , 571-586. 
      D. Moazami , H. Behbahani  and  R. Muniandy , Pavement rehabilitation and maintenance prioritization of urban roads using fuzzy logic, Expert Systems with Applications, 38 (2011) , 12869-12879. 
      D. Moazami  and  R. Muniandy , Fuzzy inference and multi-criteria decision making applications in pavement rehabilitation prioritization, Australian Journal of Basic and Applied Sciences, 4 (2010) , 4740-4748. 
      M. S. Pishvaee  and  J. Razmi , Environmental supply chain network design using multi-objective fuzzy mathematical programming, Applied Mathematical Modelling, 36 (2012) , 3433-3446.  doi: 10.1016/j.apm.2011.10.007.
      M. Ramezani , M. Bashiri  and  R. Tavakkoli-Moghaddam , A robust design for a closed-loop supply chain network under an uncertain environment, The International Journal of Advanced Manufacturing Technology, 66 (2013) , 825-843. 
      P. Saha  and  K. Ksaibati , A risk-based optimisation methodology for pavement management system of county roads, International Journal of Pavement Engineering, 17 (2016) , 913-923. 
      T. Scheinberg and P. Ch Anastasopoulos, Pavement preservation programming: A multi-year multi-constraint optimization methodology, In presentation at the 89th Annual Meeting of the Transportation Research Board and publication in the Transportation Research Record, 2010.
      M. Y. Shahin, Pavement management for airports, Roads and Parking lots, 2005.
      K. Smilowitz  and  S. Madanat , Optimal inspection and maintenance policies for infrastructure networks, Computer-Aided Civil and Infrastructure Engineering, 15 (2000) , 5-13. 
      O. Swei, J. Gregory and R. Kirchain, Pavement management systems: Opportunities to improve the current frameworks, In TRB 2016 Annual Meeting, volume 16, 2015.
      F. Wang , Z. Zhang  and  R. Machemehl , Decision-making problem for managing pavement maintenance and rehabilitation projects, Transportation Research Record: Journal of the Transportation Research Board, 1853 (2003) , 21-28. 
      Z. Wu , G. W. Flintsch  and  T. Chowdhury , Hybrid multiobjective optimization model for regional pavement-preservation resource allocation, Transportation Research Record, 2084 (2008) , 28-37. 
      Z. Wu  and  G. W. Flintsch , Pavement preservation optimization considering multiple objectives and budget variability, Journal of Transportation Engineering, 135 (2009) , 305-315. 
      V. Yepes , C. Torres-Machi , A. Chamorro  and  E. Pellicer , Optimal pavement maintenance programs based on a hybrid greedy randomized adaptive search procedure algorithm, Journal of Civil Engineering and Management, 22 (2016) , 540-550. 
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