Optimization models for network-level transportation asset preservation strategies

Transcription

1 The University of Toledo The University of Toledo Digital Repository Theses and Dissertations 2014 Optimization models for network-level transportation asset preservation strategies Shuo Wang University of Toledo Follow this and additional works at: Recommended Citation Wang, Shuo, "Optimization models for network-level transportation asset preservation strategies" (2014). Theses and Dissertations This Dissertation is brought to you for free and open access by The University of Toledo Digital Repository. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of The University of Toledo Digital Repository. For more information, please see the repository's About page.

2 A Dissertation entitled Optimization Models for Network-Level Transportation Asset Preservation Strategies by Shuo Wang Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Engineering Dr. Eddie Y. Chou, Committee Chair Dr. Defne Apul, Committee Member Dr. Liangbo Hu, Committee Member Dr. George J. Murnen, Committee Member Dr. Hongyan Zhang, Committee Member Dr. Patricia Komuniecki, Dean College of Graduate Studies The University of Toledo December 2014

3 Copyright 2014, Shuo Wang This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author.

4 An Abstract of Optimization Models for Network-Level Transportation Asset Preservation Strategies by Shuo Wang Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Engineering The University of Toledo December 2014 The aging transportation network and significantly constrained budget environment in the U.S. have prompted many transportation agencies to search for optimal asset preservation strategies. This dissertation presents the development and implementation of a networklevel, multiple-year optimization process for managing multiple transportation assets. The optimal preservation strategy is determined in three stages. At the first stage, the relative importance of different asset types is estimated using the analytic hierarchy process (AHP) method to include consideration of various factors such as asset value, asset condition, and safety. A linear programming model is established to determine the optimal budget allocation and treatment policy considering multiple asset types simultaneously. At the second stage, work plans for each asset component are generated based on the networklevel optimization results and using project selection models based on AHP method and multiple attribute utility theory (MAUT). At the third stage, the selected projects are further optimized considering the geographic locations by project coordination models based on constraint programming and integer programming. The objective of project coordination is to maximize the total number of the projects that can be combined to iii

5 achieve cost savings, by rescheduling some projects subject to budget constraints and project timing constraints. The main advantages of the optimization models developed in this study are the ability to generate the optimal budget allocation among different asset types and various rehabilitation treatments, forecast future asset condition, generate candidate project lists for a large scale transportation network, and coordinate multiple asset projects in nearby locations. A set of example problems were solved using the four-lane divided highway network in District 2 of Ohio. Pavement and bridges were the two types of assets considered. The results show that the proposed models can be used by transportation agencies to support their cross-asset management decisions. iv

6 Acknowledgements Many people have assisted me in conducting this study. I would like to thank my advisor Dr. Eddie Y. Chou for providing the opportunity and financial support for me to continue my graduate education. I appreciate his valuable guidance on my dissertation. I am also grateful to the members of my dissertation committee, Dr. Defne Apul, Dr. Liangbo Hu, Dr. George J. Murnen, and Dr. Hongyan Zhang, for their helpful suggestions and allowing me to defend this dissertation. I would also like to acknowledge the Ohio Department of Transportation for providing graduate assistantship during the course of my doctoral study. v

7 Table of Contents Abstract... iii Acknowledgements...v Table of Contents... vi List of Tables...x List of Figures... xiii Chapter Introduction Transportation Asset Management Limitations of Existing Approaches New Integrated Approach Objective of Research...6 Chapter Literature Review Decision Support Techniques Analytic Hierarchy Process Linear Programming Goal Programming Multiple-Attribute Utility Theory...12 vi

8 2.1.5 Integer Programming Constraint Programming Existing Transportation Asset Management Systems Pavement Management Systems Bridge Management Systems Cross Asset Management Systems Application of Macroscopic Approach Application of Microscopic Approach Application of Integrated Approach Summary and Comments...34 Chapter Methodology Overview Stage 1: Network-Level Optimization AHP Model to Prioritize Asset Components Cross-Asset Optimization Model Stage 2: Project Selection Overview AHP Model Multiple Attribute Utility Model Stage 3: Project Coordination Overview Integer Programming Model...61 vii

9 3.4.3 Constraint Programming Model...64 Chapter Implementation Overview Network Selections Asset Types Prioritization Network-Level Optimization Project Selection and Coordination...70 Chapter Results and Discussion Stage 1: Network-Level Optimization Dataset Description Asset Types Prioritization Effect of Budget Level on Asset Condition Optimization Results Stage 2: Project Selection Dataset Description Project Selection by AHP Project Selection by MAUT Stage 3: Project Coordination Dataset Description Project Coordination Results Additional Examples viii

10 5.4.1 Parametric Study Project Coordination with Additional Constraints Comparison of Historical Data and Optimization Results Discussion Network-Level Optimization Discussion Project Selection Discussion Project Coordination Discussion Chapter Conclusions and Recommendations Summary and Conclusions Network-Level Optimization Project Selection Project Coordination Recommendations for Future Research References Appendix A Appendix B Appendix C Appendix D ix

11 List of Tables Table 2.1 Random Index Values (Saaty 1980) Table 2.2 Constraint Programming vs. Integer Programming (Milano 2004; Thorsteinsson 2001; Focacci et al. 2002; Edis and Ozkarahan 2011) Table 2.3 Summary of Individual Management Systems Table 2.4 Summary of Cross Asset Management Systems Table 3.1 Asset Condition Index Definition Table 3.2 Example of Criteria Comparison Matrix Table 3.3 Example of Pairwise Comparison Matrices under Each Criterion Table 3.4 Example of Project Selection Criteria Comparison Matrix Table 3.5 Example of Intensity Level Pairwise Comparison Matrix Table 5.1 Unit Costs of Preservation Treatments Table 5.2 Allowable Treatments Table 5.3 Markov Transition Matrices for Condition Prediction Table 5.4 Budget Allocation across Pavement and Bridge Decks ($Million) Table 5.5 Recommended Amount of Pavement to be Repaired (Lane-Mile) Table 5.6 Recommended Amount of Bridge Decks to be Repaired (1,000 Square-Foot) 81 Table 5.7 Predicted Asset Condition Distribution (%) Table 5.8 Sample Pavement Inventory Data for Project Selection x

12 Table 5.9 Sample Bridge Deck Inventory for Project Selection Table 5.10 Criteria Pairwise Comparison Matrix Table 5.11 Intensity Level Definition Table 5.12 Condition Intensity Level Pairwise Comparison Matrix Table 5.13 Traffic Volume Intensity Level Pairwise Comparison Matrix Table 5.14 Age Intensity Level Pairwise Comparison Matrix Table 5.15 Climate Intensity Level Pairwise Comparison Matrix Table 5.16 Relative Weights of Intensity Levels Table 5.17 Pavement Project List Generated by AHP (2014) Table 5.18 Bridge Deck Project List Generated by AHP (2014) Table 5.19 Pavement Project List Generated by MAUT (2014) Table 5.20 Bridge Deck Project List Generated by MAUT (2014) Table 5.21 Sample Uncoordinated Project List (Henry County) Table 5.22 Sample Coordinated Project List (Henry County) Table 5.23 Allowable Treatments (Revised for Parametric Study) Table 5.24 Budget Allocation across Pavement and Bridge Decks with Revised Allowable Treatments ($Million) Table 5.25 Recommended Amount of Pavement to be Repaired with Revised Allowable Treatments (Lane-Mile) Table 5.26 Recommended Amount of Bridge Decks to be Repaired with Revised Allowable Treatments (1,000 Square-Foot) Table 5.27 Comparison of Annual Expenditure for Historical Data and Optimization ($ Million) xi

13 Table 5.28 Comparison of Average ACI for Historical Data and Optimization Table A.1 Pavement Inventory for Project Selection in Ohio District Table A.2 Bridge Deck Inventory for Project Selection in Ohio District Table B.1 Pavement Project List Generated by AHP Table B.2 Bridge Deck Project List Generated by AHP Table C.1 Pavement Project List Generated by MAUT Table C.2 Bridge Deck Project List Generated by MAUT Table D.1 Coordinated Project List Based on Integer and Constraint Programming xii

14 List of Figures Figure 3-1 Flowchart of the cross-asset decision support models Figure 3-2 Hierarchy structure for AHP models Figure 3-3 Structure of AHP model to prioritize asset components Figure 3-4 Project selection from a list of candidates Figure 3-5 Structure of AHP model for project selection Figure 3-6 Example of asset project coordination Figure 4-1 Network selection Figure 4-2 Determine relative importance of different asset types Figure 4-3 Network-level cross-asset optimization Figure 4-4 Project selection by AHP and MAUT Figure 5-1 Initial pavement condition distribution Figure 5-2 Initial bridge deck condition distribution Figure 5-3 Impact of budget level on asset deficiency level Figure 5-4 Impact of budget level on average asset condition Figure 5-5 Budget allocation across pavement and bridge decks Figure 5-6 Recommended amount of pavement to be repaired Figure 5-7 Recommended amount of bridge decks to be repaired Figure 5-8 Predicted asset deficiency level xiii

15 Figure 5-9 Predicted average asset condition index Figure 5-10 Predicted pavement condition distribution Figure 5-11 Predicted bridge deck condition distribution Figure 5-12 Utility function of condition (ACI) Figure 5-13 Utility function of traffic volume (ADT) Figure 5-14 Utility function of age Figure 5-15 Utility function of climate (Snowfall) Figure 5-16 Original uncoordinated five-year asset work plan Figure 5-17 Coordinated five year-asset work plan (constraint programming) Figure 5-18 Coordinated five-year asset work plan (integer programming) Figure 5-19 Budget allocation across pavement and bridge decks with revised allowable treatments Figure 5-20 Recommended amount of pavement to be repaired with revised allowable treatments Figure 5-21 Recommended amount of bridge decks to be repaired with revised allowable treatments Figure 5-22 Comparison of predicted asset deficiency level Figure 5-23 Comparison of predicted average asset condition index Figure 5-24 Certain projects that should not be performed simultaneously Figure 5-25 Coordinated five-year asset work plan with additional constraints Figure 5-26 Initial pavement condition distribution in Figure 5-27 Comparison of annual expenditure from optimization results and historical data xiv

16 Figure 5-28 Comparison of asset condition obtained from optimization results and historical data xv

17 Chapter 1 Introduction 1.1 Transportation Asset Management Transportation is essential for a nation s development and growth (Garber and Hoel 2001). Optimal use of the available maintenance and rehabilitation budgets has become critical for transportation agencies, because of the aging highway network and the budget cuts at most agencies (Wang 2011). Transportation Asset Management is defined by AASHTO (2013) as a strategic and systematic process of operating, maintaining, upgrading and expanding physical assets effectively throughout their lifecycle. It aims to assist transportation agencies in viewing the current condition of physical assets, allocating budget for various asset categories, determining the best long-term funding strategy, and so on (AASHTO 2013). Maintenance and rehabilitation treatments for transportation assets can be grouped into several types, such as preventive maintenance, minor rehabilitation, and reconstruction. The unit costs of those treatments vary significantly, and their effect on condition improvement also varies (Abaza 2007). It is often a complicated problem for highway agencies to determine the best treatment policy and budget allocation to maintain the 1

18 overall network condition above an acceptable level with minimum cost. Some transportation agencies determine the annual budget level and allocate the available funds based upon experience or engineering judgment, which is not always an efficient way of managing transportation assets, especially in a constrained budget environment such as now. Therefore, an effective decision support tool for transportation asset management has become a necessity for many agencies. Asset management systems for pavement and bridges, which are two key components of the transportation infrastructure system, have been developed and used for several decades (Golabi et al. 1982; Ravirala et al. 1996; Chen et al. 1996; Abaza 2007; Lounis 2005; Elbehairy et al. 2009). However, most of the existing systems consider different types of assets individually and lack the capability of conducting cross-asset management. High level decision makers often need the capability of network-level trade-off analysis to determine the best resource allocation among different assets. In this case, a cross-asset management decision support tool which can to take into account multiple assets would be very useful for decision makers. In addition, optimizing each asset category individually without coordination may not be the most cost-effective way of asset management. For instance, a bridge repair project might occur just a few months after a pavement reconstruction project in the same location, causing unnecessary traffic delays and additional equipment cost (Zhang et al. 2002). In this case, it would be more reasonable if the two projects could be implemented at the same time to minimize the agency cost as well as the user cost (Zhang et al. 2002). 2

19 Therefore, determining the optimal cross-asset maintenance and rehabilitation strategies has attracted the attention of many researchers (Sinha and Fwa 1989; Zhang et al. 2002; Sadek et al. 2003; Smadi 2008; Ravirala and Grivas 1995; Guerre et al. 2005; Fwa and Farhan 2012; Boadi and Amekudzi 2013; Selih et al 2008; Dehghani 2013). A review of the existing literature is presented in Chapter 2 of this dissertation. 1.2 Limitations of Existing Approaches Two main approaches adopted by researchers in optimal transportation asset management are the macroscopic approach and the microscopic approach (Abaza 2007; Abaza 2009). In a macroscopic approach, assets are grouped into different condition categories, and then mathematical optimization or trade-off analysis is performed to determine the overall condition distribution and budget allocation plan among various asset components (Golabi et al. 1982; Chen et al. 1996; de la Garza et al. 2010; Grivas and Schultz 1994; Abaza 2007; Dehghani et al. 2013). As a traditional way of managing transportation assets, the macroscopic approach is able to perform relative long term analysis on large transportation networks efficiently. However, this approach often only provides theoretical solutions, as it is not able to generate a practical and specific project list to implement the optimal results. In a microscopic approach, each individual asset unit (i.e. a pavement segment or a bridge) or project candidate is considered, and specific maintenance and rehabilitation work plans can be generated by either optimization models or analytical ranking methods (Ravirala 3

