An Automated System for Prioritizing Highway Improvement Locations and Analyzing Project Alternatives
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1 An Automated System for Prioritizing Highway Improvement Locations and Analyzing Project Alternatives Albert Gan, Ph.D. Professor Florida International University Priyanka Alluri, Ph.D., P.E.* Assistant Professor Florida International University Md Asif Raihan, M.S. Graduate Research Assistant Florida International University Kaiyu Liu, Ph.D. Senior Research Associate Florida International University Dibakar Saha, Ph.D. Research Associate Florida International University Rax Jung, Ph.D., P.E. Project Development Engineer Florida s Turnpike Enterprise rax.jung@dot.state.fl.us *Corresponding Author Department of Civil and Environmental Engineering Florida International University 0 West Flagler Street, EC Miami, FL Phone: (0) -; palluri@fiu.edu Total words:,0 words + figures 0 =,0 words Revised Paper Submitted for: Publication and Presentation The th Annual Meeting of the Transportation Research Board November 0
2 Gan et al. 0 0 ABSTRACT The Florida Department of Transportation (FDOT) District One first deployed a web-based system in 00, called the Congestion Management Process (CMP), to screen and prioritize highway locations on its Strategic Intermodal System (SIS) for low-cost, near-term improvements. The system prioritizes highway locations on the SIS within the District based on a simple scoring method with seven performance measures, i.e., crash ratio, fatal crash, volumeto-capacity (v/c) ratio, Average Annual Daily Traffic (AADT), truck volume, truck percent, and delay. Since its development and following the adoption of the Highway Safety Manual (HSM) by FDOT, there was a desire to apply safety performance measures that are consistent with the HSM methodology. There was also a desire to explore and implement a more advanced project prioritization method for better location screening and prioritization. The District further desires to add mapping capabilities to improve data visualization. This paper describes the District s effort to incorporate these improvements in the CMP system. The CMP system has the capability to automatically calculate performance measures including two safety-related measures based on the HSM methodology, and prioritize highway locations using the Analytic Network Process (ANP), an advanced multi-criteria decision-making technique. The system can also create thematic maps of performance measures and other input variables on Google Maps for data visualization. The system also has the capability to evaluate potential projects and record project level information. While the system was developed for FDOT District One, it can serve as prototype and be customized for prioritizing highway locations in other states. Keywords: Highway improvement location prioritization, performance measures, Analytic Network Process (ANP), data visualization, information system.
3 Gan et al INTRODUCTION The Florida Department of Transportation (FDOT) District One represents counties in Southwestern Florida, constituting,0 centerline miles of state highway network. The District deployed a web-based system in 00, called the Congestion Management Process (CMP), to help its transportation planners screen and prioritize highway locations on its Strategic Intermodal System (SIS) for low-cost, near-term improvements (). The SIS is composed of specially designated facilities considered to be of statewide and regional significance for aviation, highway, intermodal rail, seaport, space and transit systems, and accommodations for bicycles and pedestrians. The CMP system prioritizes highway locations on the SIS within the District based on seven performance measures, i.e., crash ratio, fatal crash, volume-to-capacity (v/c) ratio, Average Annual Daily Traffic (AADT), truck volume, truck percent, and delay. The system further implements a simple scoring method for highway location prioritization. In this method, each of the seven performance measures is pre-assigned a maximum score, depending on their relative importance. For each highway location, a score is then assigned to each measure based on the corresponding site-specific condition. The scores from all seven measures of a location are then totaled to obtain the overall score which is then used in the final ranking of locations. Although the main function of the CMP is to screen highway segments that have significant safety and mobility issues, it also includes functions to record project-specific information such as site characteristics and costs associated with specific improvements at potential improvement locations. Accordingly, the CMP is a two-tier process: () screening for highway segment locations with potential for improvement; and () prioritizing project improvement alternatives. Tier one is an automated process where a long-list of candidate locations is generated based on the seven performance measures. Tier two is mainly a manual process where the long-list is reviewed to identify the short-list of potential candidate projects. In this tier, the short-list locations are further analyzed for specific improvements and include non-transportation performance goals and project-specific details such as benefit and cost estimates, potential funding sources, type of improvement (i.e., localized vs. systemic), etc. Since the development of the CMP system in 00 and following the adoption of the Highway Safety Manual (HSM) by FDOT (), there was a desire to replace the two safetyrelated performance measures, namely, crash ratio and fatal crash, with safety measures that are consistent with the methodology used in the HSM. There was also a desire to explore and implement a more advanced project prioritization method for better location screening. The District further desires to add mapping capabilities to the system to take advantage of the increasingly available web mapping tools. Accordingly, this paper describes the District s effort in accomplishing these objectives in the system, namely: () replacing existing safety measures to be consistent with the HSM methodology; () implementing an advanced project prioritization method; and () incorporating mapping capabilities to visualize project locations, performance measures, and system output. PERFORMANCE MEASURES As aforementioned, FDOT District One uses seven measures for implementation in the CMP ():
