Goal Programming Framework for Prioritization of Low-Volume Road Projects Considering Network Accessibility and Stakeholders’ Preferences

Abstract

One of the benefits of implementing transportation infrastructure projects is the maximization of network accessibility performance, so that system users’ mobility is optimized. However, infrastructure investment decisions rarely consider stakeholders’ preferences to network performance measures and the impact of project selection and prioritization on the network accessibility performance. This paper presents a goal programming framework that considers network accessibility performance and the total cost of road infrastructure projects or project bundles to prioritize investments, taking into account stakeholders’ preferences to the performance criteria. Results of the case study using the low-volume road (LVR) network showed that the accessibility benefits of LVR projects depend on their relative spatial location in the network, their total project cost, target performance goals, and stakeholders’ preferences to performance criteria. The study results also showed that LVR projects could maximize network accessibility even after the occurrence of network disruption events. Therefore, the proposed framework could help the decision-makers develop efficient infrastructure investment plans to mitigate natural and human-made network disruption events.

One of the benefits of implementing transportation infrastructure projects is the maximization of network accessibility performance, so that system users’ mobility is optimized. However, infrastructure investment decisions rarely consider the impact of project selection and prioritization on the network accessibility performance and the contribution of each network element (such as a node or a link) to the network’s accessibility performance ( 1 – 3 ). In most cases, transportation investment decisions focus on solving corridor-level transportation problems such as traffic congestion, air pollution, or travel time reduction ( 1 , 2 ). However, corridor-level decisions may adversely affect network accessibility performance. For example, corridor-level infrastructure investment decisions may not consider each road section’s contributions in avoiding or minimizing the negative impacts of network disruptions that may be caused by natural or human-made disasters such as floods, earthquakes, and so forth. A single road section’s contribution during those disruption events may even be very significant in cases of sparse networks, such as rural and low-volume roads (LVRs), that do not have a higher level of connectivity between road links.

Various evaluation criteria were used in the past to make investment decisions for proposed projects or evaluate past projects. These evaluation criteria include travel time, vehicle operating cost (VOC), safety, and economic efficiency ( 4 – 12 ). Other criteria were employed to assess transportation projects’ impacts on land use, the social and biological environments, economic development, asset resilience, aesthetics, air quality, water resources, and noise ( 6 , 13 – 21 ).

Road project investments may bring change in accessibility and therefore mobility of road users in the network ( 22 ). Therefore, prioritization of road projects should be conducted systematically to understand how those implemented projects could affect the network accessibility performance. The policy associated with project prioritization methodology should also incorporate all the stakeholders’ preferences to equitably distribute the costs and benefits related to network accessibility among the stakeholders.

A single roadway link could be very critical for an LVR network accessibility performance. Therefore, the LVR project prioritization process needs to incorporate each LVR project’s contribution to network accessibility. From an equity perspective, all the costs and benefits of infrastructure projects should be shared among all transportation stakeholders (such as road users, businesses, and communities). These days, human-made and natural events that cause network disruptions (and therefore, reduction in network accessibility) are becoming very common worldwide. Therefore, consideration of network accessibility in the LVR project prioritization process is essential to mitigate the adverse impacts of network disruptions such as traffic congestions, traffic accidents, and evacuation-related problems after network disruptions. The motivation of this study is to develop a project prioritization framework that helps local transportation agencies prioritize LVR projects, considering project cost and preferences of transportation stakeholders to network performance measures. The study specifically addresses the following investment planning problems: How can local transportation agencies prioritize LVR projects to improve network accessibility considering project cost requirements and all transportation stakeholders’ preferences to network performance measures? How can investment decision-makers plan to improve or maintain their LVR network accessibility in areas where network disruptions events (such as earthquake or flooding) are prevalent?

The remainder of this paper is organized as follows. First, the problem statement and objectives of the paper are presented. Then, a literature review is provided, followed by a description of the proposed methodology. Then, the results of a case study are presented. Finally, the summary and conclusions of the study are provided.

Problem Statement and Objectives of the Paper

Transportation infrastructure investment can help improve network accessibility ( 23 ). Therefore, investment decisions may require input on accessibility performance of a network to design a completely new network at the planning stage; evaluate the contribution of a road link on the overall accessibility performance of the road network; decide on implementing a proposed link that connects two nodes in the network and significantly maximizes network accessibility; or incorporate accessibility performance in a multi-criteria evaluation framework that also considers other performance criteria ( 24 – 27 ). These investment decision criteria do not directly assess the impacts of projects on network accessibility, considering project cost and performance goals specified by decision-makers. Various definitions of LVRs exist in the literature. Faiz defines LVRs as having a maximum average daily traffic (ADT) of 1,000 vehicles per day (vpd) ( 28 ). The Federal Highway Administration (FHWA) defines LVRs as roads with annual average daily traffic (AADT) less than 400 ( 29 ). LVRs generally serve daily traffic volume that is fewer than 400 vehicles ( 30 ). Regardless of this definition, the accessibility performance of LVRs is very significant as they account for about 69% of road miles in the United States (U.S.) ( 31 ). LVRs generally serve daily traffic volume that is fewer than 400 vehicles ( 30 ). Since LVR networks operate under capacity under normal conditions, LVR projects may not necessarily be prioritized and implemented based on system performance as measured by traffic congestion ( 32 ).