20 and Grivas 1995; Bonyuet et al. 2002; Xiong et al. 2012; Selih et al. 2008; Li 2009; Abaza 2009; Fwa and Farhan 2012; Augeri et al. 2011; Boadi and Amekudzi 2013). Most researchers introduce binary variables in the microscopic approach optimization model to provide practical results for each asset unit. However, the computational requirement for solving an integer or mixed-integer programming model is much higher especially when the problem size is large (Hillier and Lieberman 2010). Although some researchers use genetic algorithms to obtain a heuristic solution of the optimization model, it may not find the true optimal solution and it requires high programming complexity (Wu 2008). Other researchers apply prioritization techniques, such as benefit cost ratio analysis, multiple attribute utility theory and analytic hierarchy process, in the microscopic approach model to avoid the high computational requirement, but the results are often not optimized (Sadek et al. 2003; Guerre et al. 2005; Farhan and Fwa 2009; Dabous and Alkass 2008; Boadi and Amekudzi 2013; Zavitski et al. 2008). Therefore, the microscopic approach is often difficult to implement when the transportation network is relatively large. Considering the disadvantages of both approaches, some researchers employ the integrated approach in their asset management models (Gharaibeh et al. 1999; Zhang 2002; Sadek et al. 2003; Guerre et al. 2005). However, the existing integrated models still have limitations: (1) Some models cannot provide the optimized solution. (2) Some are not flexible enough for practical implementation. If some parameters need to be modified, many procedures have to be performed before conducting actual cross asset analysis. 4

21 (3) Most of the models cannot schedule the asset preservation projects in a coordinated way considering the adjacent projects. 1.3 New Integrated Approach This dissertation presents a new approach for transportation asset management to overcome the limitations of the existing models for the following reasons: (1) The linear goal programming model can generate optimal network-level budget allocation strategy for large-scale transportation asset networks considering multiple asset types simultaneously. The performance target of each asset type is considered to be a goal in the optimization model. This provides a flexible approach for practical implementation without performing tedious procedures before conducting actual cross asset analysis. (2) Multiple criteria should be taken into account in selecting asset project candidates. Both analytic hierarch process (AHP) and multiple attribute utility theory (MAUT) are powerful techniques for multi-criteria decision analysis. These two techniques are applied to select the most beneficial asset preservation projects considering multiple criteria. (3) By integrating the network-level optimization model (linear goal programming model) and the multi-criteria project selection model (AHP and MAUT), the decision support tool can generate optimal solution for large scale networks and provide work plans considering individual asset items. This integrated approach can take advantage of both the macroscopic approach and the microscopic approach. 5

22 (4) Coordination models are developed to systematically generate coordinated work plans for multiple asset types to achieve cost savings. The cross-asset project coordination problem is modeled as a scheduling problem with the objective of combining as many adjacent projects as possible subject to a set of constraints. Constraint programming is a relatively new technique, powerful in dealing with scheduling problems and handling complicated constraints. Integer programming is a traditional optimization method which can handle scheduling problem as well. Both integer programming model and constraint programming model are formulated and their results are compared. 1.4 Objective of Research The major purpose of this research is to develop a decision support tool for cross-asset optimization using an innovative approach to overcome the limitations of existing models. The new approach is capable of (1) dealing with large networks of multiple transportation assets, (2) providing optimal solutions regarding budget allocation and preservation strategies, (3) generating specific work plans for each individual asset considering multiple criteria, (4) coordinating projects of different asset types according to their geographical locations. This research will focus on the optimization of pavements and bridge decks for the following reasons. First, pavement and bridge are two key transportation asset components and they consume most of the preservation funds compared to culverts, guardrails, noise walls, and signs. Second, the deck system is the weakest part of a bridge and requires 6

23 rehabilitation every years, while other parts could last several decades (Morcous 2006). Although this model considers only two types of assets, it has the potential to be extended to include more assets types. Specifically, the objectives of this study include: 1. To review existing research in transportation asset management systems, including individual systems and cross-asset systems. 2. To develop analytic hierarchy process models (AHP) for estimating the relative importance of multiple criteria. 3. To develop a linear programming model for optimal budget allocation and treatment strategy across different asset types at network-level. 4. To develop a multiple attribute utility model to implement the network-level optimization results by selecting project candidates from the asset network based on multiple criteria. 5. To develop a coordinated project scheduling model considering adjacent asset units with the application of goal programming, integer programming, and constraint programming. 6. To develop a decision support tool by implementing the mathematical models using ASP.NET, SQL Server, LP Solve and IBM ILOG CPLEX. 7

24 Chapter 2 Literature Review 2.1 Decision Support Techniques Analytic Hierarchy Process The theory of Analytic Hierarchy Process (AHP), developed by Thomas L. Saaty in the 1970s, is a powerful multiple criteria decision-making process (Saaty 1980). AHP can deal with decision-making problems when both qualitative and quantitative factors have to be considered (Saaty 1990; Saaty 1994). It was initially utilized to solve problems of contingency planning for Department of Defense. This theory has been applied in many fields, such as medicine, business, government, resource allocation, and engineering (Doubas and Alkass 2008). Many researchers have employed AHP in transportation asset management problems. Farhan and Fwa (2009, 2011) developed a pavement maintenance prioritization system considering multiple distresses using AHP. Smith and Tighe (2006) illustrated two examples of applying AHP in transportation infrastructure management. Dabous and Alkass (2008) presented a decision support method based on AHP for selection of bridge rehabilitation strategy considering multiple criteria and uncertainty. Cafiso et al. (2002) described a method of providing multicriteria analysis framework for pavement 8

25 maintenance management using AHP. Ramadhan et al. (1999) illustrated the application of AHP in calculating the weights of the relative importance of pavement maintenance priority ranking factors. The basic steps of AHP include (Farhan and Fwa 2011; Saaty 1980): (1) Modeling the problem as a hierarchy. A problem is decomposed into individual independent elements, including an overall goal, a set of alternatives, and a group of criteria. The criteria are often broken down into subcriteria, sub-subcriteria, and etc. (2) Prioritization based on pairwise comparison. First, the relative importance of each criterion is evaluated using pairwise comparison, expressed as a criteria comparison matrix. Then, the ranking of the alternatives under each criterion is also evaluated through pairwise comparison, expressed as alternative comparison matrices. Saaty (1980) recommends using a nine-point scale to estimate the comparative difference in a pairwise comparison of two elements. Value 1 represents equal importance, value 3 represents weakly more importance, value 5 represents strongly more importance, value 7 represents very strongly importance, and value 9 represents absolutely more importance. An example of such matrices is as follows (Equation 2.1): 1 a12 a1 n 1 a12 1 a2n A a1 n 1 a2n 1 where n is the number of elements within one group of pairwise comparison; aij is the importance of element i over element j. 9

26 (3) Combination of pairwise comparisons to form a priority vector. The most common approach of deriving the priority vectors is Saaty s eigenvector method. The priority vector (w) is found by satisfying Aw max w, where max is the largest eigenvalue of matrix A. w is then normalized by replacing w with w n w i i 1. (4) Examination of consistency of the decision maker s judgment. The consistency ratio (CR) is defined by Saaty as the ratio of consistency index (CI) to the average random index (RI) (Table 2.1) for the same order matrix, as expressed in equation 2.2: CR CI RI 2.2 where CI ( max n) ( n 1). Table 2.1 Random Index Values (Saaty 1980) Number of elements (n) Random Index (RI) Linear Programming Linear programming is a powerful mathematical technique for dealing with the problem of allocating limited resources among competing activities in a best possible way (Hillier and Lieberman 2010). All functions and constraints of a linear programming model are required to be linear functions. Thanks to the efficient solution algorithms and the rapid progress in computation power, linear programming models can be solved within an 10

27 acceptable time period even if the problem size is quite large (Hillier and Lieberman 2010). Therefore, many researchers, such as Golabi et al. (1982), Bako et al. (1995), Chen et al. (1998), and Abaza (2007), have developed network-level optimization models using linear programming Goal Programming Goal programming (GP) is a mathematical programming technique, which is an extension of linear programming to handle multiple-objective and conflicting-goal problems, and has been widely used as a decision support tool since the end of 1960s and the early 1970s (Schniederjans 1984). Charnes et al. (1955) first presented the basic idea of GP, which is minimizing the deviations of the objective functions (Wu 2008; Schniederjans 1995). The term goal programming did not appear until Charnes and Cooper (1961) s linear programming textbook was published (Schniederjans 1995). There are two types of GP models based on the algorithm solution: weighted model and preemptive model (Schniederjans 1995). In the weighted model, each goal is assigned a relative weight, and the objective function is to minimize the total weighted deviation from the goals. In the preemptive model, all goals are prioritized in order of importance, and one goal is optimized at a time (Taha 2003). GP is capable of capturing critical elements of a problem and is easy to implement, so it has been applied in many asset management systems (Wu 2008). Grivas and Schultz (1994) and Ravirala and Grivas (1995) presented the application of GP in the development of an integrated bridge and pavement management system. Millar (1993) proposed a GP model for pavement project selection, which incorporated all conflicting goals and the priority structure. Wu et al. (2008) published a decision support 11

28 model based on GP for the optimization of the short-term pavement preservation budget across maintenance activities and districts. Bertolini et al. (2006) developed an approach to deal with the maintenance selection problems in an oil refinery using GP. Many researchers such as, Millar (1993), Wu et al. (2008), and Bertoline (2006), use AHP to determine the relative weights or priority rank of the goals, forming a combined GP-AHP model. The formulation procedure of a GP problem is as follows (Schniederjans 1984): (1) Definition of the decision variables. (2) Definition of the goal constraints. (3) Determination of the preemptive priorities. (4) Determination of the differential weights. (5) Definition of the objective function. (6) Statement of the non-negativity constraints Multiple-Attribute Utility Theory Multiple-Attribute Utility Theory (MAUT) is an efficient technique for ranking alternatives considering multiple criteria. One of the first applications of MAUT is the research on selecting location for a new airport in Mexico City in 1970s (de Neufville 1990). According to Wu (2008), MAUT is based on the utility theory proposed by Neumann and Morgenstern (1947). Keeney and Raiffa (1976) developed the specific evaluation techniques and procedures of MAUT. Patidar et al. (2007) and Goicoechea et al. (1982) presented the typical steps of applying MAUT. 12

29 The utility theory is an approach of ranking and qualifying the relative preference between sets of consequences on a particular scale (de Neufville 1990). Neumann and Morgenstern (1947) suggested a lottery approach to estimate the one-dimensional utility function. When the two assumptions, preferential independence and utility independence, are satisfied, the multiple attribute utility function can be decomposed into a set of one-dimensional functions that can be recombined. The multiattribute utility function is then determined by Equation 2.3(de Neufville 1990): Kk U( X ) KU X ) ( i i where U(X) is the multiattribute utility function; U X ) is one-dimensional utility function; k i is the scaling factor for each individual utility; K is a normalizing parameter. ( i When the interactions between different attributes can be ignored, the multiattribute utility function can be defined simply as U X ) wu( X ), where wi are scaling factors or ( i i weights between different attributes. This elementary method has been used widely in transportation asset management systems (Bai et al 2013; Selih et al 2008; Wu 2008; Patida et al. 2007; Johnson 2008; Rashid and Herabat 2008) Integer Programming The complete name for integer programming is integer linear programming, which indicates that the integer programming model is derived from the linear programming 13

30 model by adding a restriction that some or all the variables must be integer or discrete values (Taha 2003; Hillier and Lieberman 2010). Solving an integer programming model is much more difficult than solving a linear programming model, especially when the problem size is large or the constraints are complicated (Taha 2003). However, binary integer programming models, which contain only 0-1 variables, are easier to handle than general integer programming models (Hillier and Lieberman 2010). Therefore, binary integer programming models have been widely used in transportation asset management systems (Li et al. 1998; Ferreira et al. 2002; Tack and Chou 2002; Wang et al. 2003; Fwa et al. 2001; Abaza 2009; Ng et al. 2009; Ravirala and Grivas 1995; Bonyuet et al. 2002; Selih et al. 2008). In these models, each asset unit is assigned a set of binary variables representing whether or not an applicable repair activity should be conducted. A specific maintenance and rehabilitation plan can be generated for each asset unit. The computational requirement for a binary integer programming model is still relatively higher than linear programming. Hence, the application of this technique is limited in very large-scale transportation networks Constraint Programming Constraint programming (CP) was developed in the 1980s based on artificial intelligence and computer programming languages (Hillier and Lieberman 2010). CP has been used to solve mathematical programming problems, such as combinatorial optimization problems and integer programming problems (Baptiste et al. 2001). One of the main advantages of 14

