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This study investigates the pavement network maintenance and rehabilitation (M&R) programming problem, over a certain planning horizon and in the context of limited funding. We designed an integer programming model to fulfill three purposes, namely, optimize the road conditions, minimize user disturbance costs, and minimize agency costs. We present a case study in which this model is applied to the pavement network of Shanghai. We investigate the results through the use of five M&R strategies, to identify the Pareto-optimal trade-offs inherent in developing pavement network M&R planning. The results demonstrate that there is a positive relationship between PCI improvement and user disturbance costs and between PCI improvement and agency costs. Additionally, we conduct a comparative analysis between agency and government-oriented strategies to evaluate the effectiveness and equity consideration. The findings suggest that the government-oriented strategy improves the pavement condition effectively with low user disturbance costs, and the agency-oriented strategy accounts for more equity consideration. Finally, we formulate an extension model that considers multiple road types, for application to pavement network M&R programming. The results show that light rehabilitation and preventive maintenance are the most frequently implemented treatments on arterial roads and secondary trunk roads from the case network implementation. This study helps decision-makers identify the trade-offs made when developing a pavement network M&R program.

With the rapid development of Shanghai’s pavement networks, by the end of 2016, the total length of the city’s roads exceeded 13,000 km; this increase has necessarily resulted in a constant increase in tasks related to urban pavement maintenance and management. To improve the effectiveness and efficiency of pavement management strategies, it is necessary to evaluate scientifically the service level of pavement conditions and use such evaluations to develop an efficient road network maintenance management planning system.

Road maintenance decision-making often involves addressing multiple and conflicting objectives and factors, such as road condition performance, maintenance costs, and user disturbance impact. Because funds are limited, decision-makers need to undertake pavement maintenance treatments only on certain sections of the road network, and this parameter increases the challenge inherent in this work.

Therefore, this study looks to help decision-makers develop an optimal pavement network maintenance and rehabilitation (M&R) program over a planning horizon. Multiobjective optimization techniques are often used to create optimal pavement network maintenance programs (i.e., in which pavement sections are maintained at an acceptable service-condition level while incurring low agency costs and not creating significant amounts of user disturbance, environment pollution, or traffic hazard). However, trading off maintenance strategies under such conflicting objectives is difficult, and for each strategy, it requires salient knowledge [

This paper presents a multiobjective pavement network maintenance optimization model that considers three conflicting objectives, namely, the maximization of pavement condition improvement, the minimization of user disturbance costs, and the minimization of agency costs over the planning horizon. The remainder of this paper is organized as follows. Section

Pavement maintenance programming related studies have been a popular research topic. Friesz and Fernandez [

Contributing to the large scale of the road network and the limited M&R funds, the optimization techniques have become very essential to the road network M&R planning. Traditionally, researchers have used single-objective optimization techniques, given the complexity inherent in multiobjective analysis [

Additionally, M&R planning that considers only a single objective will tend to ignore other important objectives, making it difficult to undertake comprehensive analysis. Therefore, in recent decades, several researchers have conducted optimization analysis that involves multiple objectives. For example, Fwa et al. [

The aforementioned literature on multiobjective optimization for pavement network maintenance tends to focus on M&R planning for pavement networks, but principally from the perspective of a department of transportation. In practice, however, other stakeholders are also involved in the decision-making process. For example, government requirements vis-à-vis road conditions and budgetary control influence road agencies’ M&R planning; this means there exists a conflict between the government and the road agency. To the best of our knowledge, a limited body of literature proposes models that consider the conflict of various stakeholders in the decision-making process. He and Sun [

This paper also relates to the literature on “equity” consideration in M&R programming, which considers how M&R funds should be fairly distributed since social equity is the most overlooked element of the decision-making process [

This study makes a threefold contribution to the literature. First, as it considers three conflicting objectives, it uses multiobjective optimization techniques to create solutions at different scales of pavement network M&R planning. Second, it conducts a detailed comparative analysis of various “optimal” solutions, from the perspective of various stakeholders involved in M&R programming development. Third, as only a few studies integrate social equity factors into pavement network M&R planning, this study contributes to the literature by explicitly evaluating and comparing the equity of the outcomes derived from various solutions.