This paper’s main objective is to present a general framework that could be used by investment decision-makers and transportation planners to appraise LVR projects and policies and prioritize LVR investments considering network accessibility and project cost requirements as one of the performance measures. The proposed methodology is applicable to LVR networks. It is useful to prioritize LVR projects under normal performance conditions and when the LVR projects are subjected to network disruption scenarios caused by natural or human-made events. Consideration of road disruptions in investment decisions is especially essential more than ever as road network interruptions caused by natural disasters are becoming very common in many parts of the world ( 33 , 34 ). An experimental case study is presented to demonstrate how agencies can apply the framework to assess the contribution of LVR projects in maximizing network accessibility for desired performance goals considering normal operating conditions and network disruptions caused by natural or human-made disasters. This research’s contribution is significant because it provides a framework for investment decision-makers to incorporate accessibility- and non-accessibility-related performance measures. The non-accessibility performance measures can be incorporated in the framework because the framework includes a value function method that allows conversion of all performance measure values into the same scale of measurement. The study also enables the investment decision-makers to consider system users’ preferences to the performance measures in prioritizing transportation infrastructure projects.

Literature Review

Transportation investment decisions are often made, mostly focusing on specific corridors without considering the relationship between the road corridors and the overall transportation network. Gurganus and Gharaibeh used visual distress, traffic volume, and pavement condition as project prioritization criteria ( 2 ). The project selection process did not consider the impact of projects on network accessibility. Some road sections may be relatively more important than others to keep the network accessibility at a higher level in cases of disruptions because of human-made or natural disasters. Chandran et al. used pavement condition index (PCI) and pavement condition rating to prioritize transportation projects ( 35 ). PCI is based on an assessment of the severity and extent level of each pavement distress type. The pavement condition rating technique is based on the overall visual pavement condition assessment. These techniques only focus on each pavement section’s condition and, therefore, may not take into account the importance of each pavement section for the overall network accessibility performance. Gokey et al. developed a methodology considering factors such as bridge, traffic, and detour length without explicitly considering the impacts of the bridge projects on network accessibility ( 3 ). Guerre and Evans reported that an approach that considers various measures of effectiveness (MOE) was used to prioritize infrastructure investments ( 36 ). The MOEs include percent of pavement or bridge in good or fair condition, vehicle miles traveled, and fatalities per 100 million vehicle miles traveled. They did not consider the significance of a bridge or a pavement section for the network-level accessibility performance.

Sinha and Labi recommended that infrastructure project prioritization should include, among other criteria, the mobility of system users and the accessibility of the transportation network ( 37 ). Still, they did not provide a detailed framework for measuring network accessibility performance. The World Bank suggests that project selection processes should consider the projects’ impact at the local level. The agency also suggests that the selection processes evaluate how the project could improve average passenger travel time, average VOC, and the number of annual vehicle-related fatalities on the project locations ( 19 ). The World Bank uses an index referred to as rural accessibility index (RAI) ( 28 ). The RAI measures the proportion of rural communities that live within 2 km (which translates into 20–25 min of walking) from an all-season road to help transport aid decisions in Sub-Saharan Africa and other developing countries. The index could be expanded to cover investment decisions over the entire transportation network, both urban and rural. The contribution of an infrastructure project to network accessibility should be considered during prioritization because, as Chacon-Hurtado et al. showed, transportation accessibility plays a vital role in regional economic resilience ( 38 ). Accessibility improvements are positively related to regional economic development ( 39 ). Besides, the incorporation of network accessibility in transportation investment plans helps address equity issues in transportation planning. A study showed that transportation system users prefer not only accessibility but also spatial equality related to the degree of accessibility ( 40 ).