31 CP is the great flexibility of expressing various types of constraints, such as mathematical constraints, disjunctive constraints, relational constraints, explicit constraints, and logical constraints (Baptiste et al. 2001; Hillier and Lieberman 2010). Therefore, CP can be used to formulate compact models for complex problems (Hillier and Lieberman 2010). The key idea of CP is to use constraints actively in the process of domain deduction and constraint propagation to reduce the computational effort (Baptiste et al. 2001; Hillier and Lieberman 2010). In traditional mathematical programming, constraints are only used to test the feasibility of a solution. On the other hand, constraint programming can eliminate some possible values from the variable domain, deduce new constraints, and test the feasibility according to the constraints (Baptiste et al. 2001). After constraint propagation and domain deduction, a search procedure is performed to find feasible solutions. Different values from the variable domain are assigned to variables and further constraint propagation and domain deduction continue (Hillier and Lieberman 2010). A brief comparison between CP and integer programming is presented in Table 2.2. Table 2.2 Constraint Programming vs. Integer Programming (Milano 2004; Thorsteinsson 2001; Focacci et al. 2002; Edis and Ozkarahan 2011) Constraint Programming Integer Programming No guidance from the objective function Objective function is used as a guide in finding the optimal solution No relaxation Relaxation is used Search for feasible solutions Focus on improvements on lower bounds Various constraint types Linear constraints Constraints are evaluated sequentially Simultaneously evaluate all constraints Hillier and Lieberman (2010) decribed the following three steps of applying CP in integer programming problems: 15

32 (1) Model formulation using various constraint types. (2) Finding feasible solutions to satisfy all constraints. (3) Searching for optimal solution. Constraint programming is powerful in the first two steps, whereas integer programming is more efficient in the third step. Much attention has been paid to the development of integrated models in which each technique is applied where it is most powerful (Hillier and Lieberman 2010; Focacci et al. 2002; Milano and Wallace 2006). CP has been applied widely in various domains. Stobbe and Engell (1999) presented a constraint programming approach for intelligent scheduling of tasks in chemical plants. Edis and Ozkarahan (2011) developed a combined approach using integer programming and constraint programming to solve resource-constrained parallel machine scheduling problems. Chan and Hu (2002) described the application of constraint programming in the production scheduling problems in the precast manufacturing plants. Quiroga et al. (2005) employed a constraint programming approach to address the scheduling problems in a flexible manufacturing system considering tool allocation and resource assignment. Lin et al. (2010) developed a constraint programming model for optimal routing and scheduling tank trailers with the objective of minimizing transportation costs. Wang and Liu (2013) formulated a road inspection scheduling model with the application of constraint programming to allocate resources efficiently and shorten the inspection time. Weil et al. (1995) developed a constraint programming model for nurse scheduling. Topaloglu and Ozkarahan (2011) presented a constraint programming approach to solve medical resident scheduling problems. 16

33 2.2 Existing Transportation Asset Management Systems Most preservation funds of transportation agencies are invested in pavement and bridges, which are the two essential components of a transportation asset network. Pavement management systems and bridge management systems have been developed and implemented by many agencies for several decades. The cross-asset management, a relatively new topic, has begun to receive the attention of many researchers. This section will briefly review the existing research in individual management systems (i.e. pavement and bridge) first, and then it will focus on the existing cross-asset management systems. The results of literature review are summarized in Table 2.3 and Table 2.4. Table 2.3 Summary of Individual Management Systems Approach Techniques References Limitations Golabi et al. (1982) Linear Chen et al. (1996) programming; No specific work Macroscopic De la Garza et al. non-linear plan (2010) programming Wu and Flintsch (2009) Microscopic Integer Programming; Goal Programming Heuristic algorithm Li et al. (1998) Wang et al. (2003) Abaza (2009) Gao and Zhang (2013) Ravirala et al. (1996) Lounis (2005) Elbehairy et al. (2009) Fwa et al. (2001) Tack and Chou (2002) High computational requirement; not applicable to large scale networks Might not be optimal; high programming complexity 17

34 Table 2.4 Summary of Cross Asset Management Systems Approach Techniques References Limitations Linear Grivas and Schultz Macroscopic programming; (1994) Goal Posavljak et al. (2013) No specific work plan Programming Sinha et al. (1981) Microscopic Integrated Integer Programming; Goal Programming Heuristic algorithm Prioritization Linear programming; Decision tree; Prioritization Ravirala and Grivas (1995) Bonyuet et al. (2002) Selih et al. (2008) Li and Sinha (2004) Li (2009) Fwa and Farhan (2012) Xiong et al. (2012) Bai et al. (2012) Niemeier et al. (1995) Boadi and Amekudzi (2013) Augeri et al. (2011) Gharaibeh et al. (1999) Guerre et al. (2005) Zavitski et al. (2008) Dehghani et al. (2013) Zhang et al. (2002) Sadek et al. (2003) High computational requirement; not applicable to large scale networks Might not be optimal; high programming complexity No optimization Independent optimization for each asset category, no global optimization; not flexible for practical use; unable to coordinate asset projects efficiently Pavement Management Systems Golabi et al. (1982) developed a modern network-level pavement management system for Arizona Department of Transportation (ADOT) (Ferreira et al. 2002). In Golabi et al. s optimization model, a total of 120 pavement conditions states are defined by the variables including present amount of cracking, change in amount of cracking during the previous year, the present roughness, and index to the first crack. The statewide pavement network is divided into nine road categories (sub-networks) based on traffic volume and a regional environmental factor. The maintenance actions are grouped into 17 types ranging from 18

35 routine maintenance to substantial corrective measures. Golabi et al. (1982) developed a Markov transition probability prediction model using historical pavement condition data to address the probabilistic aspect of pavement deterioration. The outcome of this optimization model includes the optimized maintenance policy, the expected minimum budget required, and the predicted pavement condition (Golabi et al. 1982). Another network-level optimization model was established by Chen et al. (1996) for the Oklahoma Department of Transportation with the application of linear programming and the Markov decision process. Pavement conditions are divided into five states, namely excellent, good, fair, poor, and bad, in terms of the overall pavement condition index. Nine treatments are defined: thin, medium, thick overlay on both asphalt and concrete pavements, medium and thick asphalt reconstruction, and concrete reconstruction. Chen et al. (1996) uses a global optimization model which seeks the optimal solution for the entire network, although the network is divided into six pavement groups by traffic volume and pavement types. Both cost minimization and benefit maximization approaches are implemented in Chen et al. s optimization model. Wu and Flintsch (2009) proposed a non-linear pavement preservation optimization model which can handle multiple objectives and consider budget variability. Decision variables were introduced to represent the percentage of pavement network in certain condition states in each analysis year. The stochastic constraints were applied to take into account the budget variability. Two objective functions were minimizing the total preservation cost and maximizing the weighted average condition. The condition of pavement network were 19

36 classified into four categories: excellent, good, fair, and poor. Markov transition probabilities were used in predicting the pavement condition. The major advantage of this model is that multiple objectives can be considered simultaneously. De la Garza et al. (2010) developed a network-level linear programming optimization model, in which a deterministic prediction model is utilized for pavement condition deterioration. Five pavement condition states are defined based on the Combined Condition Index (CCI) values. Nine maintenance and rehabilitation treatments, ranging from ordinary maintenance to reconstruction, are identified. Each treatment is allowed to be conducted on only one pavement condition category. De la Garza et al. s model assumes that the deterioration rates are fixed for each pavement condition state and that pavements only deteriorate from an upstream condition to the next downstream condition. The pavement deterioration rates are calculated deterministically from historical data. Li et al. (1998) presented an integer programming optimization model for pavement network maintenance and rehabilitation. A time-related Markov probabilistic model is established for pavement condition prediction considering both the immediate treatment effects and the potential impact on the rate of future condition deterioration, which is similar to the prediction model developed by Chen et al. (1996). The major difference between the two Markov models is that Li et al. s model predicts the exact pavement condition state (PCS) score, such as pavement condition index (PCI) or pavement serviceability index (PSI), rather than the pavement condition category, such as excellent or poor. The network optimization model developed by Li et al. (1998) uses a multiyear integer programming model on a year-by-year basis. The objective of the optimization 20

37 model is to maximize the total value of cost-effectiveness in each analysis year, given the available budget constraints and other applicable constraints. The main output of this program consists of the optimal maintenance and rehabilitation treatment strategy and the predicted condition state for each pavement segment in each analysis year (Li et al. 1998). Tack and Chou (2002) developed a multiyear pavement repair scheduling optimization tool based on a genetic algorithm and dynamic programming. Integer variables are introduced to represent the repair treatment on each pavement section in each year. The objective is to maximize the overall average condition of the entire network. A simple genetic algorithm model, a pre-constrained genetic algorithm model, and a dynamic programming model are implemented in a spreadsheet. The results obtained from the three approaches are analyzed and compared (Tack and Chou 2002). Wang et al. (2003) presented an integer linear programming model for optimal multiyear pavement project selection. Budget constraints and minimum pavement condition level constraints are considered. A constant condition deterioration rate is calculated for each pavement section based on historical data to estimate the future condition. Binary variables are introduced to represent the selected repair treatment for each section in each year. Two objective functions are developed: maximizing the improvement in overall network condition and minimizing the total disturbance cost to users due to the pavement repair project. The disturbance cost is estimated for each type of repair treatment, such as major rehabilitation and minor rehabilitation. 21

38 Fwa et al. (2001) employed a genetic algorithm in solving a mixed-integer programming model for optimal pavement management programming. A Markov transition probability model is used to predict the future condition of individual pavement segments. Binary variable are used to indicate whether or not a particular repair action is applied to the given segment. The objective is to minimize the total required expenditure subject to condition constraints and available annual budget constraints. Abaza (2009) developed a constrained integer linear programming model to determine the best pavement maintenance and rehabilitation strategy. Integer variables are incorporated to represent the number of pavement segments in a particular condition state to be treated by a proper repair activity. Two pavement condition indicators are developed: pavement condition rating gain and age gain. The objective of this model is to maximize the overall condition or minimize the total cost. Once the optimal result is obtained, the project candidates can be selected using an integer programming model based on prevailing segment size distribution. Gao and Zhang (2013) presented a new optimization model which is able to combine the projects on adjacent pavement segments automatically when searching the optimal work plan. Network partition is used to divide the pavement network into groups of sections with similar condition and repair needs. An integer programming model is then established to find the most cost-effective preservation strategy within the budget constraint. 22

39 2.2.2 Bridge Management Systems Ravirala et al. (1996) developed a multicrieria optimization method to support capital investment decisions in bridge management at network level. Condition ratings are estimated for the four major components of a bridge, including wearing surface, structural deck, superstructure, and substructure. Bridge states are defined by three state variables: bridge type, component type, and component condition rating. A state increment model is used to identify proper treatment actions and to predict bridge condition. The optimization process consists of three major steps: (1) identification of objective functions; (2) assessment of the importance of each objective function; (3) formulation of a mixed-integer goal programming model. The weighted sum of deviations from the goals is minimized. The four major components are analyzed separately due to high computational requirements. Lounis (2005) presented a multiobjective optimization decision model for network-level bridge management, considering minimization of maintenance cost, maximization of overall network condition, and minimization of traffic disruption. A first-order Markov chain model is used to predict bridge conditions. Compromise programming is employed to determine the optimal ranking of bridge maintenance projects considering the three objectives. Elbehairy et al. (2009) developed a bridge management system to support maintenance and rehabilitation decisions considering multiple elements at both project- and network-level. The project-level model suggests the best repair strategies for each element of each bridge 23

40 to maximize the benefit cost ratio. The network-level model determines the most beneficial repair year for each bridge to maximize the overall network condition. The system decomposes the large problem into a set of smaller sequential optimizations to reduce the computational complexity Cross Asset Management Systems This section focuses on existing transportation cross asset management systems and models. Sinha and Fwa (1989) defined the concept of total highway management which includes the proper coordination of individual systems. The prior research works are grouped into three categories mainly based on the approach adopted. Macroscopic approach treats the entire transportation asset network as a whole and determines the overall condition distribution and budget allocation plan. This approach is able to perform relatively long term analysis on large transportation networks efficiently. Microscopic approach takes into account each individual asset unit and generates a specific maintenance and rehabilitation work plan for the asset network. Both approaches have their advantages and limitations, so many researchers utilize an integrated approach in developing cross asset management models Application of Macroscopic Approach Sinha et al. (1981) developed a goal programming model for funds allocation in highway system maintenance and preservation. Multiple objectives can be considered such as system condition, level of service, system safety, and energy efficiency. The objective function is to minimize the weighted deviations from the goals. Six types of improvement 24

41 treatments and four types of maintenance treatments were considered for various highway assets. This optimization model allows decision makers to perform trade-offs among system objectives, among different repair treatments, and among different highway classes. Although a single year analysis was conducted in the example problem, it was mentioned that this model had the potential to handle multi-year analysis. Grivas and Schultz (1994) presented a macroscopic approach used in an integrated pavement and bridge system for New York State Thruway Authority. The system-level integration was implemented by formulating a goal programming model. Decision variables were introduced to represent the population of pavement segments and bridges within each condition category that should receive a type of rehabilitation treatment in a certain year. Posavljak et al. (2013) proposed a strategic total highway asset management integration (STHAMi) approach by developing the conceptual structural integration factor (CSIF). The bridge condition index (BCI) is integrated into the pavement performance index with the application of CSIF, so that the bridge can be treated as an equivalent pavement segment. The investment strategy plans obtained from the mutually exclusive planning and STHAMi were compared. It was concluded that STHAMi yields a higher network performance with the same amount of budget. The results of this study mainly include the predicted asset network condition and the budget allocation plan among different rehabilitation treatment categories, which are useful for long term investment planning. However, a practical work plan is not provided to implement the results. 25