The problem addressed in this study relates to the allocation of limited funds to pavement network M&R programming over a certain planning horizon. Three stakeholders are involved in developing the pavement maintenance program, namely, the government, the agency, and the users. Each decision-maker needs to consider a variety of objectives and factors, and so when creating a maintenance plan for a pavement network in a certain planning period and with limited funding, trade-offs are inevitable. For example, the execution of too many heavy maintenance treatments will effectively improve the road condition, but it will also increase the user disturbance costs. More importantly, funding limitations mean that only a few road sections can be considered for heavy maintenance. The execution of a lower-cost maintenance treatment may reduce both user disturbance costs and agency costs, but it will also lead to poor road conditions—conditions that are perhaps even lower than those dictated by the government—and thus reduce road safety. Therefore, for decision-makers, it is especially important to decide upon a pavement network M&R plan under limited budgets, while considering conflicting objectives that involve a variety of maintenance treatments. This constitutes a multiobjective optimization problem.

In this section, we formulate an integer programming model for the problem. The model is formulated for a pavement network of

Our model considers three main objectives, namely, pavement condition improvements, users disturbance cost, and agency costs. These objective functions are formulated in the following equations, respectively:

Objective 1 focuses on the total pavement network condition improvement over the planning periods. Objective 2 is formulated as the total user disturbance costs for the pavement network throughout the planning horizon. Objective 3 is the total agency costs of all maintenance treatments for the pavement network during the planning horizon.

In this problem, the agency faces a dilemma in determining a balance among three objectives (i.e., the pavement condition score, user disturbance costs, and agency costs). This means the agency needs to minimize the agency costs while meeting the requirement of pavement condition score and concurrently reducing to some extent the user disturbance costs. This constitutes a multiobjective optimization problem, and so the weightage factors (

In this problem, the government’s goal is to maximize the road condition score of pavement network while minimizing the user disturbance costs, subject to funding limitations over the planning horizon. Thus, the objective function (

Constraints (

In this section, we apply the proposed models to a practical problem: developing a pavement network M&R program in Shanghai, China, which features limited funding. In order to validate the proposed model’s feasibility efficiently, it is appropriate to use a mathematical programming solver. Here, the integer programming model is solved by the branch-and-bound algorithm from the CPLEX Optimizer since it can produce the precise results efficiently. The optimization studio provides the NET API, and the solving process of the experiments is implemented based on that API. The mathematical model is coded in C# language with Visual Studio 2015 on a personal computer (Inter Core i7, 3.4 GHz; memory, 8 G).

The model was used with data pertaining to a subset pavement network in Shanghai, China. That network comprises 16 major arterial pavement sections with a total of over 100,000 m^{2} of maintenance area. We adopt a five-year planning time horizon for developing a pavement network M&R program; this is practical and allows for a better evaluation of the trade-offs inherent in various maintenance treatments. Table

Basic information of pavement segments.

Segment | Starting | Ending | Length (m) | Width (m) | PCI | AADT |
---|---|---|---|---|---|---|