Existing literature shows that various transportation network performance measures have been proposed. Sullivan et al. developed a network-level performance measure, called network trip robustness, that could be used to compare different networks ( 24 ). However, the developed performance measure does not allow decision-makers to incorporate its degree of importance to all stakeholders in the system. Forkenbrock and Weisbrod provided network accessibility measures and detailed steps for network-level and local-level accessibility measurements ( 6 ). Still, they did not incorporate steps on how to incorporate stakeholders’ preferences to proposed infrastructure projects. Cambridge Systematics, and Sinha and Labi provided average travel time between origin and destinations and average trip length as accessibility performance measures for passenger and freight travel ( 37 , 41 ). Travel time was mentioned as a measure of the level of satisfaction by the Organization for Economic Cooperation and Development (OECD) ( 42 ). Travel time and hours of congestion delay are mentioned by Karlaftis and Kepaptsoglou as topological performance measures ( 43 ). Novak et al. have developed and demonstrated a network-level performance metric called the network trip robustness (NTR), which takes into account the network-level travel time and the total number of trips between all origins and destinations in the network ( 25 ). Sullivan et al. developed an index called the network robustness index (NRI) and used network-wide travel time as a performance measure ( 24 ). Scott et al. evaluated a highway section’s impact on the change in network-level travel-time using NRI ( 44 ). Reynaud et al. expanded the NRI developed by Scott et al. and proposed the greenhouse gas emission-based NRI instead of congestion to evaluate link criticality in the transportation network ( 44 , 45 ). Dehghani et al. developed a conditioned vulnerability assessment framework for a roadway system that considers network-level travel time, travel cost, and congestion level as performance measures ( 46 ). Bell considered the cost of traversing a link in the network as a performance measure ( 47 ). All these developed performance measures and evaluation frameworks do not allow decision-makers to incorporate stakeholders’ preferences in the investment decision-making process.

By using a goal programming (GP) framework proposed in this paper, not only can decision-makers include various performance measures in the decision-making process, but they also can incorporate stakeholders’ preferences to the performance measures. Transportation stakeholders are entities that affect or are affected by transportation investment decisions. Therefore, the impact of investment decisions should incorporate the stakeholders’ preferences in the LVR project selection process. The stakeholders’ preferences are indicated by the weight the stakeholders provide to various network performance measures that are considered by investment decision-makers to improve the LVR network performance. For example, as a stakeholder of the transportation system, a road user may provide higher preference (i.e., weight) for travel time reduction in the network. On the other hand, communities living inside the network location may give more weight to safety than travel time. Furthermore, a local agency may want to implement its network performance improvement plan by reducing travel time by 10% and maximizing safety by reducing the number of accidents in the network by 5% by implementing one of several proposed LVR projects. The local agency will have full information about the percent reductions of network-level travel time and the number of accidents that each project would provide if implemented. Then, the stakeholders’ preferences to the performance measures will affect which proposed LVR project is the closest to the target performance set by the local agency. The GP framework will help identify the best LVR project that should be selected to achieve the target goal.

Methodology

The study methodology is given in Figure 1. The first step in the analysis procedure is the delineation of the study area in which investment decision-makers plan to implement LVR projects. The study area should be the jurisdiction on which decision-makers can make infrastructure investment decisions. Then, the LVR network in the study area is developed, that is, the network topology is established, and each node and link in the network is labeled for easy identification purposes. The nodes could represent road intersections, rural cities, and so forth, in the LVR network. Besides, the cost of traversing each road link is determined using appropriate parameters such as link length or link travel time. Then, candidate LVR projects that compete with each other for implementation are identified. All possible single projects and project bundles should be considered because it is unclear which project could provide superior network performance because of the cost and spatial variations that can affect the LVR network performance. The costs of implementing the candidate projects are then determined to be used as one of the project performance criteria in the GP methodology. Next, the network accessibility performance measure is developed. Then, a suitable network accessibility measure is developed in the GP methodology. The decision-makers should establish a network performance goal based on the desired level of network performance improvement related to given infrastructure investment. A GP methodology is then applied considering the various project alternatives, performance criteria, and performance goals to select the best LVR project.

Figure 1.

General methodology.

Network Accessibility Measure

Accessibility has been defined and used in various ways. Some of the definitions of accessibility include “the potential of opportunities for interactions,”“the ease with which a land-use activity can be reached from a location using a particular transport system,”“the freedom of individuals to decide whether or not to participate in different activities,” and “the benefits provided by a transportation/land-use system” ( 48 ). Accessibility is also defined as the ease with which one can reach their destination ( 49 , 50 ). Various accessibility measures are useful for addressing different accessibility-related problems, as it is impossible to derive a single accessibility measure that best fits all situations ( 51 , 52 ).

From the perspective of transportation, accessibility measures are often implemented considering the distance traveled or the time it takes to reach destinations ( 53 ). LVRs are roads with daily traffic volume of fewer than 400 vehicles ( 30 ). Thus, LVR projects may not necessarily be prioritized and implemented based on system performance as measured by traffic congestion since the LVR networks operate under capacity under normal conditions. In this study, network-level travel time is therefore used as a measure of network accessibility for the LVR network. The network accessibility metric is given by

NA = {(\sum_{i = 1}^{n} \sum_{j = 1}^{n} t_{ij})}^{- 1}

(1)

where NA = network accessibility; t_ij = travel time between nodes i and j in the network. Equation 1 is used to determine the network accessibility performance of the base LVR network and the LVR network with the implementation of single or bundle LVR projects.