42 Application of Microscopic Approach Niemeier et al. (1995) developed five optimization models for selecting optimal transportation projects based on a basic linear programming. Model 1 just utilizes a simple priority index to rank the projects. Model 2 incorporates the capability of making tradeoffs between ranks and cost by using a linear programming model to maximize the priority index within a budget range. Model 3 uses a goal programming model to take into account the policy objectives, such as desired travel time savings, vehicle operating savings, and accident savings, by setting a fixed goal for each objective. The deviations from policy objectives are minimized. Model 4 is developed based on Model 3 by adding a strict budget constraint. Model 5 combines the relative ranking and the fixed policy objectives by adding objective constraints to Model 2. A scaling factor is introduced for both Model 4 and 5 to determine the outermost boundary of the percentage of the policy objectives that can be achieved. Ravirala and Grivas (1995) developed a nonpreemptive goal programming model for integration of pavement and bridge projects. Pavement segments and bridges are categorized into three types, which are pavement, bridge, and integrable units. Every integrable unit consists of a bridge and the adjacent pavement segments whose repair or maintenance activities can be conducted simultaneously. The project candidates are grouped into five categories including pavement, bridge, integrated, independent, and deferred. The basic variables of this model are binary variables representing whether or not a highway unit should receive a treatment. 26

43 Bonyuet et al. (2002) developed a mixed non-linear programming model with linear constraints to support road rehabilitation and bridge replacement decisions simultaneously. Minimizing user travel costs under the available budget constraints is the objective of the model. Binary variables are introduced to indicate whether the bridge should be replaced or not. The mixed non-linear problem is reduced to a traffic assignment problem (TAP) and a road rehabilitation budget allocation problem (RBAP). By solving the TAP and RBAP iteratively, the solution of the non-linear model can be obtained. Li and Sinha (2004) proposed a methodology for multi-criteria decision making in transportation asset management using multi-attribute utility theory and integer programming. A series of surveys were conducted among both highway agency group and highway user group to identify a set of system goals, to determine the relative weights of the goals, and to estimate the utility function of the performance indicator under each goal. Binary variables were introduced for each project candidate to indicate if it should be selected or not. The objective was to maximize the total gain in utility by selecting a subset of candidate projects subject to budget constraints. The results were compared with the actual programming practice and the matching rate of at least 85% was achieved. Selih et al. (2008) developed a multiple-criteria decision support model to prioritize transportation asset rehabilitation projects. In the case study, criteria that are taken into account include facility rating, facility age, overpass grouping, indirect cost, and MR&R project cost. The importance of different criteria is captured by assigning them relative 27

44 weights using the analytical hierarchy process (AHP). Each project is then assigned a utility score based on the multiple criteria and their weights. Binary variables are introduced for each project to indicate whether or not the project should be performed. The objective of this decision support model is to choose the projects that result in the maximum total utility score within the budget limit. The model is solved using MS Excel software. The case study indicates that grouping the projects whenever possible can result in larger total utility score. Li (2009) presented a stochastic multi-choice multi-dimensional Knapsack model to take into account the budget uncertainty issue in transportation project selection process. The budget uncertainty is handled using a budget recourse function. Budget constraints for each analysis year and the cumulative budget constraints are considered in this model. An efficient heuristic algorithm is developed to solve the model. Augeri et al. (2011) used a dominance-based rough set approach (DRSA) to develop a highway asset decision support system for an Italian highway agency. This system is able to allocate available resources to improve highway safety, considering all highway components, such as pavements, bridges, culverts, signs, guardrails, and vegetation. The DRSA can take into account multiple criteria including both quantitative and qualitative criteria. The decision model is developed by using the preference information provided by the decision maker in the form of exemplary decisions. The maintenance activities are ranked according to the degree of urgency evaluated by the DRSA based on the agency s current policy, engineering criteria, practices, and experiences. The budget resources are 28

45 then allocated to the maintenance activities that are the most urgent. The main advantage of this system is the high degree of transparency, as the decision maker is able to control and understand the model by updating the exemplary decisions. Fwa and Farhan (2012) proposed a two-stage approach for optimal budget allocation in highway asset management considering pavements, bridges, and appurtenances. In Stage I, a group of optimal solutions are obtained for each type of assets. The relationship between available budgets and resultant optimal asset performance can be established for the individual asset systems. Pavement condition index (PCI), bridge health index (BHI), and remaining service life are used as performance measurement for pavements, bridges, and appurtenances respectively. In Stage II, the optimal solutions calculated in Stage I are used as inputs to perform a cross-asset trade-off to determine the optimal budget allocation. The objective is to achieve equitable condition improvements for each asset system with respect to their individual performance thresholds. Stage I employs genetic algorithms as the optimization tool, and Stage II utilizes the dynamical programming method. Xiong et al. (2012) formulated a compromise programming model for resource allocation between pavement and bridge deck maintenances. Resources including funds, labor, and equipment are classified into three types: resources only usable for pavement, resources only usable in bridge, and resources usable for both pavement and bridge. Binary variables are introduced to represent the maintenance activities for each pavement segment and bridge deck. Genetic algorithms are used in solving the compromise model. This model is solved in two steps. In the first step, optimized solutions are obtained for pavement and 29

46 bridge deck maintenance independently without resource sharing. In the second step, the solutions from step one are used as input to generate the final maintenance solution with resource sharing between the two types of asset. It is concluded that the performance of both pavement and bridge deck can be improved significantly if the resources are shared. Bai et al. (2012) presented a methodology for trade-off analysis for multi-objective optimization in transportation asset project selection. Each candidate project was represented a binary decision variable to indicate if the project should be selected or not. A multi-objective optimization model is formulated considering the various network-level performance measures such as IRI, Bridge Condition Index, and travel speed. The Extreme Points Nondominated Sorting Genetic Algorithm II was applied in generating Pareto frontiers to conduct the trade-off analysis. Boadi and Amekudzi (2013) presented a multi-attribute utility model to identify high-risk corridors for project prioritization with simultaneous consideration of various types of assets. Three objectives are included in evaluating the overall system performance: minimizing the number of incidents, maximizing the mobility, and improving the preservation of assets. An expected utility score (EUS) is estimated for each segment of the transportation network based on the three decision criteria mentioned above. The attributes used to calculate the EUS are the number of incidents, the average peak-speed, and the pavement rating. It is suggested that the segment with higher EUS have more risk of failure, and should be prioritized as a higher priority segment. 30

47 Application of Integrated Approach Gharaibeh et al. (1999) presented a prototype methodology for integrating highway asset management activities, such as pavements, bridges, culverts, intersections, and signs. The network level integration is implemented in two steps. Stage 1 generates a set of optimal solutions for each infrastructure component system independently without considering the total budget constraint. The relationship between the available budget and the asset performance for each asset category is obtained. Stage 2 uses the results of Stage 1 to perform a trade-off analysis among various asset components. At project level, competing project candidates for each asset category are selected on the basis of incremental benefit cost (IBC) analysis. The available budget is allocated to a collection of projects that can provide the maximum benefits. The project level integration is then performed in a spatial manner using geographic information system based software. Adjacent projects from various components of the highway asset that can be conducted at the same time are identified to decrease traffic delays. The effect of project coordination is estimated by the number of vehicle-miles driven through work zones, which is an indicator of traffic delay resulting from on-going road construction. The main limitation of this system is the lack of flexibility in determining the cross asset budget allocation. A set of optimization results has to be generated for each asset component before the cross asset analysis can be performed. Zhang et al. (2002) developed an integrated management system for urban transportation infrastructure. The system consists of two subsystems: a pavement management system 31

48 and a bridge management system. The two subsystems are integrated at both network and project level. A combined priority index is developed, using common variables such as traffic, condition, width, and age, to compare pavements and bridges on the same scale. At network level, users are able to view the statistic values of the entire infrastructure network and to make budget allocation plans. At project level, both pavement and bridge subsystems are capable of generating specific maintenance and rehabilitation projects according to decision trees. The integration is based on the ultimate data sharing and the combine evaluation index. The major disadvantage of this system is that it relies on decision trees to determine the repair project list rather than optimization methods. Therefore, the budget allocation may not be optimal. Sadek et al. (2003) presented the development of a framework for integrated infrastructure management system (IIMS) by describing the experience of a small urban area in northwestern Vermont. Six different transportation system components, including pavement, bridge, transit, nonmotorized multiple path, sidewalk, and traffic signal, are considered. A condition measure methodology and a deterioration prediction model are developed for each component system. Budget allocation among different transportation system components is determined using a two-stage mathematical programming approach. Prioritization scheme, rather than true optimization, is applied to allocate budget at component level, according to the value of condition measure and section s significance. The results of budget allocation are linked to GIS layers to help decision makers identify potential projects that can be coordinated. This model is similar to Gharaibeh et al. 32

49 (1999) s model, and it also lacks the flexibility in the budget allocation across different assets. Guerre et al. (2005) presented a candidate-based approach used in the executive support system (ESS) to integrate the pavement and bridge management systems for the Ministry of Transportation of Ontario, Canada. The ESS is capable of evaluating the relationship between asset network performance and budget using data from the ministry s pavement and bridge management systems. Similar to Gharaibeh et al. (1999) s approach, an incremental benefit/cost (IBC) approach is utilized in to prioritize the competing work candidates generated by individual asset management systems. All work candidates from different asset types are ranked in a list based on the IBC. The system selects working candidates starting from the top of the list within the budge limit, therefore candidates that provide the most benefits are chosen. The resulting asset performance is predicted by calculating the performance measures, such as remaining asset value, average pavement condition index, and average bridge index. Users can define the operating assumptions, such as minimum budget and required projects, in the candidate selection process. The cross asset budget allocation is based on the results obtained from independent systems, which requires the preexistence of such systems for individual asset types. Zavitski et al. (2008) presented the integration of a pavement management system into a comprehensive strategic asset management system for Utah Department of Transportation. At strategic level, funding allocation decisions across different asset groups, such as pavement, bridge, safety, maintenance, and mobility, are made using economic trade off 33

50 analysis. At tactical level, funding allocation and project recommendations are determined for each individual asset. At operational level, a region specific tool is developed to make maintenance and rehabilitation plans for each section. This system utilizes economic tradeoff analysis rather than mathematical optimization. Although it is easier to understand by decision makers, the results may not be optimized. Dehghani et al. (2013) proposed a cross-asset resource allocation framework considering functional, structural, and environmental performance indicators. The framework is able to allocate resources across different asset categories, select treatments, predict asset performance, and evaluate overall asset network performance. An initial resource allocation scenario is determined based on expert opinions, goals, and constraints. The optimal allocation is achieved by revising the initial scenario iteratively according to the results of each scenario Summary and Comments The macroscopic approach is a traditional way of managing transportation assets, and it is able to perform relative long term analysis on large transportation networks efficiently. However, this approach often can only provide a theoretical solution because it is not capable of generating a specific work plan for each individual asset unit to achieve the optimized network condition. The microscopic approach is generally implemented using two main methods: optimization and prioritization. In an optimization model, binary variables are introduced for each individual asset unit (i.e. a pavement segment or a bridge) or project candidate to generate a specific work plan. However, the model is extremely 34

51 difficult to solve especially when the problem size is large, so the entire network has to be divided into a set of small sub-networks. In a prioritization model, the individual asset units or project candidates are ranked according to a computed index, such as a benefic cost ratio or a utility score. Although it is capable of dealing with large scale asset networks, the results are often not optimized. To overcome the disadvantages of the two approaches mentioned above, more researchers employ an integrated approach in their asset management models. A model based on a macroscopic approach is formulated to determine the overall condition distribute, budget allocation across different assets, and preservation treatment category. The microscopic approach is then applied to generate a specific project candidates list. However, the existing models still have limitations: (1) some models cannot provide the optimized solution; (2) some are not flexible enough for practical implementation; (3) most of the existing models cannot efficiently schedule the asset projects considering the adjacent projects. 35

52 Chapter 3 Methodology 3.1 Overview In order to overcome the limitations of existing transportation asset management models, this research developed a decision support tool for cross asset preservation optimization based on a new combined approach using AHP, linear goal programming, multiple attribute utility theory, integer programming, and constraint programming. These techniques were selected in developing this decision support tool for the following reasons: (1) The linear goal programming model can generate optimal network-level budget allocation strategy for very large-scale transportation asset networks considering multiple asset types simultaneously. The performance target of each asset type is considered to be a goal in the optimization model. This model provides a flexible approach for practical implementation without performing tedious procedures before conducting actual cross asset analysis. (2) Multiple criteria should be taken into account in selecting asset project candidates. Both analytic hierarch process (AHP) and multiple attribute utility theory (MAUT) are powerful techniques for multi-criteria decision analysis, while each method has its own advantages and disadvantages. These two techniques were applied to select 36

53 the most beneficial asset preservation projects considering multiple criteria. The results obtained from the two methods were compared and discussed. (3) By integrating the network-level optimization model (linear goal programming model) and the multi-criteria project selection model (AHP and MAUT), the decision support tool can generate optimal solution for large-scale networks and provide work plans considering individual asset items. This integrated approach can take advantage of both the macroscopic approach and the microscopic approach. (4) Coordination models are developed to systematically generate coordinated work plans for multiple asset types to achieve cost savings. The cross-asset project coordination problem is modeled as a scheduling problem with the objective of combining as many adjacent projects as possible subject to a set of constraints. Constraint programming is a relatively new technique, powerful in dealing with scheduling problems and handling complicated constraints. Integer programming is a traditional optimization method which can handle scheduling problem as well. Both integer programming model and constraint programming model were formulated and their results were compared. Figure 3-1 presents the flowchart of optimization models for transportation asset management. 37