4 Gan et al Crash ratio: The ratio of the annual crash rate for each highway segment to the corresponding year s District One average system-wide crash rate for that type of highway segment.. Fatal crash: The average number of fatal crashes per year over the past three years divided by the length of the highway segment.. Volume-to-capacity ratio: The ratio of the two-way peak-hour traffic volume and the capacity.. Average Annual Daily Traffic (AADT) per lane: The AADT normalized by the number of travel lanes.. Truck volume per lane: The truck volume normalized by the number of travel lanes.. Truck percent: Percentage of trucks in the traffic stream.. Delay: Three general levels of the delay condition are defined: a) Fails if the existing Level of Service (LOS) is F, b) Exceeds Standard if the existing LOS exceeds its corresponding LOS standard, and c) At or Below Standard if the existing LOS is at or below its corresponding LOS standard. It was recognized that a main issue with the two existing safety performance measures was that they do not account for the regression-to-the-mean (RTM) effect. This bias may cause locations with high crashes that were due merely to random fluctuations in crash numbers to be erroneously selected for safety improvements, thus, reducing the cost-effectiveness of safety programs. In other words, when locations are identified for safety improvements based on high crash frequencies and crash rates, they will often experience fewer crashes after the safety improvement even if the improvement is not effective. Therefore, because of the RTM bias, safety countermeasures often appear to be more effective than they really are. It was recommended that the two existing safety-related performance measures, i.e., fatal crash and crash ratio, be replaced with number of excess fatalities and number of excess injuries. The number of excess fatalities is the expected number of excess fatalities for the final year of the analysis period for the location. Similarly, the number of excess injuries is the expected number of excess injuries for the final year of the analysis period for the location. These two measures give the prediction of the number of excess fatalities and injuries at the person level given the location s existing traffic volume and roadway geometric characteristics. Any location with excess fatalities (or injuries) greater than zero would be experiencing more fatalities (or injuries) than expected, and larger values of excess fatalities (or injuries) indicate greater potential for safety improvement. On the other hand, negative excess number of fatalities (or injuries) suggests that the location experiences fewer fatalities (or injuries) than expected. PRIORITIZATION METHOD Transportation agencies have been prioritizing highway locations using a variation of simple scoring and ranking methods (-). The general approach in this method is that each of the selected performance measures is first assigned a maximum score. The actual score of each measure is then determined based on site-specific characteristics. Finally, for each project location, scores from all the performance measures are summed up to obtain the overall score which is then used in project prioritization.
5 Gan et al One major limitation with the simple scoring method is that it does not consider the impacts on the final ranking and thus the decisions due to the presence of correlation among the performance measures used. Furthermore, some of the performance measures could also be qualitative, requiring subjective judgment. The simple scoring method cannot efficiently address these issues, and thus agencies have become more interested in advanced prioritization methods that are transparent, effective, accountable, and defendable (0, ). In decision making involving multiple criteria, the Analytic Hierarchy Process (AHP) has been widely used for its ability to organize quantitative and qualitative criteria in a systematic manner, and provide a structured yet relatively simple solution to decision making problem (). Developed by Professor Thomas L. Saaty in 0, the method stresses the importance of the intuitive judgments of a decision maker as well as the consistency of the comparison of criteria (alternatives) in the decision-making process (). However, as AHP structures the problem hierarchically, it does not consider the impacts of interdependencies that exist among the criteria. For example, it was quite clear from this set of performance measures used in CMP that AADT and v/c ratio are interdependent, so are truck volume and truck percentage. Further, delay and v/c (thus AADT) are also interdependent as delay is a function of v/c. In fact, it can be concluded that most if not all the performance measures are interdependent to an extent and would benefit from a method that can take account of the impacts of such interdependencies. This led to the consideration of the Analytic Network Process (ANP), developed also by Professor Saaty, which is a generalized methodology of AHP. Unlike AHP, ANP not only has the capability of breaking down a decision problem into a logical