The Goal Programming (GP) Approach

GP is a mathematical programming method that is very useful to solve problems considering multiple performance criteria ( 37 ). Equation 2 shows the GP formula.

Z = {[\sum_{j = 1}^{J} {[w_{j}^{*} | G_{j} - V_{j} (A_{i j}) |]}^{p}]}^{1 / p}

(2)

where Z = the sum of deviations from the desired performance goal; $V_{j} (A_{ij})$ = the value function of alternative i corresponding to goal j; $G_{j}$ = the target or goal j; $w_{j}^{*}$ = the relative weight of goal j; and p = parameter that defines the type of distance metrics and could attain different values. For example, p = 1 represents a city block distance that indicates the distance between two points where the path is along the lines connecting the origin and destination points by traversing in a block system in a city where it is impossible to have a straight-line connection between the two points. On the other hand, p = 2 represents Euclidean distance (also called Manhattan distance), the shortest straight-line distance between the two points ( 37 ). In the context of this study, p = 2 is used since the aim is to find an alternative whose overall performance is close to target performance. So, in this study, Euclidean distance is used, as it is more relevant to the distance-minimization problem.

Transportation planners and investment decision-makers often specify target performance goals based on agency policies to improve road network performance. For example, a transportation agency may plan to allocate a $1.5 million budget to an LVR project to achieve a 5% increase in network accessibility. A decision-maker should provide a relative weight and the desired performance goal for each performance criterion to utilize the GP method. The value functions help transportation decision-makers to represent all performance criteria on the same scale of measurement. For instance, one of the performance criteria could be accident reduction in relation to average fatalities per 1,000 mi traveled, and the other could be travel time reduction in minutes. These performance criteria’ values should be converted to the same scale of measurement to apply the GP approach. The objective is to minimize Z, which represents the weighted deviation from the performance goals.

In this study, project cost and network accessibility are used as performance criteria. The GP methodology is then applied to select the best LVR project that provides performance outcomes equal or close to performance goals specified by road infrastructure investment decision-makers.

Illustration of the Goal Programming (GP) Procedure

Consider an example LVR network. It is assumed that three new link construction projects, named A-1, A-2, and A-3, are considered for implementation. The three projects are compared in relation to three performance criteria named p-1, p-2, and p-3, which have different measurement units, and the best alternative is selected based on the three performance criteria. Table 1 provides the data for the three alternatives. Since the performance criteria have different measurement units, it is essential to use a common scale of measurement so that the performance criteria can be used in the GP framework. One of the techniques to convert values of the performance criteria into the same scale of measurement is to use a value function approach, in which the maximum value of a given performance criterion is taken as 1, and the minimum as 0, with the other function values determined considering interpolation techniques between the maximum and minimum values. In this paper, a linear interpolation technique is used to find function values between the minimum and maximum performance criterion values. For example, considering p-1, a value of 1 is provided for alternative A-1 because it has the highest p-1 value among all alternatives, and a value of 0 is given for alternative A-3 as it has the lowest p-1 value. In this example, it is assumed that higher values of p-1 and p-2, and lower values of p-3 are favorable. Then, by considering a linear relationship, it is possible to get a p-1 value of 0.333 for alternative A-2. Using a similar procedure, it is possible to determine all values for each performance criterion associated with each alternative. Table 2 provides value functions and their results. In Table 2, V_p–i(x) = y implies that y is the function value for the performance value of x associated with the performance criterion i. The function value, V_p–i(x), is computed for each performance criterion associated with each alternative. For the performance criterion p-3 in Table 2, the lower function value is preferred.

Table 1.

Goal Programming Example Data

		Alternatives
Performance criteria	User-defined weight	A-1	A-2	A-3
p-1	0.3	45	35	30
p-2	0.3	1.1	1.4	1.8
P-3	0.2	1.4	1.3	1.2

Note: p-i = performance criterion i; A-i = alternative i.

Table 2.

Value Function Estimation

Performance criteria	Value functions for alternatives
	A-1	A-2	A-3
p-1	V_p-1(45) = 1	V_p-1(35) = 0.333	V_p-1(30) = 0
p-2	V _p-2(1.1) = 0	V_p-2(1.4) = 0.429	V_p-2(1.8) = 1
p-3	V_p-3(1.4) = 0	V_p-3(1.3) = 0.500	V_p-3(1.2) = 1

Note: V_p-i(x) = y implies that the function value for the performance measure value of x associated with the performance criterion i is y. A-1 = alternative 1; A-2 = alternative 2; A-3 = alternative 3.