54 Asset Condition Data Stage 1: Network Optimization Allocate Budget using Linear Goal Programming Cross-Asset Optimization Model Prioritize Asset Components using AHP Treatment Policy Budget Allocation Future Condition Rank Project Candidates by MAUT Project Selection Model Stage 2: Project Selection Rank Project Candidates by AHP Separated Project Lists Stage 3: Project Coordination Constraint Programming Project Coordination Model Integer Goal Programming Coordinated Project Lists Figure 3-1 Flowchart of the cross-asset decision support models 38

55 The optimal preservation strategy is determined in three stages. At the first stage, the budget allocation plan among different assets, the optimized treatment policy, and the corresponding overall network condition are determined using a linear goal programming model. At the second stage, the results obtained from the first stage are implemented by selecting project candidates that provide the maximum benefit using a MAUT model and an AHP model. The asset conditions are updated for each planning year based on the repair treatment and the deterioration trend. At the third stage, the selected projects are further optimized using a project coordination model based on constraint programming and integer programming. The optimal multiyear work plan is obtained by combining adjacent projects and rescheduling some projects subject to the budget constraints and project timing constraints. The main advantages of the new decision support tool include the capability of: (1) dealing with large scale networks of multiple transportation assets, (2) providing optimal solutions regarding budget allocation and preservation strategies, (3) generating candidate project lists for each individual asset type based on multiple criteria, and (4) coordinating projects of different asset categories considering geographical locations. The condition rating systems for different types of assets are not the same at most transportation agencies. Many researchers, such as Zhang et al. (2002) and Posavljak et al. (2013), developed unified asset performance measurement for cross asset management. In this study, Asset Condition Index (ACI) is defined and used as the performance 39

56 measurement for all types of asset. Assets are categorized into five condition states (i.e. excellent, good, or poor) according to their own rating system. The ACI is defined based on the condition categories as shown in Table 3.1. Table 3.1 Asset Condition Index Definition Condition Category Excellent Good Fair Poor Very Poor ACI Markov transition probability models are used to predict the future asset conditions. The transition probabilities are estimated based on historical condition data using the approach mentioned in the author s prior research (Wang 2011). 3.2 Stage 1: Network-Level Optimization This section presents the development of a network-level cross-asset optimization model based on AHP and linear goal programming. The AHP approach is utilized to determine the relative importance of different asset components. These weights are then incorporated in a linear goal programming model to achieve the optimal budget allocation across different assets AHP Model to Prioritize Asset Components As discussed in section 2.1.1, an AHP problem is firstly decomposed into individual independent elements, including an overall goal, a set of alternatives, and a group of criteria as shown in Figure 3-2 (Farhan and Fwa 2011). 40

57 Overall Goal Criterion 1 Criterion 2 Criterion n Alternative 1 Alternative 2 Alternative m Figure 3-2 Hierarchy structure for AHP models The relative importance of each criterion and the ranking of the alternatives under each criterion are then estimated by pairwise comparisons based on a nine-point scale (Saaty 1980). Finally, a priority vector representing the prioritization of the alternatives considering all the criteria are derived by combining the results of the pairwise comparisons. The consistency of the decision maker s judgment during the pairwise comparison is examined by the consistency ratio (Saaty 1980). Many highway agencies are suffering from a constrained budget environment. The available preservation funds are often not enough to keep every asset system at an ideal condition level. The trade-off between different types of asset has become a critical issue for high level decision makers. Therefore, an AHP model is developed to estimate the relative weights of different asset components under a set of criteria. The asset component with higher priority receives more attention during cross-asset optimization. 41

58 Figure 3-3 shows the structure of the AHP model developed in this study to prioritize asset components. Overall Goal: Prioritize Asset Components Criteria: Asset Value Current Condition Safety Alternatives: Pavement Bridge Deck Figure 3-3 Structure of AHP model to prioritize asset components The overall goal is to determine the relative importance of different asset components. The criteria can include current asset condition, total asset value, and safety consideration. The alternatives are asset types, such as pavement and bridge decks. An application example of the AHP model is described as follows: (1) The overall goal is to determine the relative importance of pavement and bridge deck. It is assumed that there are three criteria: asset value, safety, and current condition, and that there are two alternatives: pavement and bridge deck. (2) Prioritization based on pairwise comparisons. The criteria comparison matrix is estimated based on a nine-point scale as presented in Table 3.2. Table 3.2 Example of Criteria Comparison Matrix Asset Value Safety Current Condition Asset Value Safety Current Condition

59 The pairwise comparison between each alternative under each criterion is shown in Table 3.3. Table 3.3 Example of Pairwise Comparison Matrices under Each Criterion Criteria Asset Value Safety Current Condition Asset Bridge Bridge Bridge Pavement Pavement Pavement Type Deck Deck Deck Pavement Bridge Deck (3) Combination of pairwise comparisons to form a priority vector. The priority vectors are derived by Saaty (1980) s eigenvector method. The eigenvector of the criteria comparison matrix is (0.105, 0.637, 0.258), representing the weights of asset value, safety, and current condition. The eigenvectors of the pairwise comparisons under each criteria are (0.75, 0.25) for asset value, (0.167, 0.833) for safety, and (0.6, 0.4) for current condition. Considering all three criteria, the weight of pavement is , and the weight of bridge deck is Therefore, the vector (0.34, 0.66) could represent the relative importance of pavement and bridge deck. (4) Examination of consistency of the decision maker s judgment. The consistency ratio (CR) is defined by Saaty (1980) as the ratio of consistency index (CI) to the average random index (RI) (Table 2.1) for the same order matrix, as expressed in the following equation: CR CI RI where CI ( max n) ( n 1). A CR less than 0.1 is acceptable as suggested by Saaty (1980). The CR for the criteria 43

60 comparison matrix is The CRs for other pairwise comparisons under each criterion are all Cross-Asset Optimization Model This section presents the development of a linear goal programming model for cross-asset optimization using a macroscopic approach. The objective is to achieve the best network condition given a certain amount of budget. The network-level asset condition performance is estimated using two measurements, the deficiency level (percentage of assets in poor and very poor condition) and the average ACI. In this study, the primary objective is to achieve the desired deficiency level specified by the user. After the deficiency level requirements are satisfied, the remaining budget is utilized with the purpose of maximizing the overall weighted average ACI. The model employs a macroscopic approach, where the proportions of assets in different condition categories are represented by decision variables. The budget allocation among different asset types, the optimized treatment policy, and the corresponding overall network condition are the main output of this model. The linear goal programming model presented in this section is partly adapted from the author s prior research (Wang 2011). The objective function consists of two parts. The first part represents the weighted deviations from the desired deficiency level target. The second part represents the weighted average ACI. The primary goal is to minimize the total deviations from the deficiency level target, and the secondary goal is to maximize the overall average ACI. A 44

61 very small factor is introduced in the objective function to ensure that the primary goal is satisfied first. Minimize T w N I K M I L d1 w d w X s w Ymtil si 3.1 p t b 2t p ntik i b t 1 n 1 i 1 k 1 m 1 i 1 l 1 where N = number of pavement types; M = number of bridge types, K = number of pavement treatment types, L = number of bridge treatment types; I = number of condition states; T = number of analysis years; Xntik = decision variable representing the proportion of pavement type n in condition state i receiving recommended repair treatment k in year t; Ymtil = decision variable representing the proportion of bridge deck type m in condition state i receiving recommended repair treatment l in year t; wp = weight of pavement; wb = weight of bridge deck; si = ACI score for condition state i as shown in Table 3.1; dpt = deviations from pavement deficiency level target in year t; dbt = deviations from bridge deck deficiency level target in year t; = a very small number (e.g ). There are six types of required constraints namely deficiency target constraints, nonnegativity constraints, sum-to-one constraints, initial condition constraints, state transition constraints, and budget constraints. The goal of achieving the desired deficiency level specified by the user is formulated as a set of soft constraints with non-negative deviation variables (Equation 3.2 and 3.3). It 45

62 should be noted that I represents the number of condition states. State i =I represents very poor condition, and state i =I-1 represents poor condition. N I K X ntik d1 t deficiency 1t n 1 i I 1k 1 for all t = 2,, T 3.2 M I L Ymtil d2t deficiency 2t m 1 i I 1 l 1 for all t = 2,, T 3.3 where d1t = deviations from pavement deficiency level target in year t; d2t = deviations from bridge deck deficiency level target in year t; deficiency1t = deficiency level target for pavement in year t; deficiency2t = deficiency level target for bridge decks in year t. The non-negativity constraints (Equation 3.4 and 3.7) ensure that all variables in the optimization model are non-negative. X 0 for all n, t, i, k 3.4 ntik Y 0 for all m, t, i, l 3.5 mtil d 0 for all t 3.6 pt d 0 for all t 3.7 bt The sum-to-one constraints (Equation 3.8 and 3.9) ensure that each proportion of the entire asset network is represented by a decision variable. N I K n 1 i 1 k 1 M I L m 1 i 1 l 1 X 1 for all t = 1,, T 3.8 ntik Y 1 for all t = 1,, T 3.9 mtil 46

63 The initial condition constraints (Equation 3.10 and 3.11) pass the values representing current condition distribution to the optimization model. K X n1ik Q1 ni k 1 L Ym1il Q2mi l 1 for all n = 1,, N; i = 1,, I 3.10 for all m = 1,, M; i = 1,, I 3.11 where Q1ni = proportion of pavement type n in state i in initial year; Q2mi = proportion of bridge type m in state i in initial year. The state transition constraints (Equation 3.12 and 3.13) integrate the Markov prediction model with the linear goal programming model. From the second year on, the proportion of an asset type in condition state j in year t is derived from the transition of assets in various condition states in year t-1. K X ntjk k 1 i 1 k 1 I K X n( t 1) ik P1 nkij for all n = 1,, N; t = 2,, T; j = 1,, I 3.12 L Y mtjl l 1 i 1 l 1 I L Ym( t 1) il P2 mlij for all m = 1,, M; t = 2,, T; j = 1,, I 3.13 where P1nkij = probability that pavement type n receiving treatment k moves from state i to state j; P2mlij = probability that bridge type m receiving treatment l moves from state i to state j. The budget constraints (Equation 3.14) ensure that the required budgets recommended by the optimized solution do not exceed the maximum available budget for each year. 47

64 N I K M I L X ntik C1 nk Length Ymtil C2ml Area Bt for all t = n 1 i 1 k 1 m 1 i 1 l 1 1,, T 3.14 where Length = total length of the pavement network; Area = total deck area of the bridge network; Bt = maximum available preservation budget in year t; C1nk = unit cost of applying treatment k to pavement type n; C2ml = unit cost of applying treatment l to bridge type m. In order to make the optimization model more practical, several sets of optional constraints are also introduced. The condition constraints (Equation 3.15 to 3.18) ensure that the proportion of assets in certain condition states is in a prescribed range. For instance, it may be desirable to maintain the amount of assets in excellent or good condition at current level. N K X ntik 1 i n 1 k 1 for all t = 2,, T; selected i 3.15 N K X ntik 1 i n 1 k 1 for all t = 2,, T; selected i 3.16 M L Ymtil 2i m 1 l 1 for all t = 2,, T; selected i 3.17 M L Ymtil 2i m 1 l 1 for all t = 2,, T; selected i 3.18 where ε1i = upper limit of proportion of pavement in condition i; ξ1i = lower limit of proportion of pavement in condition i; ε2i = upper limit of proportion of bridge in condition i; ξ2i = lower limit of proportion of bridge in condition i. 48

65 The allowable treatment constraints (Equation 3.19 and 3.20) ensure that certain treatments can only be applied to assets in certain condition states. X ntik 0 for all t = 1,, T; selected n, i, k 3.19 Y 0 for all t = 1,, T; selected m, i, l 3.20 mtil The budget level stabilization constraints (Equation 3.21 and 3.22) ensure that the budget allocated to an asset component does not vary too much from year to year. N I K X C Length X C Length n 1 i 1 k 1 ntik 1 nk for all t = 1,, T-1 M I L N I K n 1 i 1 k 1 n( t 1) ik Y C Area Y C Area m 1 i 1 l 1 mtil 2 ml for all t = 1,, T-1 M I L m 1 i 1 l 1 m( t 1) il 2ml 1nk where Length = total length of the pavement network; Area = total deck area of the bridge network; C1nk = unit cost of applying treatment k to pavement type n; C2ml = unit cost of applying treatment l to bridge type m; = maximum budget level difference from year to year. 3.3 Stage 2: Project Selection Overview This chapter describes an AHP model and a multiple attribute utility model for selecting project candidates that can provide the maximum benefit. The network-level optimization results, including the budget allocation, the optimized treatment policy, and the predicted 49

66 asset condition distribution, are only theoretical solutions without a specific implementation plan considering individual asset items. Multiple criteria should be taken into account during project selection process. For example, assets with higher traffic volume tend to affect more road users. Assets at an older age are likely to have been in an undesirable condition for a longer time. Therefore, projects on these assets could result in more benefits. In this study, four criteria, age, condition, traffic volume, and climate, were included in the project prioritization process for illustration purposes. Age is defined as the number of years since the last repair was conducted, traffic volume is the total average daily traffic (ADT), condition is measured by the ACI, and climate is assessed by snowfall (inch/year). The project candidates are ranked based on the scores calculated by AHP or MAUT considering the above criteria. The system then selects projects starting from the top of the list until the budget limit obtained from the network-level optimization for this type of treatment is reached. Therefore, candidates that provide the most benefits can be chosen and the network-level optimization results can be achieved. An example of such project selection process is presented in Figure

