Planning Pavement Maintenance and Rehabilitation Projects in the New Pavement Management System in Texas 3. Feng Hong, PhD, PE

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1 Planning Pavement Maintenance and Rehabilitation Projects in the New Pavement Management System in Texas 0 Feng Hong, PhD, PE Texas Department of Transportation, Austin, TX Feng.Hong@TxDOT.gov Eric Perrone, PE AgileAssets Inc. 00 Bee Caves Rd. Suite 00, Austin, TX Eric@agileassets.com Magdy Mikhail, PhD, PE (corresponding author) Texas Department of Transportation, Austin, TX Magdy.Mikhail@TxDOT.gov Ahmed Eltahan, PhD, PE AgileAssets Inc. 00 Bee Caves Rd. Suite 00, Austin, TX Aeltahan@agileassets.com Total Number of Words: words + table + figures = 0 words 0

2 0 ABSTRACT The Texas Department of Transportation (TxDOT) manages a network of over,000 lane miles. Optimum management of the pavement can lead to improved performance at lower costs. TxDOT invested significant effort to develop a new generation pavement management system in the past two years. The new state of the art pavement management system, integrates the engineering experience and research results of over three decades at TxDOT. The capacity of the system includes data archival, database management, mapping, reporting, performance prediction and optimization analysis for decision makers. This paper shows how the new system was used to plan, optimize, analyze, and evaluate pavement maintenance and rehabilitation projects. The advanced analytical functionality of the system is highlighted. As an initial step the new system was used to replace the current four-year plan reporting methodology utilized by TxDOT. The results demonstrate that the new system can serve as an effective tool in support for decision makers, pavement engineers, budget planners, and administrators. 0 0

3 BACKGROUND The Texas Department of Transportation (TxDOT) manages over,000 lane miles of pavement network (), which is the largest in the United States. Pavement management at TxDOT is carried out at two levels. The Headquarters office is responsible for data collection, archival, database management, network-level analysis, and annual status reporting. Project level Pavement Maintenance and Rehabilitation (M&R) decisions are decentralized. The state is divided into districts. Each district is responsible for design, construction, and M&R of pavements. The pavement network size varies between around,000 to,000 lane miles among the districts. In the past decade, over $ billion was spent annually for M&R to keep the pavements in good condition. There are two sources of funding for pavement M&R projects, the Unified Transportation Program (UTP) and the Maintenance budget. The UTP includes a category dedicated to preventive maintenance and rehabilitation projects; and the maintenance budget is used in routine maintenance, preventive maintenance, and light rehabilitation projects. M&R funds are distributed among the districts based on formulas that include pavement conditions, network size, traffic level, environment, etc. According to the Texas Rider appropriation bill as a legislative requirement, TxDOT must provide the state legislative budget board and the Governor s office with a plan on how the M&R funds are allocated for a four-year period and demonstrate the expected performance of the pavement network over that time. TxDOT has set a performance goal to have 0 percent of the pavements in good condition across the entire network. This requirement is also consistent with the Moving Ahead for Progress in the st Century Act (MAP) by the Federal government for performance measures and accountability (). In order to develop the four year projections, the planning and selection of M&R projects is conducted in two stages. In the first stage, each district selects a list of M&R projects along a -year planning horizon based on the local assessment of their network. The assessment matrix involves a series of variables such as surface distress, ride quality, surface age, structural capacity, traffic, and percentage of truck traffic. It can also include other variables such as safety, heavy oil vehicle impact, etc. Historically the selection methodologies in the districts vary from ranking equations to engineering judgement. The planned projects selected by the districts include the following information: plan year, district, county, location (e.g., reference marker limits), treatment type and cost, work description, and other related information. The planned projects information is stored in two different TXDOT systems, the Design and Construction Information System (DCIS) and Maintenance Management System (named Compass ). The former corresponds to the funding from the UTP while the latter corresponds to the funding from the Maintenance budget. After the districts have selected and entered the information for their projects into these systems a second stage follows focusing on analysis and performance prediction. The main effort is to predict the network-level performance. This will include ) quantifying pavement deterioration for the planned horizon, and ) predicting the effect of the planned M&R projects on the pavement performance. In many cases the districts do not specify exact projects and locations for the budgets allocated if significant uncertainty exists. In some districts the planning of M&R projects includes identified