order, but can also account for the interdependencies among the criteria, the alternatives, and the overall goal in a decision network (). The ANP is composed primarily of the following steps (, ): Model construction and problem structuring Pairwise comparison matrices and priority vectors Supermatrix, weighted supermatrix, and limit matrix formations Ranking of alternatives ANP Model Structure The goal of this application is to prioritize highway locations on the FDOT District One s SIS network based on several performance measures. Figure illustrates the hierarchical structure for this scenario. As can be observed from the figure, Level 0 is the analysis goal, i.e., to prioritize the highway improvement locations. Level is the multi-criteria that consist of seven performance measures. Finally, Level consists of the alternative choices, i.e., the highway locations. The lines between the three levels indicate the relationship between goal, performance measures, and the alternatives (i.e., highway locations). As can be observed from Figure, the problem can be disintegrated into three levels (similar to hierarchical structure): goal to rank the alternatives, performance measures to achieve the goal, and alternatives (i.e., the highway locations that need to be prioritized). The ANP addresses the interdependency of the criteria (i.e., performance measures) by including an inner
6 Gan et al. dependence loop in the network structure. Figure depicts the potential network structure for this scenario. FIGURE Hierarchical structure of highway improvement location selection. 0 0 FIGURE ANP network model structure. In this figure, each arrow and loop has specific impacts on the interrelation of different levels, and on the next steps. W represents the impact of goal on each of the criterion and W represents the impact of criteria on each of the alternatives. The interdependency within the criteria (i.e., performance measures) is represented by W. The direction of arrows is dependent on the rationale of this problem structure. For the stated scenario, the goal of prioritizing highway locations can be achieved through the criteria, i.e., the criteria are impacting the goal; and these criteria determine the ranking of the alternatives. On the other hand, the criteria can be interdependent in nature. Pairwise Comparisons and Priority Vectors Once the ANP model structure is established, the next step is to determine the relative importance of each performance measure and each alternative (i.e., highway segment) with respect to each performance measure. It is achieved via pairwise comparisons that aim to compare the relative importance of two performance measures (or, alternatives) at a time. This
7 Gan et al approach theorizes that an analyst can better assess the relative importance of a set of performance measures when given only two measures to compare at a time, than when given all measures at once. The pairwise comparisons are performed on a pre-defined relative scale of -, which translates to comparing how much preference one measure gets over the other. These pairwise comparisons might not always be completely logical. For example, if Measure A is more important than Measure B, and Measure B is more important than Measure C, the selections would be inconsistent if Measure C is considered to be more important than Measure A, which is not logical. However, such conflicts will arise naturally, especially when several performance measures are involved. Professor Saaty () developed the consistency ratio to help gauge the degree of consistency in a set of pairwise comparisons made. A 0% consistency ratio indicates that the pairwise comparisons are perfectly consistent. This is not acceptable as inconsistency itself is important, for without it new knowledge that changes preference order cannot be admitted. In general, a consistency ratio of around 0% is considered acceptable. This is because the priority of consistency to obtain a coherent explanation of a set of facts must differ by an order of magnitude from the priority of inconsistency which is an error in the measurement of consistency (). Thus, on a scale from 0-, inconsistency should not exceed 0.0 by very much (). Otherwise, the pairwise comparisons should be revised to improve their consistency. Once the pairwise comparisons are performed, and the consistency of the comparisons are found to be acceptable, the next steps in the ANP model are to generate pairwise comparison matrices and priority vectors. Level corresponds to one n n comparison matrix for the pairwise comparison between n performance measures with respect to the goal. Similarly, since the y locations are connected to each of the n performance measures, n number of y y comparison matrices are created to evaluate the y locations. The pairwise comparison matrices are then used to generate priority vectors, which are the normalized Eigen vectors of the comparison matrices. Priority vectors are generated for all the y highway locations and the performance measures at sub-cluster level with respect to the n performance measures. Supermatrix, Weighted Supermatrix, and Limit Matrix Formations A supermatrix is a comparatively large square matrix where the cluster priority vectors are entered in appropriate columns to obtain global priorities with interdependent influence (). The general supermatrix framework takes the following form: Goal Criteria Alternatives Goal Criteria W W 0 Alternatives 0 W I Note that each of the elements in this supermatrix represents a submatrix. Zero (0) elements correspond to those elements which do not have any influence. Since each alternative depends only on itself, identity matrix (I) submatrix is used in the supermatrix framework in row: Alternatives and column: Alternatives.