1 | Qingchi Road | Jinzhong Road | 190.50 | 11.50 | 86.77 | 15000 |

2 | Qingchi Road | Jinzhong Road | 190.50 | 27.20 | 86.77 | 15000 |

3 | Wuzhong Road | Chengjia Bridge | 901.00 | 9.00 | 75.00 | 15000 |

4 | Wande Road | Luoshan Road | 403.00 | 19.00 | 88.58 | 21000 |

5 | Deping Road | Wande Road | 255.00 | 16.20 | 83.99 | 21000 |

6 | Longju Road | Depin Road | 278.00 | 22.00 | 84.45 | 21000 |

7 | Weifang Road | Pudian Road | 256.00 | 18.90 | 89.70 | 15000 |

8 | Miaopu Road | Juye Road | 229.00 | 29.00 | 52.61 | 15000 |

9 | Xiangyin Road | Jiamusi Road | 683.00 | 21.80 | 74.68 | 15000 |

10 | Jiamusi Road | Songhuajiang Road | 364.00 | 23.70 | 75.00 | 15000 |

11 | Jingjiang Road | Jiaotong Road | 101.00 | 6.00 | 72.26 | 15000 |

12 | LiuYing Road | Taishan Branch Road | 82.50 | 17.70 | 75.00 | 15000 |

13 | Huayin Road | LiuYing Road | 165.50 | 23.10 | 75.00 | 15000 |

14 | Hutai Branch Road | Hutai Road | 352.00 | 31.40 | 71.50 | 15000 |

15 | Xinhu Road | Baojia Bridge | 388.00 | 24.10 | 88.74 | 15000 |

16 | Luochuan Road | Huayin Road | 257.50 | 23.10 | 75.00 | 15000 |

The outcomes of M&R planning are often evaluated in terms of the road condition score improvement, which may be assessed by different overall condition indices such as the Pavement Condition Index (PCI) [

Description and key parameters of each M&R treatment.

M&R treatment | Treatment description | Average unit cost (￥/ | User disturbance unit cost (￥10,000/AADT/ | PCI improvement |
---|---|---|---|---|

DN | No M&R projects applied | 0 | 0 | 0 |

PM | Chip seal; microsurfacing treatments | 20 | 1.34 | 3 |

LR | Thin overlays (2-3 in. thick) | 84 | 2.68 | 15 |

MR | Overlays (3–5 in. thick) | 195 | 4.69 | 25 |

HR | Reconstruction includes thick overlays and milling | 350 | 6.70 | 40 |

Other data used in this study include annual budget, the discount rate, and deterioration-rate parameters. We assume the annual budget for this problem to be 10 million yuan and the annual discount rate to be 5%. Finally, in line with historical data, we assume the parameters of the deterioration rate (

In this section, we define five pavement treatment strategies in response to this problem, to identify the trade-offs made when developing a pavement network M&R program; these strategies are discussed in terms of agency and government perspectives. The first three strategies are extreme options that focus on only one objective; from both the agency and government perspectives, the other two strategies are equal-priority strategies. Table

The description and weightage set of the five strategies.

Strategy number | Strategy objective(s) | Weightage ratios of each strategy |
---|---|---|

1 | Optimal pavement condition improvement | |

2 | Optimal user disturbance costs | |

3 | Optimal agency costs | |

4 | Equal priority (agency perspective) | |

5 | Equal priority (government perspective) |

In this study, we measure the performance of M&R programs in terms of PCI improvement firstly. Figure

Average PCI of each strategy, in each study year.

The comparison results of each strategy are shown by a radar map (Figure

Results of each strategy throughout the planning horizon (16-segment experiment).

In this section, we propose the optimal solution as determined during our experiment. As mentioned, strategies 1–3 involve extreme situations, while strategies 4 and 5 are equal-priority policies that consider multiple objectives and are representative of agency and government strategies, respectively. Here, we compare the results of these two latter strategies to illustrate M&R planning. The best M&R plans under the two strategies in this experiment are illustrated in Figure

Solutions of 16-segment experiment: (a) results of strategy 4; (b) results of strategy 5.

Types of M&R projects in optimal maintenance programs.

In this section, we compare the results of the agency-oriented strategy (i.e., strategy 4) to those of the government-oriented strategy (i.e., strategy 5). In this case, strategy 5 is more effective than strategy 4 in terms of PCI improvement, even as the user costs of these strategies over the entire analysis period are nearly identical. Therefore, in this experiment, strategy 5 emerges as an “effective” strategy.

However, when developing an M&R project plan for a pavement network, effectiveness is not the only standard to evaluate performance: recent studies [

PCI range and standard deviation of PCI (16-segment experiment).