4 0 0 locations for most projects for the first two years but for years and the planning process only allocates funding for preventive maintenance activities by county rather than specific project locations. For example, it is difficult to plan projects for years and especially for districts experiencing a lot of heavy load activities from the energy sector. In order to provide the required projections to management, the funds for projects without specified locations must be assigned to specific projects so that the conditions of those locations can be projected into the future. In typical pavement management systems there are many approaches to allocating the budget to projects (). For example, it can be based on worst condition first criterion or alternatively a benefit-cost ratio can be used as a criterion, with the higher benefit-cost ratio projects being given the priority. Ideally, an optimization approach should be used to allocate the budget so that it is used in the most efficient manner. This approach is highlighted in the paper. Furthermore, it is highly valuable that the district users are provided a hands-on tool to assist them with project selection during the planning stage. It is important to allow district users the capability of running an evaluation of their network performance based on their preliminarily selected projects. It is also desirable that the district users can adjust the list of planned projects and evaluate the effect on the predicted performance as their needs change and new information becomes available. The newly developed Pavement Management System (PMS) at TxDOT allows for evaluation of selected projects and also for running different scenarios to evaluate the performance. 0 TXDOT NEW GENERATION OF PMS: AGILEASSETS PAVEMENT ANALYST Effectively managing a pavement network heavily relies on a modern PMS (, ). The TxDOT legacy mainframe-based PMS has been used since the early 0 s. Significant effort has been used in the past two years to develop a new generation of PMS for TxDOT. The new system is referred to as the Pavement Analyst (PA hereafter). The implementation was a joint effort by teams from TxDOT and AgileAssets. PA is a fully web based system that allows access to the pavement management data and analytics through a web browser to any users within TxDOT. It integrates the engineering experience and research results of over three decades in TxDOT (,,,, ). The capacity of the new system includes data archival, management, mapping, reporting performance prediction, optimization analysis for decision making, etc. The core pavement management system is composed of six main modules as illustrated in Figure with the content briefly introduced below. Figure : TxDOT Pavement Analyst Main Modules Interface

5 0 Database: Pavement condition, construction, inventory, and other data related to pavement in TxDOT system such as crash data and heavy vehicle permit/route data. Analysis: Performance prediction and network-level optimization functionality. Reports: A series of standard or customized reports to accommodate TxDOT annual reporting and other needs. Setup: Defines the system parameters that control all analysis and engineering decision making within the system Utilities: System management utilities GIS: Displays the data such as pavement condition or projects on a Texas-based Geographical Information System (GIS) map. Among these modules, the components involved in the TXDOT four year plan analysis are highlighted herein. These include prediction models, decision trees, and optimization analysis Prediction Models Prediction models play a critical role in the pavement management system (, ). Two categories of models can be used in pavement condition prediction, empirical and mechanistic models. Empirical models are widely used in pavement management (0). Furthermore, the empirical models are mainly composed of Markov models and regression models (,,, ). Markov models are mainly used for network level condition prediction and budget allocation. In order to accommodate both project selection at project level and network-level condition evaluation at the network level, the regression models were adopted in PA. The prediction models serve the system in two ways. First, they are used to predict conditions on a section by section basis as part of the network level analysis. These predictions can then be rolled up to provide projections of condition on the network in part or in whole. Second, the predicted conditions are used as input in the optimization-based decisions. The predictions are used for treatment selection and estimation of treatment effectiveness. The TXDOT prediction models were initially developed and calibrated over time (, ) and now configured for use within the Pavement Analyst system. The modeling framework accounts for the large network covering different conditions in Texas by allowing separate models to be used in different situations. The prediction models developed through TXDOT research are categorized into varying groups based on the following factors: Climate subgrade zones: Zone, Zone, Zone, and Zone across the state of Texas. Zone covers wet-cold climate and poor, very poor, or mixed subgrade. Zone covers wet-warm climate and poor, very poor, or mixed subgrade. Zone covers dry-cold climate and good, very good, or mixed subgrade. Zone covers dry-warm climate and good, very good, or mixed subgrade. Pavement families: asphalt pavement, Continuous Reinforced Concrete Pavement (CRCP), Jointed Concrete Pavement (JCP). The asphalt pavement is further divided into subgroups of A, B, and C mainly based on the structural capacity. Treatment types: Preventive Maintenance (PM), Light Rehabilitation (LR), Medium Rehabilitation (MR), and Heavy Rehabilitation (HR).