Figure 2 provides the three-dimensional (3-D) representation of the the three alternatives’ spatial location relative to a target performance goal set by road investment decision-makers such as state departments of transportation (DOTs). Figure 3 presents in 3-D form the spatial locations of the three alternatives’ value functions relative to the value function of the target performance goal. Figure 4 provides a comparison of the z-value of the three alternatives. As shown in Figure 4, alternative 2 has the least z-value (i.e., 0.17) followed by alternative 3 (with z-value of 0.25) and alternative 4 (with z-value of 0.55), respectively. Since the z-value measures the distance from the performance goal, alternative 2 should be selected for implementation because of its lowest z-value compared with the other two alternatives.

Figure 2.

A 3-D representation of spatial locations of investment alternatives.

Figure 3.

A 3-D representation of spatial locations of value functions.

Figure 4.

Comparison of alternatives based on their z-values.

Case Study

A case study was conducted to demonstrate the developed framework using an LVR network example. The LVR network example shown in Figure 5 consists of 17 nodes and 24 links ( 54 ). The nodes may represent intersections, rural cities, distribution centers, and so forth, in the LVR network. The numbers along each link represent the impedance of the link, measured by travel time in hours. The dotted lines in Figure 5 represent candidate LVR Projects A, B, C, and D, which, if implemented, will have travel times (in hours) of 0.7, 1.4, 0.6, and 1.9, respectively.

Figure 5.

Case study network ( 54 ).

Performance Criteria

In this study, the performance of an LVR network was measured by two main performance criteria: (1) network accessibility, and (2) project cost. Three scenarios which differ in average weights for accessibility (W_acc) and project cost (W_cost) performance measures were considered: Scenario 1: W_acc = 0.4 and W_cost = 0.6; Scenario 2: W_acc= W_cost = 0.5; and Scenario 3: W_acc = 0.6 and W_cost = 0.4. The two performance criteria’ desired performance goals are specified by transportation planners and investment decision-makers considering transportation policies set for their districts. For example, a transportation agency may establish a goal of investing $3 million on a single or multiple LVR project and reducing the network-level travel time by 10%. In short, the desired goal is to invest $3 million and reduce the network-level travel time by 10%. This desired goal is used in the GP framework to select the best single or bundle LVR projects that provide performances that are the same as or close to the desired performance goal.

Project Cost

Transportation costs are generally categorized as agency costs, user costs, and community costs considering the incurring party. Agency costs include capital costs, facility operating costs, and preservation costs incurred by a transportation agency such as state DOTs. The agency cost could also include life-cycle costs, such as annual maintenance expenditures ( 55 ). User costs refer to the operator’s usage costs, including fees associated with facility usage, VOCs, delay and travel time costs, and safety cost. Community costs refer to expenses incurred by communities residing in the road network and include costs associated with air pollution, noise pollution, and other environmental factors ( 37 ). Whenever data are available, it is beneficial to include all types of factors associated with implementing a road project and their related costs to evaluate the network accessibility performance more accurately.

Cost Scenarios and Simultaneous Implementation of Low-Volume Road (LVR) Projects

The developed methodology is demonstrated by considering the total project cost assumed to vary from $1.2 million per mile per lane to $1.8 million per mile per lane, with increments of $ 0.2 million per mile per lane. These cost scenarios represent cost variations that exist in real-world applications because of differences in highway classes that affect pavement design requirements, spatial locations, and so forth ( 56 ).

When two or more LVR projects are considered for simultaneous implementation, the study framework provided in Figure 1 may provide different combinations of projects. Therefore, it is not clear which combination of projects minimizes the deviation from the target performance goal because the network accessibility contribution of each LVR project is dependent on the relative spatial location of the project in the network. Therefore, it is imperative to conduct a thorough analysis considering each possible combination of LVR projects. For example, for the given four LVR candidate projects (namely, projects A, B, C, and D) in Figure 5, $11$ combinations of multiple projects should be considered, that is, six 2-project bundles (AB, AC, AD, BC, BD, CD), four 3-project bundles (ABC, ABD, ACD, BCD), and one 4-project bundle (ABCD). For each of these project bundles, all cost combination scenarios should be evaluated. The spatial locations of these LVR project bundles are shown in Figure 5.

Holistic Approach in Cost Estimation

In this framework, the cost requirements for two or more LVR projects are assumed to be equal to the sum of the individual projects’ cost requirement due to the unavailability of sufficient data. This assumption may not hold in real-world situations, because the simultaneous implementation of two or more projects is likely to be less expensive than the sum of individual projects’ costs because of existing economies of scale in implementing multiple projects simultaneously. This cost reduction in implementing multiple projects depends on the projects’ spatial locations in the LVR network, which may affect the construction duration and material, human, and equipment resource allocation and utilization. Therefore, whenever those relevant data are available, it is beneficial to consider them in this framework.