67 Bridge Candidates for Minor Rehabilitation Sorted by Scores Selected or Not Score = 0.78 Yes 52.4% Score = 0.77 Yes Bridges in Poor Condition Score = 0.61 Score = 0.60 Yes No 47.6% Score = 0.37 No Figure 3-4 Project selection from a list of candidates In this example, the bridges in poor condition are candidates for minor rehabilitations and are ranked based on their relative importance scores calculated using AHP or MAUT. The 52.4% of the candidates with higher scores are selected due to the available budget limit. The future condition of each asset item is estimated based on the same transition probabilities utilized in the network-level optimization. It is assumed that older assets would deteriorate first. For example, if the transition probability from poor to very poor condition is 12%, then all the pavement segments in poor condition are ranked based on their age and the oldest 12% would drop to very poor condition next year. The condition data for the asset items are updated for each planning year based on the repair treatment 51

68 and the deterioration trend. The assets that are fixed will be given excellent condition in the next year, and the assets that do not receive any repair treatments will deteriorate according to Markov transition probability model. The updated condition data are used in generating the project lists for each year AHP Model As discussed in section 2.1.1, the AHP method requires the problem to be decomposed into individual independent elements such as an overall goal, a group of criteria, and a set of alternatives. The overall goal of the project selection is to rank the project candidates, the criteria can include asset age, condition, traffic volume and climate. The alternatives are the individual asset items, such as a pavement segment or a bridge deck. The AHP model developed in this section is partly adapted from the Farhan and Fwa (2011) s study. Saaty (1980) provided an absolute AHP approach to reduce the number of pairwise comparisons for large-scale problems. Each alternative is assigned a level of intensity under each criterion during alternative evaluation process. The structure of the AHP model for project selection is presented in Figure

69 Overall Goal: Prioritize Project Candidates Criteria: Condition Traffic Volume Age Climate Sub-Criteria (Intensity): High High High High Medium High Medium High Medium High Medium High Medium Medium Medium Medium Medium Low Medium Low Medium Low Medium Low Low Low Low Low Alternatives: Asset Item 1 Asset Item 2 Asset Item 3... Asset Item n Figure 3-5 Structure of AHP model for project selection The steps of applying AHP in project selection are described as follows: (1) The overall goal is to prioritize the project candidates. It is assumed that there are four criteria: condition, traffic volume, age and climate. The alternatives are individual asset items, such as a pavement segment or a bridge deck. (2) Prioritization based on pairwise comparison. The criteria comparison matrix is estimated based on a nine-point scale as presented in Table

70 Table 3.4 Example of Project Selection Criteria Comparison Matrix Condition Traffic Volume Age Climate Condition Traffic Volume Age Climate An example of pairwise comparison between each intensity level under each criterion is shown in Table 3.5. Table 3.5 Example of Intensity Level Pairwise Comparison Matrix High Medium Medium Medium High Low Low High Medium High Medium Medium Low Low (3) Combination of pairwise comparisons to form a priority vector. The eigenvector of the criteria comparison matrix is (0.56, 0.25, 0.095, 0.095), representing the relative weights of condition, traffic, age, and climate. The eigenvectors of the intensity level pairwise comparison matrix is (0.51, 0.26, 0.13, 0.06, 0.03), representing the relative weights of high, medium high, medium, medium low, and low. For simplicity purpose, it is assumed that the intensity level comparison matrices are the same for all the four criteria. (4) Examination of consistency of the decision maker s judgment. The consistency ratio (CR) is defined by Saaty (1980) as the ratio of consistency index (CI) to the average random index (RI) (Table 2.1) for the same order matrix. The CR of the 54

71 criteria comparison matrix is 0.02, and the CR for the intensity level comparison is Both of the CRs are less than 0.1 and are acceptable. (5) Each alternative (i.e. a pavement segment or a bridge deck) can be assigned a ranking score based on the priority vectors obtained in Step (3). For instance, if a pavement segment is in high intensity (very poor) condition, has medium traffic volume, has a medium high age, and is in a low intensity climate region, then the ranking score of this segment can be calculates using the following equation: Similarly, all other alternatives can be assigned a score and then all the project candidates can be ranked in a list Multiple Attribute Utility Model Similar to the AHP model for project selection, four attributes, including age, condition traffic volume, and climate, can be considered in the MAUT model. The multi-attribute utility model developed in this research is adapted from the models formulated by Bai et al. (2013), Boadi and Amekudzi (2013), and Selih et al. (2008). A lottery approach is used to estimate the one-dimensional utility functions as recommended by Neumann and Morgenstern (1947). de Neufville (1990) described a stepby-step procedure for measuring utility: (1) Defining X. The nature, range, and scale of the criterion (X) are defined. (2) Setting context. A way of interviewing to the decision maker regarding the utility of X is developed. 55

72 (3) Assessment. The indifference between a lottery and a certainty equivalent is determined. (4) Interpretation. The results of the previous step are used to solve for the utility values. (5) Functional approximation. An analytic function is fitted to estimate the utility more easily. An example of estimating the utility function of traffic volume (ADT) is presented as follows: (1) Defining X. The average daily traffic (ADT) represents the traffic volume of the transportation assets. The range is from X * 0 to X * 100, 000. ADT values that are greater than 100,000 are considered to be equivalent to the maximum traffic volume, and have a utility value of 1. (2) Setting context. It is assumed that the decision maker is asked to compare the preference of repairing two asset items, such as two pavement segments. Some percentages of the first pavement segment have the maximum traffic volume, but the rest have zero traffic. The second pavement segment have a certain traffic volume between the two extreme cases. (3) Assessment. Consider two pavement segments: A and B. 50% of segment A has an ADT of 0, and the other 50% has an ADT of 100,000; segment B has a certain ADT of x. The following questions are developed to determine the indifference between the two choices. Would you prefer to repair segment B if x equals to 10,000? Yes No 56

73 20,000? Yes No 30,000? Yes No 40,000? Yes No 50,000? Yes No 60,000? Yes No 70,000? Yes No 80,000? Yes No 90,000? Yes No It is assumed that the indifference is at x=30,000. (4) Interpretation. According to the certainty equivalent estimated above, U( 30,000) 0.5 U(0) 0.5 U(100,000). Based on the convention, the worse extreme U ( 1) 0 and the best extremeu ( 100,000) U( 30,000) 0. 5is then obtained. c (5) Functional approximation. The power functionu( X ) a bx is chosen as the function form of this utility. Using the results of the previous step, it can be solved 3 that a , b 0.58, c 0. Therefore, the utility function of ADT is U( X ) X The utility functions for other attributes can be determined by following the same procedure. According to de Neufville (1990), the multi-attribute utility function can be estimated by adding up the individual preference function when the interactions between different 57

74 attributes can be ignored. Therefore, the overall utility i is expressed in Equation 3.23: U i for each individual asset item U i J j 1 w u j ij 3.23 where wj = relative weight of criterion j; uj = utility of conducting the project under criterion j; J = total number of criteria. Similar to the AHP approach, the project candidates for a certain type of treatment can be ranked in a list based on the multiple attribute utility score. Then the project candidates are selected using the procedure described in Figure Stage 3: Project Coordination Overview In many transportation agencies, different asset components are managed by different offices and preservation work plans are generated independently. Coordination of projects among different assets in the same, adjacent or nearby locations is often performed only on an ad hoc basis. Poorly coordinated projects might cause unnecessary traffic disruptions and increased agency cost. For example, a bridge project might be conducted only one year after a pavement project in the same location, and road users have to suffer from traffic delays twice. Another example is that a brand new pavement segment might need to be removed and reconstructed in order to repair a culvert underneath the road. These inefficiency could be reduced through project coordination. It is often acceptable for some 58

75 projects to be postponed or brought forward for one or two years to coordinate with another adjoining projects. For instance, if a bridge project can be rescheduled to be done at the same year or even combined with an adjacent pavement project, both roadway users and the transportation agency could benefit significantly from such coordination. Some researchers, such as Ravirala and Grivas (1995), Gao and Zhang (2013), and Selih et al. (2008), have recognized the importance of integrating adjacent projects. However, most current models combine neighboring projects based on a single year s work plan, but cannot handle multi-year scheduling problems. To overcome the limitation of the existing models, this chapter presents a new project coordination model developed using integer programming and constraint programming. The project coordination model is capable of generating coordinated multi-year work plans for multiple types of assets in a systematic way subject to budget limitations, project timing constraints, and user preferences. Figure 3-6 shows the basic idea of project coordination. The light rectangles represent the originally scheduled projects according to an uncoordinated work plan. The dark rectangles represent the projects that are rescheduled by the coordination models with the objective of combining as many adjacent projects as possible subject to the budget constraints. The integrated adjacent projects are marked by a circle. 59

76 ID Originally Scheduled Rescheduled Figure 3-6 Example of asset project coordination There are 26 projects in this example asset preservation work plan and some of them are adjacent to each other (e.g. Project 1 and Project 2). By implementing project coordination, Project 1 is rescheduled from 2018 to 2017 and Project 2 is rescheduled from 2016 to 2017, so that the two adjacent projects could be combined and conducted simultaneously. Some 60

77 projects that are not neighboring projects such as Project 8 and Project 10 are also rescheduled due to the available annual budget limitation Integer Programming Model The main objective of the project coordination model is to maximize the number of combined adjacent projects. Binary variables are introduced for individual projects to indicate the time when they are conducted. Adjacent projects are identified based on the location information such as county, route, and log points. The concept of goal programming is utilized in combining the neighboring projects. Decision variables representing deviations from the goal of integrating adjacent projects are also introduced. The goal of conducting all possible adjacent projects simultaneously can be stated as a set of soft constraints with decision variables representing the deviations. All projects are sorted according to their location, and possible adjacent projects are identified. The corresponding project numbers, i and j, are extracted and saved for the pth pair of adjacent projects. To combine two adjacent projects, the difference between the two decision variables Xit and Xjt representing the pth pair of adjacent projects i and j in year t should be as close to 0 as possible (Equation 3.24). X X d d 0 for all t, all p, selected i, j 3.24 it jt pt pt 61

78 where X it = the binary decision variable representing whether the project i is conducted in year t; d pt and d pt = deviations from the goal of conducting the pth pair of adjacent projects at the same time in year t. There are four more sets of constraints, namely non-negativity constraints, sum-to-one constraints, allowable conducting year constraints, and budget constraints. The non-negativity constraints ensure that all decision variables are not negative (Equations ). X 0 for all i, all t 3.25 it d 0 for all p, all t 3.26 pt d 0 for all p, all t 3.27 pt The sum-to-one constraints ensure that every project is conducted only once in the analysis period (Equation 3.28). T t 1 X 1 for all i 3.28 it The allowable conducting year constraints ensure that the projects are not conducted in the years other than the acceptable time intervals (Equation 3.29). X 0 for all i, selected t 3.29 it 62

79 The annual budget constraints ensure that the total cost of the projects conducted in each year does not exceed the available annual budget (Equation 3.30). I Ci X it i 1 F t for all t 3.30 where F t = available funding in year t; units with scheduled projects; project i is conducted in year t. C i = cost of the project on unit i; I = number of asset X it = the binary decision variable representing whether the The objective function is to maximize the number of combined adjacent projects (Equation 3.31). Maximize P T 1 d pt d pt 3.31 p 1 t where d pt and d pt = deviations from the goal of conducting the pth pair of adjacent projects at the same time in year t; P = number of pairs of adjacent projects; T = number of planning years. It should be noted that the minimum value of d pt d pt is 0 if the pth pair of adjacent T t 1 projects are integrated successfully, otherwise its minimum value is 2. Therefore, 1 T 1 d pt d pt can be used to indicate if the pth pair of adjacent projects are integrated. t

80 3.4.3 Constraint Programming Model The constraint programming model is formulated as a scheduling problem using IBM ILOG CPLEX with the application of logic constraints and cumulative functions. Interval decision variables are introduced for each project to represent the starting and ending time of a project. A set of logic constraints is included to indicate if the adjacent projects are integrated. A cumulative function is established to calculate the total cost of all projects in each year, and then used in the budget constraints. The interval decision variable X i has a start, an end, and a length. It represents the starting year, ending year, and the duration of project i. X i has a domain of multiple values, which represent the acceptable time interval that project i can be conducted. In this model, the duration of all maintenance and rehabilitation projects is assumed to be one year. Therefore, all the decision variables are one-year-length intervals. The project timing constraints are included by setting the domains of the decision variables. The variable (Equation 3.32). X i must be within the time interval in which project i must be completed where X S, E ) for all i 3.32 i [ i i S i = the earliest starting year of project i; E i = the latest ending year of project i. 64

81 The goal of integrating adjacent projects can be stated as a set of logic constraints. All projects are sorted according to their location, and possible adjacent projects are identified. The corresponding project numbers, i and j, are extracted and saved for the pth pair of adjacent projects. If the starting time of the two projects is equal, then the indicator A p is set to be 1, otherwise it is set to be 0 (Equation 3.33 and Equation 3.34). The function startof is provided by ILOG CPLEX to retrieve the starting time of an interval variable. If startof X ) startof ( X ), then A 1 for all p, selected i, j 3.33 ( i j p If startof X ) startof ( X ), then A 0 for all p, selected i, j 3.34 ( i j where startof X ) = starting year of project i; startof X ) = starting year of project j; Ap ( i = binary variable which is equal to 1 if the pth pair of adjacent projects are combined, otherwise it is equal to 0;; i and j= project number of the pth pair of adjacent projects. p ( j The annual budget constraints are implemented by using a cumulative function. A cumulative function can be used to model a quantity that varies over time and depends on the values of the decision variables. The function pulse is an elementary type of cumulative function, which represents the contribution of an individual interval variable (IBM-ILOG 2009). In this model, the annual cost of the projects is defined as the summation of the individual pulse functions for each project (Equation 3.35). If project i is conducted in year t, then the value of the cumulative function Cost at year t is increased by the cost of project i. Cost I i 1 pulse( X i, C i )