6 Traffic loading levels: low, medium, and heavy traffic based on the predicted 0 years of Equivalent Single Axle Loads (ESALs). Within each of the families defined by the criteria above a sigmoidal curve is used to project the pavement conditions. The model specification adopted for each model group is as follows: = Where, () 0 is the dependent variable, which refers to the level of distress (e.g., alligator cracking, transverse cracking, longitudinal cracking, rutting etc., for asphalt pavement, spalled cracking, punchout, etc., for CRCP, and slabs with longitudinal cracking, failed slabs etc., for JCP) or ride quality loss for all pavement types (); is the age of pavement since last treatment; and,, and are the model coefficients. These parameters were recently calibrated for each model group respectively (). Once the is predicted for each distress type and ride quality, all are combined into a distress, ride and combined condition score based on their utility or weight values () as developed by TXDOT in the past 0 years. Overall condition of the pavements is captured in a -00 condition score where to is Failure condition, to is Poor condition, 0 to is Fair condition, 0 to is Good condition, and 0 to 00 is Very Good condition respectively (). 0 0 Decision Trees The analysis process involves a huge network composed of a large number of pavement sections, which might require significant amounts of time to run the optimization. For practical purposes, a modification/simplification is required to reduce the running time. Thus a set of engineered decision trees are introduced to provide recommended treatments appropriate for given input pavement conditions and inventory. The idea is to determine a rational treatment type for each section. That is, before the optimized project selection analysis, a feasible treatment type is selected based on relevant engineering variables. This will result in a need-based treatment for the individual section. Whether that treatment will be finally selected will be determined by the optimization problem objectives and user supplied constraints. Since the optimization engine focuses on the recommended treatments from the decision process the size of the optimization problem is greatly reduced. For example, instead of trying five alternatives among do-nothing, PM, LR, MR, and HR for a given section in a given year, only one that fits into the decision tree will be used in the optimization process, thus reducing the running time significantly. The TXDOT decision trees have been established based on engineering experience and interviews with TXDOT engineering staff () and the system will allow these criteria to be reviewed and updated as needs arise. The trees use available pavement data in the system and

7 they provide the criteria by which appropriate treatment types can be assigned to each pavement section. Critical pavement information used within the decision process is: pavement type, traffic, predicted pavement distress and ride quality amongst other factors. Note that the recommended treatment supplied by the decision process does not necessarily mean that a project on that section with that treatment will be selected in a given analysis. The actual selection of projects from a list of decision process recommendations is controlled by the optimization in the PA system. The following figures give a few examples of the decision trees configured into the PA. These examples do not include all trees in the TxDOT system.

8 Traffic & Condition Score (a): Decision Tree Based on Variables of Traffic and Condition Score

9 Transverse Cracks (b): Decision Tree Based on Variable of Transverse Cracks Longitudinal Cracks (c): Decision Tree Based on Variable of Longitudinal Cracks Figure : Examples of Decision Trees 0 When it comes to decision making, variables are fed into the corresponding trees, which will generate a series of treatment recommendations. The most severe treatment is finally picked as the output. For example, for a given asphalt pavement section, if the Traffic & Condition Score tree recommends HR; the Transverse Cracks tree recommends LR; the Longitudinal Cracks tree recommends Do-nothing; the Fatigue Cracks tree recommends PM; and so on, the output recommendation will be the HR. 0 Optimization Analysis PA provides the flexibility to run network level analysis to model the problem of interest in various scenarios. For example, varying scenarios could be run under different budget levels. Scenarios can be configured to run for the entire state or for individual districts and counties. The optimization analysis allows the system to use the configured parameters to select projects that will maximize conditions given a particular budget or minimize costs given desired condition goals. The PA uses an integer programming based optimization approach described elsewhere (,, ).

10 0 PROJECT PLANNING AND NETWORK PERFORMANCE EVALUATION Data preparation Two interfaces are especially designed in PA to import data from TxDOT DCIS and Compass systems respectively, as shown in the drop-down menu in Figure. As a result, two tables are used to store the imported projects, referred to as DCIS Staging Table and Compass Staging Table. Changes involving data quality checks could be made in the staging tables. Then the cleansed data are moved into the final tables, referred to as DCIS Table and Compass Table. The analysis then uses these projects to conduct the four-year plan projections. It includes two major steps: budget allocation and performance prediction. The details are discussed below. 0 Figure : Menu of Network Analysis Functionality in PA 0 Budget Allocation/Project Selection through Optimization Analysis The four-year plan analysis for TxDOT projects the performance of the network into the future given the preselected projects and unallocated budgets from the districts. As discussed previously the district selected projects in the -year plan include both location specific and funds allocated only by counties for projects to be selected in years and. The system is able to directly project the condition of the located projects but the optimization analysis is used to select the projects for the county based funds specified by the districts. The PA system uses its integer programming based optimization algorithm to select the candidate projects and then project condition of the network based on the optimized projects selected. For this analysis the system is configured with an objective to maximize the network-level pavement performance improvement under the budget constraints for each plan year. The formulation of the optimization problem is described below.