Estimation of Value Functions

Table 3 provides the results of estimating value functions for each LVR network. The unit for accessibility performance criterion is hours, and that of the project cost is million dollars per mile per lane. The value functions were estimated considering a linear function between the highest and lowest values associated with each performance measure. The value functions of the accessibility performance measure were determined by first ordering the accessibility values of the networks from the lowest to the highest; the lowest value belongs to the BN, (which is 29.92 h) and the highest value (which is 28.24 h) obtained from network BN + AD, as shown in Table 3. The value function of the BN for the accessibility performance measure, V_acc(29.92), is considered zero because higher network level travel time is not desired. The value function of network BN + AD, V_acc(28.24), is regarded as 1 as this LVR network has the lowest network-level travel time. All other networks’ value functions are estimated considering a linear relationship between the accessibility values and the estimated value functions. For example, the value function of network BN + ACD was estimated considering a linear relationship between the accessibility value and value function of the BN (which are 29.92 and 0, respectively) and the accessibility value of the network BN + AD, which is 28.24.

Table 3.

Value Function Estimation

	Value functions
Performance criteria	Base network (BN)	BN + A	BN + B	BN + C
Accessibility	V_acc(29.92) = 0	V_acc(29.48) = 0.149	V_acc(29.91) = 0.003	V_acc(29.20) = 0.244
Project cost	V_cost(0) = 1.000	V_cost(1.2) = 0.500	V_cost(1.2) = 0.500	V_cost(1.2) = 0.500
Performance criteria	BN + D	BN + AB	BN + AC	BN + AD
Accessibility	V_acc(28.66) = 0.427	V_acc(29.48) = 0.149	V_acc(29.03) = 0.302	V_acc(28.24) = 1.000
Project cost	V_cost(1.2) = 0.500	V_cost(2.4) = 0.333	V_cost(2.4) = 0.333	V_cost(2.4) = 0.333
Performance criteria	BN + BC	BN + BD	BN + CD	BN + ABC
Accessibility	V_acc(29.20) = 0.244	V_acc(28.61) = 0.444	V_acc(27.94) = 0.671	V_acc(28.76) = 0.393
Project cost	V_cost(2.4) = 0.333	V_cost(2.4) = 0.333	V_cost(2.4) = 0.333	V_cost(3.6) = 0.250
Performance criteria	BN + ABD	BN + ACD	BN + BCD	BN + ABCD
Accessibility	V_acc(28.17) = 0.593	V_acc(27.63) = 1.363	V_acc(27.92) = 0.678	V_acc(27.63) = 0.776
Project cost	V_cost(3.6) = 0.250	V_cost(3.6) = 0.250	V_cost(3.6) = 0.250	V_cost(4.8) = 0

Note: BN + XY represents a base network with the implementation of projects X and Y. For example, BN + A = base network with the implementation of project A; BN + AB = base network with the implementation of projects A and B. V_acc(x) = z implies that the function of the accessibility performance measure with x accessibility value is equal to z.

Results and Discussion

The network accessibility values of all LVR networks were determined using Equation 1. The percent change in network accessibility because of an LVR project was calculated using Equation 3.

{PNA}_{x} = (\frac{N A_{BN} - N A_{x}}{N A_{BN}}) X 100

(3)

where ${PNA}_{x} =$ percent change in network accessibility because of an LVR project x; $N A_{BN} =$ network accessibility of the BN; $N A_{x} =$ network accessibility of the network with LVR project x implemented.

Figure 6 shows the percent change in network accessibility (relative to the BN) because of the implementation of LVR projects considered in this case study. It is shown that the BN + ACD network has the highest percent change in network accessibility (i.e., reduction in network-level travel time) compared with the BN. On the other hand, the BN + B network has the lowest percent change in network accessibility (about 0.03%) relative to the BN. The figure also shows that the percent change in network accessibility is independent of the project cost requirement. For example, for the BN + AD network, the percent change in network accessibility was 5.61% for all costs considered (i.e., $2.4 million through $3.6 million). This result is expected because the network accessibility does not depend on the allocated budget to the given project but on the relative spatial location of LVR projects in the network. The BN + ACD and BN + ABCD networks have brought the same percent reduction in network accessibility (i.e., 7.65%) relative to the BN. The percent increase in network accessibility for the BN + D network is 4.21, whereas that for the BN + AC network is 2.97. These results indicate that the implementation of many LVR projects may not guarantee an improvement in the network accessibility performance. Figure 6 also shows that for the same project cost, different projects may bring different percent increase in network accessibility. For example, the LVR project A can improve the percent increase in network accessibility by about 1.4% (i.e., 1.47–0.03) relative to the LVR project B. These results suggest that investment decision-makers should consider both the cost requirement and the improvement that investment brings to the network accessibility performance. The percent increase in network accessibility for the BN + BCD network is 6.68%. This value is higher than the percentage increase in network accessibility for each LVR network BN + B, BN + C, or BN + D. These results indicate that it is beneficial to conduct a thorough scenario analysis of each LVR project before selecting candidate LVR projects for implementation. Multiple parameters, such as project cost and spatial distribution of the LVR projects in the network, should be simultaneously considered to maximize network accessibility by investing in less-expensive LVR projects.