82 where Cost = total cost of all projects conducted in a certain year; C i = cost of project i. The annual cost of the projects in a specific year t can be expressed by Cost (t). Therefore, the budget constraints can be stated as follows (Equation 3.36): Cost( t) for all t 3.36 F t where Cost (t) = total annual cost of all projects conducted in year t; F t = available funding in year t. In some cases, it might be desirable to avoid conducting two projects at the same time. For example, if two routes intersect with each other, repairing the two routes simultaneously might block the entire intersection. Therefore, a set of constraints could be included in the model to avoid performing the two projects at the same time (Equation 3.37). startof X ) startof ( X ) for selected i, j 3.37 ( i j where startof X ) = starting year of project i; startof X ) = starting year of project j. ( i ( j Similar to the integer programming model, the objective function is to maximize the number of combined adjacent projects (Equation 3.38). Maximize P A p p

83 where A p = binary variable which is equal to 1 if the pth pair of adjacent projects are combined, otherwise it is equal to 0; P = total number of pairs of adjacent projects. 67

84 Chapter 4 Implementation 4.1 Overview A web-based decision support tool was developed by implementing the mathematical models formulated in this research using ASP.NET, SQL Server, LP-Solve, and CPLEX. 4.2 Network Selections The first step of generating the optimal cross-asset preservation strategy is to select the road network of interest (Figure 4-1). Users are able to choose the network to be analyzed by selecting districts and priority systems. The current condition distribution and the asset quantity of the selected network can be displayed. 68

85 Figure 4-1 Network selection 4.3 Asset Types Prioritization In the second step, users are asked to determine the relative weights of different asset types by performing pairwise comparisons (Figure 4-2). Figure 4-2 Determine relative importance of different asset types 69

86 4.4 Network-Level Optimization The linear goal programming optimization model was implemented by embedding LP- Solve in the web application through LP-Solve API for.net. Users are able to set objective functions and customize the constraints. The relative weights across different asset types obtained from the pairwise comparison are included in the optimization model. The output of the model is presented in charts and tables. Figure 4-3 Network-level cross-asset optimization 4.5 Project Selection and Coordination The project selection models were implemented using the Visual Basic language in ASP.NET (Figure 4-4). Users are able to choose the project selection method (AHP or MAUT), and specify the preferences considering multiple criteria during the project prioritization. The project coordination models based on integer programming and constraint programming were formulated and solved using IBM ILOG CPLEX. 70

87 Figure 4-4 Project selection by AHP and MAUT 71

88 Chapter 5 Results and Discussion 5.1 Stage 1: Network-Level Optimization Dataset Description For the example problem, the four-lane divided highway network in Ohio District 2, which consists of 672 lane miles of pavement and 4,702 thousand square feet of bridge decks, was analyzed over the next five years. Both pavement and bridge networks were divided into five condition classes (1, excellent; 2, good; 3, fair; 4, poor; 5, very poor) based on the condition rating score. The ACI score assigned to the five asset condition states were 4 for excellent, 3 for good, 2 for fair, 1 for poor, and 0 for very poor as shown in (Table 3.1). Each condition class may be recommended for one of the three preservation treatments (0, do nothing; 1, minor rehabilitation; 2, major rehabilitation). The unit costs of pavement repair treatments, per lane mile, were assumed to be $200,000 for minor rehabilitation, and $400,000 for major rehabilitation. The unit costs of bridge repair treatments, per square foot, were assumed to be $30 for minor rehabilitation, and $60 for major rehabilitation (Table 5.1). 72

89 Table 5.1 Unit Costs of Preservation Treatments Asset Types Minor Rehabilitation Major Rehabilitation Pavement ($ per lane-mile) 200, ,000 Bridge ($ per square foot) Assets in excellent and good condition were only allowed to receive do nothing, assets in fair and poor conditions were allowed to receive do nothing and minor rehabilitation, and assets in very poor condition were only allowed to receive major rehabilitation. The allowable treatments for assets in different condition states are summarized in Table 5.2. Table 5.2 Allowable Treatments Condition Do Nothing Minor Rehabilitation Major Rehabilitation Excellent Yes Good Yes Fair Yes Yes Poor Yes Yes Very Poor Yes The initial pavement condition distributions were: 29.4% excellent, 28.5% good, 26.3% fair, 12.8% poor, and 3.1% very poor (Figure 5-1). The initial bridge condition distributions were: 7.0% excellent, 41.6% good, 35.9% fair, 15.1% poor, and 0.5% very poor (Figure 5-2). 73

90 Poor 12.8% Very Poor 3.1% Excellent 29.4% Fair 26.3% Good 28.5% Figure 5-1 Initial pavement condition distribution Poor 15.1% Very Poor 0.5% Excellent 7.0% Good 41.6% Fair 35.9% Figure 5-2 Initial bridge deck condition distribution 74

91 The Markov transition matrices for asset condition prediction are estimated based on historical condition data, and are summarized in Table 5.3. Table 5.3 Markov Transition Matrices for Condition Prediction Asset Types Condition Excellent Good Fair Poor Very Poor Excellent Good Pavement Fair Poor Very Poor 1 Bridge Decks Excellent Good Fair Poor Very Poor Asset Types Prioritization Three criteria including asset value (Criterion 1), current condition (Criterion 2), and safety (Criterion 3) were considered in determining the relative weights of pavement (Alternative 1) and bridge deck (Alternative 2) using AHP. It was assumed that asset value is slightly more important than current condition, safety is slightly more important than asset value, and safety is moderately more important than current condition. The criteria comparison matrix was then obtained (Equation 5.1) The eigenvector of this matrix is (0.26, 0.10, 0.64), representing the weights of asset value, current condition, and safety. 75

92 It was assumed that pavement is strongly more important than bridge under Criterion 1, bridge deck is slightly more important than pavement under Criterion 2, and bridge deck is slightly more important than pavement under Criterion 3. The alternative comparison matrices under each criterion are presented in Equation 5.2 to Equation 5.4. Criterion 1: Criterion 2: Criterion 3: The eigenvectors of the above three matrices are (0.88, 0.12), (0.25, 0.75), and (0.25, 0.75) representing the relative weights of pavement and bridge deck under each criterion. Considering all the three criteria, the weight of pavement is 0.41, and the weight of bridge deck is The weights are to be used in the objective function of the cross-asset optimization model to measure the weighted average condition of the selected highway network Effect of Budget Level on Asset Condition The current asset deficiency level is 15.9% for pavement, and 15.6% for bridge decks. The objective is to reduce the deficiency level to 5% in five years subject to the constraints of budget availability, allowable treatments, and so on. 76

93 Three budget scenarios were analyzed to investigate the impacts of different budget level on the overall asset conditions. The available annual budget limits in the three scenarios were 15, 20, and 25 million dollars. The corresponding weighted average deficiency level and average asset condition index of bridge decks and pavement are presented in Figure Deficiency Level (%) Year 15 $Million 20 $Million 25 $Million Target Figure 5-3 Impact of budget level on asset deficiency level 77

94 ACI Year 15 $Million 20 $Million 25 $Million Figure 5-4 Impact of budget level on average asset condition It can be seen from Figure 5-3 that $15 million each year is not sufficient to keep the overall asset condition at the current level, $20 million each year can improve the asset condition from 15% to 11% in five years, and $25 million each year can reach the 5% deficiency level target in five years. Therefore, $25 million was assumed to be the available annual budget for this example problem Optimization Results The network-level cross-asset optimization results include the budget allocation, the amount of assets to be repaired, and the predicted highway network condition. The optimal budget allocation across different asset types (pavement and bridge decks) is presented in Figure 5-5 and Table

95 30 25 Budget ($ Million) Year Pavement Bridge Figure 5-5 Budget allocation across pavement and bridge decks Table 5.4 Budget Allocation across Pavement and Bridge Decks ($Million) Year Pavement Minor Major Total Bridge Deck Minor Major Total The optimized treatment policy indicates the quantity of assets that should be treated by certain types of preservation treatment. According to the optimization results, the amount of pavement that should be repaired is shown in Figure 5-6 and Table 5.5, and the amount of bridge decks that should be repaired is presented in Figure 5-7 and Table

96 Lane-Mile Year Minor Rehabilitation Major Rehabilitation Figure 5-6 Recommended amount of pavement to be repaired Table 5.5 Recommended Amount of Pavement to be Repaired (Lane-Mile) Year Minor Major Total

97 Square Foot (1,000) Year Minor Rehabilitation Major Rehabilitation Figure 5-7 Recommended amount of bridge decks to be repaired Table 5.6 Recommended Amount of Bridge Decks to be Repaired (1,000 Square-Foot) Year Minor Major Total If the above budget allocation and treatment policy are followed, the corresponding asset condition over the next five years can be predicted. The forecasted average asset deficiency level and average asset condition index are presented in Figure 5-8 and Figure

98 25 Deficiency Level (%) Year Pavement Bridge Weighted Average Figure 5-8 Predicted asset deficiency level ACI Year Pavement Bridge Weighted Average Figure 5-9 Predicted average asset condition index 82

99 The predicted asset condition distributions for pavement and bridge decks are shown in Figure 5-10, Figure 5-11 and Table 5.7 Lane-mile Percentage (%) Year Very Poor Poor Fair Good Excellent Figure 5-10 Predicted pavement condition distribution Square Foot Percentage (%) Year Very Poor Poor Fair Good Excellent Figure 5-11 Predicted bridge deck condition distribution 83

100 Table 5.7 Predicted Asset Condition Distribution (%) Year Pavement Excellent Good Fair Poor Very Poor Bridge Deck Excellent Good Fair Poor Very Poor The optimal solution specifies how much budget should be spent in which type of assets and in which type of treatment each year. These results are useful in determining budget allocation and future condition distribution at network-level, but cannot provide a project list specifying which assets should be repaired. Therefore, a multi-year preservation work plan considering individual asset items is necessary to implement the budget allocation and to achieve the optimal network condition. 5.2 Stage 2: Project Selection Dataset Description The required input of the project selection model includes the optimal treatment policy obtained from Stage 1 (network-level optimization) and the inventory data for individual asset items. The treatment policy can be expressed as the amount of assets that should be 84

101 repaired in each planning year (Table 5.5 and Table 5.6). Table 5.8 presents a sample pavement inventory data and Table 5.9 shows a sample bridge deck inventory data. The complete inventory data of the pavement and bridges in Ohio District 2 are presented in Appendix A and Appendix B. Table 5.8 Sample Pavement Inventory Data for Project Selection County Route Station Blog Elog Lanes ADT Snowfall Age ACI HEN 006R DOWN HEN 006R DOWN HEN 006R DOWN HEN 006R UP HEN 006R UP HEN 006R UP Table 5.9 Sample Bridge Deck Inventory for Project Selection County Route Log Deck Area ADT Snowfall Age ACI HEN 006R HEN 006R HEN 006R HEN 006R In this example problem, four criteria, age, condition, traffic volume, and climate, were included in the project prioritization process for illustration purposes. Age is defined as the number of years since the last repair was conducted, traffic volume is the total average daily traffic (ADT), condition is measured by the ACI, and climate is assessed by snowfall (inch/year). Assets at an older age are likely to have been in an undesirable condition for a longer time. Asset condition affects the level of service of the road. Assets with higher traffic volume tend to affect more road users. Assets in a region with heavy snowfalls tend to deteriorate faster than other assets. Therefore, these four criteria were used in the project selection process. 85

102 5.2.2 Project Selection by AHP The steps of applying AHP in project selection are described in section The preferences of the user need to be provided to estimate the relative importance of the alternatives. The pairwise comparison between the four criteria for this example problem are presented in Table It should be noted that if the consistency ratio is greater than 0.1, the pairwise comparison has to be performed again until the consistency ratio meets the standard. Table 5.10 Criteria Pairwise Comparison Matrix Condition Traffic Volume Age Climate Condition Traffic Volume Age Climate Consistency Ratio = 0.02 The relative importance of the four criteria (condition, traffic volume, age and climate) is expressed by a vector (0.56, 0.25, 0.095, 0.095). The five intensity levels for each criterion are defined in Table Table 5.11 Intensity Level Definition Condition Traffic Volume Climate Age (ACI) (ADT in 1,000) (Snowfall in Inch/Year) High 0 (Very Poor) > 80 >16 >35 Medium High 1 (Poor) Medium 2 (Fair) Medium Low 3 (Good) Low 4 (Excellent)

103 The intensity level pairwise comparison matrices under each criterion for this example problem are shown in Table 5.12 through Table Table 5.12 Condition Intensity Level Pairwise Comparison Matrix High Medium Medium Medium High Low Low High Medium High Medium Medium Low Low Consistency Ratio = 0.02 Table 5.13 Traffic Volume Intensity Level Pairwise Comparison Matrix High Medium Medium Medium High Low Low High Medium High Medium Medium Low Low Consistency Ratio = 0.02 Table 5.14 Age Intensity Level Pairwise Comparison Matrix High Medium Medium Medium High Low Low High Medium High Medium Medium Low Low Consistency Ratio =