11 Objective: Max.,,, (.a) Subject to: (, ),, (.b) 0 Where,, is the decision variable, meaning treatment alternative is selected for section ; is the weight of each section, using the lane mileage of section ;, is the performance improvement of section under treatment alternative ;, is the unit cost (dollar per lane mile) for section under treatment alternative ; and is the budget for each individual county C, where C =,,,. 0 The integer decision variable,, is actually a binary variable taking the values 0 or. A indicates that the optimization assigns the decision tree recommended treatment and 0 indicating no treatment is applied ( Do Nothing ). There are four possible treatments available for each pavement type in the system, PM, LR, MR and HR. In the particular analysis type run for this exercise, the performance improvement for a section,,, is calculated as the difference in area under the treated deterioration curve and the area under untreated deterioration curve as projected by the TxDOT performance equations due. The variable, is the total budgets calculated from the projects loaded from the Compass and DCIS tables mentioned earlier. In this analysis the budget for each county is summed to get the full funding amount for each county in the system. Funds for those projects already identified with location are taken off the top leaving only the un-allocated funds behind for use by the optimization engine. Thus the optimization analysis focuses on the budget for unallocated projects. The algorithm will assign these un-allocated budgets across the candidate projects so as to maximize the overall predicted pavement performance over time. 0 Performance Prediction The performance prediction involves two types of projects, with and without treatment. For the projects with treatment, a condition improvement is applied after the treatment. Then the pavement is deteriorated according to the prediction models assigned to the treated section. For those projects without treatment, the pavements are deteriorating according to their original assigned performance curve. As a result, the condition for each pavement section in each of the plan years is obtained. The predictions of the pavement conditions are summarized to generate the network-level pavement performance statistics.

12 It is also noted that for the analysis during a -year period, the output of Year t serves as the input of Year t+, and so on. This means the performance prediction of Year t+ is based on the predicted performance of Year t. Results and Reporting Based on the above components, the optimization procedure can be run to generate the plan results and required network projections. The major output contents are discussed below. 0 0 Work Plan Results As shown in Figure, the output table for the work plan results includes a list of planned projects. Each record includes the detailed information of a project involving plan year, treatment type, estimated cost, highway name and limits, project status, length, and other information. In particular, the project status includes two types, development and recommendation. A project labeled development means that project was specified by the district as part of their initial plan; while ones labeled recommended means it is selected from the optimization algorithm by PA. These two types of projects make up the entire plan set under which the network condition projections were made. It is noted that this output can serve as an input for further analysis if any adjustment by the users is warranted. For example, a user can add, delete, or modify the projects and re-run the optimization to evaluate the results until the user achieves an optimum solution.

13 Hong, Perrone, Mikhail, and Eltahan Figure : Output Table of Work Plan Results

14 0 Constraint Results Output The Constraint Results output table for this analysis shows the budget constraints compared to the funding actually allocated by the analysis. As an example, Figure shows the budget constraint results for each county along the planning horizon. The two variables are Constraint Limit Value and Resulting Value. The former is the total budget provided to the analysis for each county in a given year and the latter is the allocated budget spent by the preselected projects and the optimized projects chosen by the algorithm. By comparing these two values, the user has an idea of how the budget is used. As shown in the Figure, in most cases the budget is fully or almost fully used as a result of the optimized allocation. If and when a gap occurs between the budgeted funding and the funding allocated, the system is unable to find candidate projects to spend the remaining money. In most cases these differences in funding are small.