Figure 6.

Accessibility versus project cost for all low-volume road (LVR) networks.

Goal Programming (GP) Results

Figure 7 shows GP results considering three scenarios associated with stakeholders’ preferences to accessibility and project cost performance measures. When the weight of network accessibility (W_acc) is 0.4, and that of the project cost (W_cost) is 0.6, the LVR network BN + BD is the best choice with a z-value of 0.036. When equal weights for network accessibility and projects were assumed, the network BN + BD is the best choice, with a z-value of 0.038. When W_acc = 0.6 and W_cost = 0.4, the LVR network BN + BD is still the best choice with a z-value of 0.041. Even though the LVR network BN + BD is the best choice in all the three cases, the z-value is different in each case. This result shows that stakeholders’ and decision-makers’ preferences to performance measures determine the selection of LVR projects. Also, the result indicates the importance of incorporating all stakeholders’ choices in the project prioritization process as the z-value may vary based on the degree of preferences of the stakeholders to performance measures. Figure 7 shows that the implementation of multiple LVR projects does not necessarily reduce the z-values compared with implementing single LVR projects. For example, the BN + ACD network with bundle LVR project A, C, and D has higher z-value (i.e., the lower percent increase in network accessibility) than BN + A, BN + B, and BN + D networks with single LVR project A, B, and D, respectively, in all weight scenario cases.

Figure 7.

Comparison of z-values of low-volume road (LVR) networks for various weights of performance measures.

General Comments on the Goal Programming (GP) Approach

The GP approach used in this paper allows consideration of any number of performance criteria and stakeholders. However, it requires all performance criteria to have the same scale of measurement. Therefore, an assumption should be made in relation to the interpolation technique used in a selected value function, affecting the project prioritization results. Besides, the GP results can be significantly affected by the weight provided to each performance criterion by stakeholders and decision-makers. Therefore, investment decision-making using the GP approach requires clear communication with all stakeholders in relation to what each performance criterion means and how it affects them to collect representative stakeholders’ preference data. Otherwise, the GP results may lead to the selection of investment alternative that causes inefficiency, that is, an increase in agency and user costs. Also, the preference data that do not adequately represent stakeholders’ preferences can lead to implementing an investment alternative that does not address the equity issues, that is, the unfair distribution of project benefits and costs among the stakeholders. In the GP approach, for n number of performance criteria, n number of dimensional spaces are needed to visualize each investment alternative’s spatial location relative to the target performance goal. Therefore, when the number of performance criteria considered in the GP framework is more than three (i.e., n > 3), it will be impossible to visualize the spatial locations of the alternatives and the target performance goal in the n-dimensional space.

Application of the Methodology in Network Disruption Cases

A Monte Carlo simulation program was written in Python to simulate network disruption events (such as flooding, earthquake, etc.) and identify network links or nodes that are likely to be affected by the network disruption event ( 57 ). The GP framework was then applied to demonstrate the impact of network disruption events on project prioritization.

Three networks were subjected to network disruption events (Table 4). These networks are: (1) Base LVR network + Project AD26 (BN + AD26); (2) Base LVR network + Project ACD42 (BN + ACD42); and (3) Base LVR network + Project ABCD60 (BN + ABCD60). Each LVR network was subjected to three disruptive scenarios: (1) scenario 1—simultaneous disruption of two links; (2) scenario 2—simultaneous disruption of four links; and (3) scenario 3—simultaneous disruption of six links. Each disruptive scenario was simulated for 10⁷ cycles, and links that were disrupted the most in the 10⁷ cycles were considered disrupted links. For example, the six LVR links that were simultaneously disrupted the most (115 times during the 10⁷ cycles) in scenario 3 of the BN were links 1–2, 16–17, 2–5, 3–6, 7–8, 8–13.

Table 4.

Network Disruption Simulation Results

	Disrupted links (10⁷ simulation cycles)
Network	Scenario 1 (2-links disruption)	Scenario 2 (4-links disruption)	Scenario 3 (6-links disruption)
BN + AD26	13–15, 15–17	11–12, 15–17, 2–3, 7–16	12–14, 15–17, 4–5, 7–8, 8–13, 9–11
BN + ACD42	10–12, 4–7	1–2, 13–16, 5–6, 9–11	11–13, 15–17, 2–3, 5–6A, 5–8, 8–13
BN + ABCD60	13–15, 9–10	11–12, 12–14, 14–15, 6–9	11–12, 11–13, 14–15, 6–9, 8–13, 9–11

Note: BN + XY12 = base network with the implementation of projects X and Y and a total project cost of $1.2 million.