104 Table 5.15 Climate Intensity Level Pairwise Comparison Matrix High Medium Medium Medium High Low Low High Medium High Medium Medium Low Low Consistency Ratio = 0.02 Based on the above pairwise comparisons, the relative weights of the intensity levels under each criterion are presented in Table Table 5.16 Relative Weights of Intensity Levels Condition Traffic Volume Age Climate High Medium High Medium Medium Low Low Total An AHP score can be estimated for each project candidates using the criteria weights and the intensity level weights. The project candidates for each type of repair treatment were then ranked based on their scores and were selected from the top of the list subject to the budget limitations. The project lists for the next five years can be generated using the project selection model and the network-level optimization results. For illustration purpose, the project lists for the first year (2014) are presented in Table 5.17 and Table The complete project lists generated by AHP method are shown in Appendix C. The project lists provide information regarding which asset items should be repaired using which type of treatment in which year. The optimization results estimated from State 1 could be achieved by following these project work plans. 88

105 Table 5.17 Pavement Project List Generated by AHP (2014) County Route Station Blog Elog Lane- Cost ACI Treatment Mile ($1,000) Year LUC 075R DOWN Minor LUC 075R UP Minor LUC 280R DOWN Minor LUC 280R UP Minor LUC 475R DOWN Minor OTT 002R DOWN Minor OTT 002R UP Major SAN 006R UP Minor SAN 020R DOWN Major SAN 020R UP Major SAN 020R UP Minor SAN 020R UP Major SAN 020R UP Major WOO 280R DOWN Major Table 5.18 Bridge Deck Project List Generated by AHP (2014) SFN County Route Log Deck Area ACI Treatment Cost ($1,000) Year LUC 075R Minor LUC 075R Minor LUC 075R Minor LUC 075R Major LUC 075R Minor LUC 075R Minor LUC 075R Minor LUC 075R Minor LUC 075R Minor LUC 475R Minor LUC 475R Minor LUC 475R Major LUC 475R Minor Project Selection by MAUT The steps of applying MAUT in project selection are described in section The preferences of the user need to be provided to estimate the utility functions of the four 89

106 criteria. The utility functions for the example problem are presented in Equations 5.5 through 5.8. U U 1 ( ACI ) (4 ACI ( ADT ) ADT ) U ( Age) Age 5.7 U ( Snowfall ) Snowfall 5.8 The plots of the individual utility functions of the four attributes are presented in Figure 5-12 through Figure Utility Value ACI Figure 5-12 Utility function of condition (ACI) 90

107 Utility Value ADT Figure 5-13 Utility function of traffic volume (ADT) Utility Value Age Figure 5-14 Utility function of age 91

108 Utility Value Snowfall (Inch/Year) Figure 5-15 Utility function of climate (Snowfall) Based on the above individual utility functions and the relative weights of the four criteria obtained using the AHP method, the multiple attribute utility function of a project candidate is expressed in Equation 5.9. U 0.56 U( ACI ) 0.25 U( ADT ) U( Age) U( Snowfall ) 5.9 The project candidates for each type of rehabilitation treatment were ranked based on the multiple attribute utility score calculated using the above equation. The system then selected projects from the top of the list until the allocated budget was used up. The complete project lists for the next five years are presented in Appendix C. For illustration purpose, the project lists for the first year (2014) are shown in Table 5.19 and Table

109 Table 5.19 Pavement Project List Generated by MAUT (2014) County Route Station Blog Elog Lane- Cost ACI Treatment Mile ($1,000) Year LUC 075R DOWN Minor LUC 075R UP Minor LUC 280R DOWN Minor LUC 280R DOWN Minor LUC 280R UP Minor LUC 280R UP Minor LUC 475R DOWN Minor OTT 002R UP Major SAN 020R DOWN Major SAN 020R UP Major SAN 020R UP Major SAN 020R UP Major WOO 280R DOWN Minor WOO 280R DOWN Major WOO 280R UP Minor WOO 475R DOWN Minor Table 5.20 Bridge Deck Project List Generated by MAUT (2014) SFN County Route Log Deck Cost ACI Treatment Area ($1,000) Year LUC 075R Minor LUC 075R Minor LUC 075R Minor LUC 075R Major LUC 075R Minor LUC 075R Minor LUC 075R Minor LUC 075R Minor LUC 475R Minor LUC 475R Minor LUC 475R Minor LUC 475R Major LUC 475R Minor The MAUT approach yields similar results in project selection compared to the AHP approach. For example, about 47 of the 57 lane-miles pavement projects generated by the two approaches are the same according to Table 5.17 and Table It can also be seen 93

110 from Table 5.18 and Table 5.20 that 11 of the 13 bridge deck projects generated by the two methods are identical. The differences between the projects lists obtained from the two approaches are due to the different estimation of user s preferences. 5.3 Stage 3: Project Coordination Dataset Description The uncoordinated five-year asset preservation work plans obtained from the project selection by AHP (section 5.2.2) were used as an example to illustrate the project coordination models developed in this study. The two work plans for pavement (Table B.1) and bridges (Table B.2) were imported into a single table and sorted by the location information such as county, route, and log points to identify the adjacent projects. The complete table is shown in Appendix D. For illustration purpose, the uncoordinated project work plan for Henry County is presented in Table

111 Table 5.21 Sample Uncoordinated Project List (Henry County) ID Type SFN County Route Blog Elog Station Treatment Year 1 Pavement HEN 006R UP Minor Pavement HEN 006R UP Major Pavement HEN 006R DOWN Major Bridge HEN 006R 11.5 Minor Bridge HEN 006R 11.5 Minor Pavement HEN 006R UP Minor Pavement HEN 006R DOWN Minor Pavement HEN 006R DOWN Major Bridge HEN 006R Minor Pavement HEN 006R DOWN Major Pavement HEN 006R UP Major Pavement HEN 006R DOWN Minor Pavement HEN 024R DOWN Minor Pavement HEN 024R UP Minor 2016 The asset items were sorted in a list based on their location information and adjacent projects can be identified. There are 161 pairs of adjacent projects in the complete asset project list (Table D.1), however, only 66 pairs of adjacent projects can be combined based on their scheduled conducting years. In Table 5.21, there are 13 pairs of projects (2, 3), (4, 5), (6, 7), (7, 8), (10, 11), (11, 12), (13, 14), (3, 4), (3, 6), (3, 5), (8, 9), (10, 9), and (8, 10). In the uncoordinated work plan, some adjacent projects are conducted in different years. For example, project 2 is scheduled to be conducted in 2016, but its adjacent project 3 is to be conducted in This type of uncoordinated projects are likely to cause the unnecessary traffic disruptions and are not cost-effective considering economies of scale. Therefore, it would be beneficial to improve the multi-year work plan by rescheduling some of the projects subjects to annual budget constraints and project timing constraints. In this example problem, it was assumed that all projects can be brought forward or postponed for one year, and the duration of all projects is one year. For instance, project 2 is originally scheduled to be conducted in 2016, so its earliest starting year is 2015 and its 95

112 latest ending year is The available annual budget is $25 million, which equals to the budget limit specified in the network-level optimization example problem (section 5.1.1) Project Coordination Results The above dataset was used as the input for both the integer programming model and the constraint programming model. The results of both models are described in this section. The coordinated work plan and the original work plan are compared. The integer programming model and the constraint programming yielded similar solutions for the example problem. The optimal solutions are expressed as five-year work plans for the 190 asset items as shown in Table D.1 in Appendix D. Both models combined 127 of the 161 pairs of adjacent projects. Table 5.22 presents a sample result extracted from the complete project list. It can be seen that some adjacent projects (i.e. Project 2 and Project 3) that were not combined in the original work plan are now rescheduled to be conducted simultaneously. In order to compare the three different work plans, maps were generated using ArcGIS for the original work plan (Figure 5-16), the coordinated work plan according to constraint programming (Figure 5-17), and the coordinated work plan according to integer programming (Figure 5-18). 96

113 Table 5.22 Sample Coordinated Project List (Henry County) ID Type SFN a County Route Blog Elog Station Treatment Cost Year b Year_C c Year_I d Group e 1 Pavement HEN 006R UP Minor Pavement HEN 006R UP Major Pavement HEN 006R DOWN Major Bridge HEN 006R 11.5 Minor Bridge HEN 006R 11.5 Minor Pavement HEN 006R UP Minor Pavement HEN 006R DOWN Minor Pavement HEN 006R DOWN Major Bridge HEN 006R Minor Pavement HEN 006R DOWN Major Pavement HEN 006R UP Major Pavement HEN 006R DOWN Minor Pavement HEN 024R DOWN Minor Pavement HEN 024R UP Minor Note: a. Structural File Number (Unique ID of bridges) b. Original project conducting year according to uncoordinated work plan. c. Project conducting year according to constraint programming results. d. Project conducting year according to integer programming results. e. Adjacent asset items belong to the group. 97

114 Figure 5-16 Original uncoordinated five-year asset work plan 98

115 Figure 5-17 Coordinated five year-asset work plan (constraint programming) 99

116 Figure 5-18 Coordinated five-year asset work plan (integer programming). 100

117 5.4 Additional Examples This section presents several additional example problems that the optimization models could solve. The main purposes are to test the model by changing parameters, demonstrate the additional functionalities, and illustrate the benefits of the models Parametric Study In order to test the optimization model, this section present a parametric study by changing some parameters within the model. The allowable treatments for certain condition category was modified in this example problem (Table 5.23). Table 5.23 Allowable Treatments (Revised for Parametric Study) Condition Do Nothing Minor Rehabilitation Major Rehabilitation Excellent Yes Good Yes Fair Yes Yes Poor Yes Yes Very Poor Yes Specifically, it was assumed that the assets in poor condition could be repaired only by major rehabilitation instead of minor rehabilitation. The treatments for other condition categories remain the same as presented in Table 5.2. The purpose was to test the impact of different allowable treatments on the asset condition performance at the network-level. The assumptions and dataset in this example problem are identical with those in Section 5.1 except the allowable treatments. The available annual budget was also assumed to be $25 million. 101

118 The optimization results with the revised allowable treatments include the budget allocation, the amount of assets to be repaired, and the predicted highway network condition. The recommended budget allocation across different asset types (pavement and bridge decks) is presented in Figure 5-19 and Table Budget ($ Million) Year Pavement Bridge Figure 5-19 Budget allocation across pavement and bridge decks with revised allowable treatments Table 5.24 Budget Allocation across Pavement and Bridge Decks with Revised Allowable Treatments ($Million) Year Pavement Minor Major Total Bridge Deck Minor Major Total

119 According to the recommended budget allocation, the amount of pavement that should be repaired is shown in Figure 5-20 and Table 5.25, and the amount of bridge decks that should be repaired is presented in Figure 5-21 and Table Lane-Mile Year Minor Rehabilitation Major Rehabilitation Figure 5-20 Recommended amount of pavement to be repaired with revised allowable treatments Table 5.25 Recommended Amount of Pavement to be Repaired with Revised Allowable Treatments (Lane-Mile) Year Minor Major Total

120 Square Foot (1,000) Year Minor Rehabilitation Major Rehabilitation Figure 5-21 Recommended amount of bridge decks to be repaired with revised allowable treatments Table 5.26 Recommended Amount of Bridge Decks to be Repaired with Revised Allowable Treatments (1,000 Square-Foot) Year Minor Major Total If the above budget allocation and treatment policy are followed, the corresponding asset condition over the next five years can be predicted. The comparison of the forecasted deficiency level obtained from the revised allowable treatments (Table 5.23) and the original allowable treatments (Table 5.2) is presented in Figure

121 Deficiency Level (%) Year Revised Treatment Original Treatment Target Figure 5-22 Comparison of predicted asset deficiency level It can be seen from Figure 5-22 that the deficiency level obtained from the revised allowable treatments remains above 15%, while the deficiency level is reduced to below 5% with the original allowable treatments. The comparison of the average ACI obtained from the revised allowable treatments (Table 5.23) and the original allowable treatments (Table 5.2) is presented in Figure

122 3.4 Weighted Average ACI Year Revised Treatment Original Treatment Figure 5-23 Comparison of predicted average asset condition index Figure 5-23 indicates that the weighted average ACI obtained from the original allowable treatments improves from 2.5 to 3.0, while the weighted average ACI obtained from the revised allowable treatments improves from 2.5 to only 2.6. Therefore, the parametric study suggests that the asset network could perform better with the original allowable treatments than with the revised allowable treatment, when the same amount of budget is given Project Coordination with Additional Constraints In order to demonstrate more functionalities of the project coordination model, this section presents an example problem with additional constraints to prevent certain projects being conducted simultaneously. In some cases, it might be desirable to not perform two projects at the same time. For example, if two routes intersect with each other, repairing the two 106

123 routes simultaneously might block the entire intersection. In the example problem presented in this section, all the dataset and the assumptions are identical to that of the problem in Section 5.3, except the constraints to avoid combining certain projects. Figure 5-24 presents two routes (024R and 475R) that should not be repaired simultaneously because they intersect with each other. This example is extracted from the coordinated work plan generated by the constraint programming model (Figure 5-17). 475R 024R 475R Figure 5-24 Certain projects that should not be performed simultaneously By adding the constraints to avoid 024R and 475R being performed at the same year, the following results were obtained from the project coordination model (Figure 5-25). 107