15 Hong, Perrone, Mikhail, and Eltahan Figure : Output Table of Constraint Results M&R Summary Based on the detailed information for each planned project, the summary of all projects is reported in the Report module in PA. For example, in the statewide scenario, Figure presents the state-wide lane miles of pavements to receive PM, LR, MR, and HR in each plan year. It is

16 0 implied that approximately to 0 percent of the entire network will receive treatment from year to year. It is also suggested that the majority of pavements will receive PM to maximize the network performance under the given budget. A similar output can be generated for each district or county in the Report module in PA. Figure illustrates the total cost distribution among the four treatment types for the entire state in the plan horizon. Similarly, as in the treatment lane miles chart, the largest portion of treatment cost will come from the PM. This also reflects the fact that lower budgets and fewer projects are planned for the later years mainly due to uncertainty with funding. It should be pointed out that the plan is updated on a yearly basis which means year in the current plan will become year when the analysis is run again in the next fiscal year. Lane Miles 0,000,000,000,000,000 0,000,000,000,000,000 0 PM LR MR HR Treatment Figure : Summary of Treatment Lane Miles in the Plan Plan Year Plan Year Plan Year Plan Year

17 Cost $,000,000,000 $00,000,000 $00,000,000 $00,000,000 $00,000,000 Plan Year $00,000,000 Plan Year $00,000,000 Plan Year $00,000,000 Plan Year $00,000,000 $00,000,000 $0 PM LR MR HR Treatment Figure : Summary of Total Cost for Each Treatment in the Plan 0 0 Network Performance Prediction Another critical aspect of the plan is to evaluate the effect of planned projects on the networklevel performance, i.e, performance prediction. The objective is to help the decision makers assess the effectiveness of the investment. By combining the predicted condition of the treated and un-treated projects, the network-level performance is obtained. As the most important network-level performance measure used by TxDOT, the predicted percentage of lane miles in good condition in each district and the entire state is presented in Table. In the meantime, the base year percentage of lane miles in good condition is provided for comparison. Overall, it shows that the network performance improves in the first plan year and then declines with time. This trend jointly reflects the reduced funding and pavement deterioration with time. In addition, different scenarios can be used to compare the network performance under varying funding levels. For example, Figure shows the curves for percentage of lane miles in good condition in the planned budget and no budget scenarios respectively. This can be used to advise upper level decision makers of the effect of funding level on the network performance. Note that the TxDOT goal is 0 percent or more of the lane miles across the entire network in good condition. For the worst scenario, i.e., without any funding for M&R, the network will deteriorate to around 0 percent of the network in good condition. Under the planned budget, there is still a funding gap to reach the state goal in the next years.

18 Table : Network Performance in the Base Year and Planned Years District Base Year Plan Year Plan Year Plan Year Plan Year.0%.0%.%.0% 0.%.%.%.0%.% 0.0%.%.%.%.% 0.0% 0.%.0%.0%.%.0%.%.%.%.%.% 0.% 0.%.%.%.%.%.% 0.0%.%.%.% 0.% 0.0%.%.%.%.%.%.%.0% 0.%.%.% 0.%.% 0.%.%.%.00%.0%.0%.% 0.%.%.%.%.%.% 0.%.0% 0.%.%.0%.%.%.0% 0.%.0%.%.%.0%.0%.0%.% 0.%.%.%.%.%.%.%.%.%.%.% 0.%.%.0% 0.%.% 0.%.%.0%.%.%.%.0% 0.%.0%.%.%.%.0% 0.%.%.%.%.0%.%.% 0.% 0.%.0%.%.%.%.%.%.%.% State.%.%.%.%.%

19 Percent Good or Better Lane Miles 00% 0% 0% 0% 0% 0% 0% 0% 0% 0% History Prediction State Goal Year Plan No Budget 0% Base Year Plan Year Plan Year Plan Year Plan Year Figure : Network Performance in Different Funding Scenarios Vs. State Goal 0 GIS-Based Projects Report The PMS users rely on maps to display and visualize the information of the planned projects. To meet this requirement, the mapping module in PA can display pavement condition and project information in a GIS environment. Basically, this provides the engineer or planner a view of the planned projects and their attributes geographically. As an example, Figure illustrates the distribution of the projects both in geographical and temporal manner in the -year planning horizon. It also includes the treatment information for each project. This tool allows users to visualize both the pre-selected projects and the recommended projects.