8 Gan et al Once the supermatrix is generated, the next step is to derive the limit priorities of influence from the supermatrix. To obtain such priorities, the supermatrix needs to be transformed to a matrix each of whose column sums to unity, known as column stochasticity (). The resulting stochastic matrix is known as weighted supermatrix. The rationale behind this transformation is to convert the elements local cluster priorities to global priorities. The limit supermatrix is next obtained by raising the weighted supermatrix to exponential powers k+, where k is an arbitrary number. It provides the long-term relative influences of the elements on each other through convergence on the importance weights. Ranking of Alternatives The final priorities of all elements are obtained by normalizing each cluster of the limit matrix. Note that detailed calculations are not included here for brevity. Readers are referred to Raihan et al. () which presents the detailed calculations in each step of the ANP process. CMP SYSTEM This section presents the design and functionalities of the web-based CMP system. The system automates the two-tier process of screening for highway segments and analyzing potential improvements at specific project locations. Specifically, the system implements the following key functions: Upload various traffic-related data and crash records. Calculate performance measures from uploaded data. Determine the importance of each performance measure based on pairwise comparisons. Prioritize highway segments by applying the ANP method with multiple performance measures. Create thematic maps of performance measures and other input variables on Google Maps for data visualization. Evaluate potential projects and record project level information. Manage user accounts and assign account privileges. User Types The CMP system supports the following four user types: User: This user type can view projects and project information sheets, and print or export information. Project Manager: This user type can upload and process data, view projects, export project list, build scenarios, apply prioritization method, make project selections, enter project information for selected projects, and generate project information sheets. Decision Maker: This user type can make final decision on project selections, in addition to all that can be done by a Project Manager. Administrator: This user type can manage user accounts and scenarios, in addition to all that can be done by a Decision Maker.
9 Gan et al. Main Screen After logging into the system, the user is presented with the main screen shown in Figure. The left panel includes a dropdown list for the user to select an analysis year, plus a list of menu items to provide access to various CMP functions. Access privilege to specific menu items is provided based on the specific roles of each user type. The right panel of the main screen includes a Google Maps application that displays the map area covered by District One. This map is used mainly to display highway locations and system inputs and outputs. 0 0 FIGURE CMP main screen. Data Preparation The first step in applying the CMP system is to upload all required input data into the system. CMP provides tools for authorized users to upload and process the required data. The data preparation process in CMP includes the following two major steps: uploading input data and calculating performance measure values. Step : Upload Input Data This step allows the user to upload all the required input data into the system database. The input data for CMP include all those that are needed to derive the seven performance measures used in project prioritization, in addition to the SIS road network covered by the District. The data are divided into three data files for crashes, segments, and RCI (Roadway Inventory Characteristics)
10 Gan et al. 0 variables, and are uploaded for each analysis year when their respective data become available. The file upload history, including the data year, the data category, the file name, the upload date, and the user who uploaded the file, are listed on the screen for reference (see Figure ) FIGURE Window for uploading data. Step : Calculate Performance Measures After all the required data files are successfully uploaded, they can be used in this step to calculate the performance measure data used in the project prioritization process. Specifically, the calculations performed in this step include: Calculating the truck volume from truck percent. Standardizing the volume data (i.e., vehicular volume and truck volume) from the total volume for all lanes to volume per lane. Calculating the excess injuries and excess fatalities consistent with the HSM method. Calculating the volume-to-capacity ratios. Determining the delay condition based on existing level of service (LOS) with respect to the design LOS. Figure shows the window for calculating performance measures. It includes a table that lists the data uploaded for each data year. Only one data set can exist in the system for each year. However, data can be uploaded multiple times to update existing data in the system. When all the required data sets have been successfully uploaded, as indicated by the Ready status indicator (otherwise, the status will indicate Missing ), a Calculate link will appear to allow the user to start calculating the performance measure data. After the calculation is completed, the table will list the date and time the calculation was initiated, in addition to the name of the user who ran the calculation, and the status of the calculation. The calculated performance measure data will also be available for export to Excel. In the case when the performance measure data have been
11 Gan et al. calculated based on previously uploaded data files, the Calculate link will be replaced with Recalculate to signal the existence of performance measure data in the system for the same year. Thus, the recalculation, if performed, will replace the existing data FIGURE Window for calculating performance measures. Location Prioritization and Project Analysis After the performance measure data are successfully calculated, they are ready to be applied to prioritize highway segments and analyze projects. The process in the CMP system includes three steps: building scenarios, prioritizing project locations, and managing selected projects. Step : Build Scenarios The Build Scenarios step allows the user to build scenarios that weigh the importance of different performance measures. As shown in Figure, the user can start building scenarios based on pairwise comparisons of performance measures. For a new scenario, the system starts by assuming that all performance measures are equally important. The user can then go through each pair of measures to assess and indicate their relative importance. This is done by marking on the scale between each pair of measure. For example, if the user feels very strongly that Excess Fatalities is more important than Delay, he/she would mark the radio button highlighted in a red box in Figure. To help the user gauge the degree of consistency in a set of pairwise comparisons made, CMP calculates a so-called consistency ratio as a quick measure of the level of consistency. This ratio, expressed in percent, is calculated and displayed with each user selection of the preference level. A 0% consistency ratio indicates that the pairwise comparisons are perfectly consistent. The literature suggests that a consistency ratio of around 0% can be considered to be acceptable. Otherwise, the pairwise comparisons shoud be revised to improve their consistency. When the consistency ratio is calculated, the system also calculates the relative weight for each performance measure based on the result from the pairwise comparisons. The relative weights, which sum up to 00%, are shown at the bottom of the window. These weights can be saved as a scenario and are available for use in the second step of the project analysis process to prioritize the projects.