It is assumed that transportation planners and road infrastructure investment decision-makers will have network disruption simulation results and therefore have prior information about areas of the network affected by the disruptive event. This assumption is reasonable because such information could be available from computer simulation models and GIS maps that help predict affected areas, roadway links, or nodes because of natural events such as flooding, storms, and so forth. For example, the U.S. Federal Emergency Management Agency (FEMA) provides an interactive flood map that could be used to identify road network elements that are likely to be affected by flooding in a U.S. district, city, or county ( 58 ).

Figure 8 shows disruption scenarios for the BN + AD26 and BN + ABCD60 networks and the no-disruption scenario of the BN. As shown in the figure, as the number of disrupted links increases, the percent decrease in network accessibility will be higher. For example, the 4-link disruption event of the BN + AD26 network (when the LVR projects A and D with a total of 2.6 million dollars are implemented) caused a 0.18% decrease in the network accessibility. The 6-link disruption event caused a 0.3% decrease in the network accessibility compared with network accessibility of the no-disruption case of the BN. For the case of the BN + ABCD60 network (when the LVR projects A, B, C, and D with a total 6 million dollars are implemented), the 6-link disruption scenario has the highest percentage decrease in the network accessibility when compared with the 4-link, the 2-link, and the BN (with no disruption). However, after the 2-link disruption, the network accessibility increased by 0.03% compared with the no-disruption case of the BN. This result indicates that the number of disrupted links is not the only factor in determining the change in network accessibility, but also the spatial location of an LVR project in the network. The increase in network accessibility after the disruption event is attributed to the implementation of the LVR projects. This type of information is beneficial to analyze how the spatial locations of LVR projects could affect the degree of network accessibility. This information could also be used to identify road links that could play a significant role during natural or human-made network disruption events.

Figure 8.

Percent change in network accessibility considering link disruption scenarios.

Figure 9 shows a comparison of the z-value of BN + AD26, BN + ACD42, and BN + ABCD60 networks based on the goal of improving the network travel time by 10% by allocating a $6 million budget and considering a 2-link disruption scenario, and 0.6 and 0.4 average weights for accessibility and project cost performance measures, respectively. As shown in the figure, the BN + ABCD60 network is the best alternative, with the lowest z-value of 0.13. This result indicates that, when 2-link disruptions because of human-made or natural events are expected, all the LVR projects (i.e., A, B, C, and D) should be implemented. The z-value of the BN + AD26 network (with the implementation of projects A and D) is lower than that of the BN + ACD42 network (with the implementation of projects A, C, and D), implying that implementing a higher number of LVR projects may not guarantee the achievement of the goal established by decision-makers.

Figure 9.

Comparison of low-volume road (LVR) networks subjected to 2-link disruption events.

Summary and Conclusions

In this study, a GP framework was proposed for the prioritization of LVR projects. The research results showed that the selection of the best LVR projects depends on their relative spatial location in the network and their total project cost, as well as the target performance goal set by a decision-maker. Therefore, it is very beneficial to employ a suitable methodology such as a GP procedure to select the best LVR project.

The GP framework used in this study is beneficial for investment decision-makers to incorporate stakeholders’ preferences for various performance criteria. Also, the framework allows the decision-makers to incorporate their desired goals for each considered performance criterion. The framework then enables the decision-makers to select the best LVR project that best satisfies the decision-makers’ performance goals.

The framework was demonstrated using LVR networks subjected to network disruption events and considering various network disruption scenarios. The study results showed that LVR projects could maximize network accessibility even after the occurrence of network disruption events. Thus, investment decision-makers could utilize the proposed framework to conduct network disruption scenario analysis and select the best candidate LVR projects, especially in areas where network disruption events (such as flooding and earthquake) are prevalent. Therefore, the proposed framework could help the decision-makers to develop efficient future infrastructure investment plans to mitigate those natural and human-made network disruption events.

The proposed GP framework could consider the impact of LVR project types (such as asphalt concrete, cement concrete, and their variations) on noise-related community cost. The consideration of different LVR project types in relation to their pavement types is useful because the noise levels on different pavement types are known to vary ( 59 , 60 ). The framework could also include other project evaluation criteria such as environmental impacts (e.g., air pollution), economic development impacts, land-use impacts, and so forth. Roadway projects should be evaluated not only for their post-construction effects but also for their during-implementation effects ( 61 ). Therefore, the proposed framework could be useful at any stage of LVR network improvement for appraisal of LVR projects.

Footnotes

Author Contributions

The author confirms contribution to the paper as follows: study conception and design: W. Woldemariam; data collection: W. Woldemariam; analysis and interpretation of results: W. Woldemariam; draft manuscript preparation: W. Woldemariam. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was financially supported by Purdue University Northwest, Department of Civil and Mechanical Engineering.

Data Accessibility Statement

The simulated data used to support this study’s findings are included within the article, and related data and codes are available from the corresponding author on request.

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