To analyze the relationships among various objectives, we discuss Pareto-optimal solutions and offer two pairs of objectives, namely, PCI improvement versus total user disturbance costs and PCI improvement versus total agency costs. We adopt the weighted sum method to construct the Pareto-optimal frontier [

Pareto-optimal frontier for total user disturbance costs and total PCI improvement.

Pareto-optimal frontier for total agency costs and total PCI improvement.

In this section, we examined a case where a pavement network includes different kinds of pavement, namely, arterial roads, secondary trunk roads, and branch roads. In reality, these different road types have different minimum road condition requirements. Thus, Constraints (

We conducted a large-scale experiment involving 121 segments of road (over 430,000 m^{2} of maintenance area in all), corresponding to an urban road network of Shanghai with 16 arterial roads, 44 secondary trunk roads, and 61 branch roads. For computation reasons, we adopted a five-year planning time horizon. The minimum requirement for the aforementioned road types is 75, 70, and 65, respectively. The annual budget for this experiment was set at 30 million yuan. Other constraints, parameters, and assumptions are identical to those in the 16-segment arterial road experiment.

As Figure

Types of M&R projects in the 121-segment experiment (S4: strategy 4; S5: strategy 5).

In reviewing and comparing the results of different experimental scales (Figure

Comparison of different pavement network scales (S4: strategy 4; S5: strategy 5).

In addition, when we compare the optimal results of the various strategies, we see that, in either the small- or large-scale experiments, strategy 4 has a higher proportion of PM than does strategy 5. However, the frequency of each of LR, MR, and HR in strategy 4 is lower than that in strategy 5, and this implies that strategy 4 is a more “friendly” strategy that employs more PM and less HR over the planning horizon.

In the 121-segment experiment, the PCI range and standard deviation are used to evaluate equity in outcome. Figure

PCI range and standard deviation of PCI (121-segment experiment).

In this paper, we present a comprehensive means of analyzing the trade-offs inherent in developing pavement maintenance plans; our method is based on an integer programming model that is defined to consider three objective functions: the pavement condition improvement objective function, the user disturbance costs objective function, and the agency costs objective function. We apply the proposed model to the case of a pavement network in Shanghai over a five-year planning horizon. Based on the proposed model, we developed five strategies and compared their performance while considering conflicting objectives. Because different decision-makers are involved in such problems, we undertook comparative analysis between agency and government-oriented strategies. Additionally, we explored Pareto-optimal solutions to identify the relationship between two pairs of objectives. Finally, we formulated an extension model to fit a large-scale pavement network that features different kinds of roads.

Our results are as follows. First, the government-oriented strategy ensures effectiveness in road condition improvement and at relatively low user disturbance costs. However, compared to the agency-oriented strategy, the government’s strategy is worse in terms of equity consideration: the agency strategy features a lower road condition differential throughout the pavement network over the planning horizon. The findings from this study provide useful information for decision-makers to choose flexible strategy to achieve specific goals. In addition, in a pavement network that features various road types, light rehabilitation and preventive maintenance are the most frequently implemented treatments on arterial roads and secondary trunk roads, respectively. For branch roads, overall M&R treatments are conducted less frequently over the planning horizon than for the two other road types. Furthermore, based on Pareto-optimal solution analysis, there exists a positive relationship between PCI improvement and user disturbance costs and between PCI improvement and agency costs. Finally, when PCI improvement exceeds a certain value threshold, the user disturbance costs show an obvious acceleration trend; this suggests that decision-makers should take the user disturbance factor into consideration when they plan the execution of a large number of medium or heavy rehabilitation activities, especially for pavement sections that have a high average amount of daily traffic.

Future research can explore multiobjective optimization for pavement network M&R programming while considering the social equity objective function. Additionally, it should be borne in mind that, for a large-scale section of pavement and a long planning horizon, it would be impossible to solve the model by using the CPLEX solver; therefore, one should consider the use of heuristic algorithms, to improve both computational efficiency and solution quality.

The data are drawn from the 2015 pavement technical condition report of Shanghai; please visit

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by the Science and Technology Commission of Shanghai Municipality (no. 18DZ1201204).