12 Gan et al. Only the transportation planner(s) who are knowledgeable of the performance measures would weigh the measures. The weighting/pairwise comparisons either could be performed by one person, or could be a team effort. Note that several scenarios with different weighting factors could be created and saved. This approach gives the users (i.e., the planners) an opportunity to compare the results from different scenarios. Only the user with the Decision Maker or Administrator privileges can make the final decisions on project selection. 0 FIGURE Window for performing pairwise comparisons and building weight scenarios. Step : Prioritize Project Locations This step allows the user to calculate scores using the ANP method and the weight scenario built in the previous step. The scores are then used to gauge a highway segment s overall need for improvements. Figure shows the main screen for performing this function. It allows the user to
13 Gan et al. select the analysis year and then select to calculate the scores for each highway segment. As soon as the scores are calculated, the list of the highway segments with their calculated scores is listed. The user can then select the highway segments from the list for further analysis in the third and final step of the process. The user can also export the list to an Excel file and display specific highway segments on Google Maps on a pop-up window. Figure shows an example. FIGURE Project prioritization window. 0 FIGURE Map display when multiple highway segments are selected. Step : Manage Selected Projects The final step of the analysis process is to analyze the highway segments selected in the previous step to further shortlist the project selections, document the selection decisions, and populate the
14 Gan et al. selected project location (i.e., the Go projects) with detailed project-level information. Figure shows that the project locations assigned a decision status of Go or No Go based on the review by the project manager and/or decision makers. Figure 0 shows a partial screen for a Go project location which allows the user to specify the general project information. In addition, the section also allows the user to enter information on the proposed improvement, the project, and other additional comments. 0 FIGURE Manage Selected Projects window. FIGURE 0 Project information data entry for a Go project location.
15 Gan et al. 0 0 After project data are entered, the user can generate a one-page pre-formatted report that includes all the project information. The user may also export the report to an available file format (i.e., Excel, PDF, or Word). Data Visualization The CMP system includes a Google Maps application to plot thematic maps of both the input variables and the performance measures. Once an analysis year is selected, the map view will display the state roads layer for the selected analysis year, along with a search box and four dropdown lists. As shown in Figure, a standard -digit roadway ID could be entered to find a specific highway segment. The four dropdown lists combine to provide the user the ability to create different thematic maps. Thematic maps can be created by selecting a variable to plot from the first dropdown list. The remaining three dropdown lists provide the following plotting options: Number of intervals: select from a range of to 0 intervals. Line width: select from a range of level to level. The default is level. Line color: select either fixed colors or one of four color ramps. Figure shows a thematic map of the Level of Service (LOS). As can be seen in the figure, the legend for the thematic map is displayed on the left panel, where additional map layers for the district, counties, and state roads could also be displayed. FIGURE A sample thematic map for level of service (LOS).