20 0 Figure : Planned Projects Displayed on A GIS Map in PA 0 0 CONCLUSIONS Planning M&R projects is a critical part of effective and efficient pavement system management. It involves a comprehensive process, which involves every step in the PMS, from data collection, quality checks, archival, performance prediction, decision making to reporting. In the recently developed new generation of PMS in TxDOT, the Pavement Analyst, all steps are integrated in a streamlined process. This paper presents the capabilities of the Pavement Analyst in the TxDOT four-year plan development and evaluation. The analysis and reporting functionality is highlighted specifically as it relates to the required four-year planning process within TxDOT. It is demonstrated that the new system can facilitate performance-based pavement management for planning M&R projects. The new system also makes the pavement analysis and data available to all users within TxDOT via their web browser. This four-year plan analysis is the first analytical process to be rolled out in the new system as it is replacing a required reporting function for the department. The new system has more capabilities that can be leveraged to assist the department. TxDOT expects to be expanding the use of the system to help decision makers with the following activities as the system is rolled out over the next few years: Initial project candidate identification Assisting the initial budgeting process to identify the effects of proposed budgets and allocations over the long term

21 Planning analyses over longer time horizons Running strategy based analysis and optimization looking at proposed long-term strategies for pavement sections REFERENCES. Condition of Texas Pavements- PMIS Annual Report FY 0-FY 0. Texas Department of Transportation, Austin, Texas, 0.. Federal Highway Administration. MAP- Moving Ahead for Progress in the st Century. <Accessed: May, 0>.. Haas, R., W. R. Hudson and J. Zaniewski. Modern Pavement Management. Krieger Publishing Company, Malabar, Florida,.. Paterson, W. D. O. Road Deterioration and Maintenance Effects: models for planning and management. The John Hopkins University Press, Baltimore, Maryland,.. Zhang, Z. and M. Murphy. A Web-Based Pavement Performance and Maintenance Management and GIS Mapping System for Easy Access to Pavement Condition Information: Final Report. Report No P-Final. Texas Department of Transportation, Austin, Texas, 0.. Dossey, T., W. Hudson, V. Anderson, and J. Wang. Texas Pavement Management System: Summary Report. Report No. TX-/0-F. Texas Department of Transportation, Austin, Texas,.. Gharaibeh, N., T. Freeman, S. Saliminejad, A. Wimsatt, C. Chang-Albitres, S. Nazarian, I. Abdallah, J. Weissmann, A. Weissmann, A. Papagiannakis, and C. Gurganus. Evaluation and Development of Pavement Scores, Performance Models and Needs Estimates for the TxDOT Pavement Management Information System Final Report. Report No. FHWA/TX-/0- -. Texas Department of Transportation, Austin, Texas, 0.. Stampley, B., B. Miller, R. Smith, and T. Scullion. Pavement Management Information System Concepts, Equations, and Analysis Models. Report No. TX-/-. Texas Department of Transportation, Austin, Texas,.. Smith, R., B. Mukherjee, M. Zulyaminayn, C. Pilson, T. Dossey, and B. McCullough. Integration of Network- and Project-Level Performance Models for TxDOT PMIS. Report No. FHWA/TX-0/-. Texas Department of Transportation, Austin, Texas, Hong, F. Modeling Heterogeneity in Transportation Infrastructure Deterioration: Application to Pavement. Ph.D. Dissertation, The University of Texas at Austin, Texas, 00.. Butt, A. A., Shahin, M. Y., Carpenter, S. H., and Carnahan, J. V. Application of Markov process to PMS at network level. Proc., rd Int. Conf. on Managing Pavements, Vol., National Academy Press, Washington, D.C.,,.. Golabi, K., Kulkarni, R.B., Way, G.B. A Statewide Pavement Management System. Interfaces, Vol., No.,, pp. -.. Medury, A., and S. Madanat. Simultaneous Network Optimization Approach for Pavement Management Systems. Journal of Infrastructure Systems, ASCE. 0(), 0.. PMIS Technical Manual. Texas Department of Transportation, Austin, Texas, 0.. Wang, F., Zhang, Z., Machemehl, R.B. Decision-Making Problem for Managing Pavement Maintenance and Rehabilitation Projects. Transportation Research Record, No., 00, pp. -.

22 . Li, N., Haas, R., Huot, M. Integer Programming of Maintenance and Rehabilitation Treatments for Pavement Networks. Transportation Research Record, No.,, pp. -.. Scheinberg, T. and Anastasopoulos, P. Pavement Preservation Programming: A Multi-Year Multi-Constraint Optimization Methodology. Paper No. 0-. Transportation Research Board th Annual Meeting CD-ROM Proceedings, 00, Washington, D.C.

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