16 Gan et al System Transferability Although the CMP system is primarily developed for FDOT District One, it can be customized to prioritize locations in other agencies. Specifically, the customization efforts will include: modifying the input data file structure depending on the agency s data, updating the performance measures to be considered, and including the GIS layer for the agency route network for data visualization. Future Enhancements A future enhancement to this system would be to provide flexibility in the performance measures being considered for prioritizing locations. Currently, the seven performance measures included in the system are fixed, and cannot be easily changed by the user. However, agencies might want to use performance measures that are different from these seven. The enhanced system would allow the user to consider a different set of performance measures. CONCLUSIONS Most transportation agencies have been using the simple scoring method to prioritize highway project locations. This simple method which assigns a fixed weight to each performance measure does not account for correlation between performance measures. Given that it is not likely that a single performance measure will be able to address all the goals and objectives of an agency, nor is it likely that multiple performance measures will be independent from each other, it becomes clear that transportation agencies would benefit from a method that can take account of the impacts of interdependencies of performance measures. This paper presented a web-based system that fully implemented an advanced method of project prioritization known as the Analytic Network Process (ANP). It is the first known application of ANP in prioritizing transportation projects. The method is specially designed to account for the impact from the interdependencies of performance measures. The system also calculates safety performance measures based on the empirical Bayes (EB) methodology. The EB methodology is recommended by the Highway Safety Manual (HSM) to specifically account for the regression-to-the-mean (RTM) bias, which could cause locations to be erroneously selected for safety improvements. The system can also create thematic maps of performance measures and other input variables on Google Maps for data visualization. The system further provides functions for evaluating potential projects and record project level information. The FDOT District One is currently considering adopting this system. While the system was developed for FDOT District One, it can serve as prototype and be customized for prioritizing highway locations in other states. ACKNOWLEDGEMENTS This research was funded by the Florida Department of Transportation (FDOT) Research Center.
17 Gan et al REFERENCES. Florida Department of Transportation (FDOT). Development of a Congestion Management Process for the Florida Intrastate Highway System/Strategic Intermodal System in District One. FDOT District One, 00.. FDOT. Highway Safety Manual Implementation Plan Timeline, June 0. Implementation-Timeline_0-.pdf Accessed May, 0.. Delaware Department of Transportation. DelDOT Project Prioritization Criteria. 0/DelDOT_project_prioritization_criteria.pdf Accessed May, 0.. Missouri Department of Transportation. Criteria for Project Prioritization. iaforprioritizationofprojects.pdf. Accessed May, 0.. North Carolina Department of Transportation. Prioritization.0 Highway Scoring Criteria: Summary Report, March 0. Accessed June, 0.. Ohio Department of Transportation. Transportation Review Advisory Council: Policy & Procedures, July 0. %0and%0Procedures%0Revisions_...pdf. Accessed April, 0.. Metropolitan Planning Council. States Approaches to Transportation Project Prioritization: Linking Policy, Planning and Programming. Accessed July, 0.. Miller, J. S., R. E. Turochy, and J. H. Lambert. Considerations in the Development of Procedures for Prioritizing Transportation Improvement Projects in Virginia, March Accessed May, 0.. Dowling Associates, Inc. WSDOT Mobility Project Prioritization Process: Benefit/Cost Software User s Guide, May Accessed July, Gan, A., A. Raihan, P. Alluri, K. Liu, and D. Saha. Updating and Improving Methodology for Prioritizing Highway Project Locations on the Strategic Intermodal System (SIS). Final Research Report, Florida Department of Transportation, Tallahassee, FL, 0.. Raihan, A., P. Alluri, A. Gan, and R. Jung. Application of the Analytic Network Process (ANP) in Prioritizing Highway Improvement Locations. In Proceedings of the th Annual Meeting of the Transportation Research Board, Washington, DC, 0.. Skibniewski, M. J., and L. Chao. Evaluation of Advanced Construction Technology with AHP Method. In Journal of Construction Engineering and Management, Vol., No.,, pp. -.. Saaty, T. L. The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation. McGraw-Hill. New York, 0.. Saaty, T. L. Decision Making with Dependence and Feedback: The Analytic Network Process. RWS Publications. Pittsburgh,.
18 Gan et al. 0. Chung, S. H., A. H. L. Lee, and W. L. Pearn. Analytic Network Process (ANP) Approach for Product Mix Planning in Semiconductor Fabricator. In International Journal of Production Economics, Vol., 00, pp. -.. Yüksel, İ., and Dağdeviren, M. Using the Analytic Network Process (ANP) in A SWOT Analysis A Case Study for a Textile Firm. In Journal of Information Sciences, Vol., No., 00, pp. -.. Saaty, R. W. The Analytic Hierarchy Process - What It is and How It is Used. In Journal of Mathematical Modelling, Vol., No.,, pp. -.. Saaty, T. L., and L. G. Vargas. Decision Making with the Analytic Network Process Economic, Political, Social and Technological Applications with Benefits, Opportunities, Costs and Risks. Springer, Pittsburgh, 00.
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