The effect of agency budgets on minimizing greenhouse gas emissions from road rehabilitation policies

Transportation agencies are being urged to reduce their greenhouse gas (GHG) emissions. One possible solution within their scope is to alter their pavement management system to include environmental impacts. Managing pavement assets is important because poor road conditions lead to increased fuel consumption of vehicles. Rehabilitation activities improve pavement condition, but require materials and construction equipment, which produce GHG emissions as well. The agency’s role is to decide when to rehabilitate the road segments in the network. In previous work, we sought to minimize total societal costs (user and agency costs combined) subject to an emissions constraint for a road network, and demonstrated that there exists a range of potentially optimal solutions (a Pareto frontier) with tradeoffs between costs and GHG emissions. However, we did not account for the case where the available financial budget to the agency is binding. This letter considers an agency whose main goal is to reduce its carbon footprint while operating under a constrained financial budget. A Lagrangian dual solution methodology is applied, which selects the optimal timing and optimal action from a set of alternatives for each segment. This formulation quantifies GHG emission savings per additional dollar of agency budget spent, which can be used in a cap-and-trade system or to make budget decisions. We discuss the importance of communication between agencies and their legislature that sets the financial budgets to implement sustainable policies. We show that for a case study of Californian roads, it is optimal to apply frequent, thin overlays as opposed to the less frequent, thick overlays recommended in the literature if the objective is to minimize GHG emissions. A promising new technology, warm-mix asphalt, will have a negligible effect on reducing GHG emissions for road resurfacing under constrained budgets.


Introduction
The United States has recently set an ambitious target of reducing greenhouse gas (GHG) emissions by 26%-28% below 2005 levels by 2025 (White House 2014), and similar or longer-term goals are being adopted or discussed worldwide. Significant actions have been taken thus far, such as investing in clean power and setting energy and fuel efficiency standards, but more investments are needed. Reducing GHG emissions will require cooperation and willingness from decisionmakers across all economic sectors, especially those with the largest contributions. The transportation sector accounts for large emissions worldwide; 28% of the total GHG emissions in the United States, most of which comes from the tailpipes of vehicles (EPA 2014). Transportation infrastructure is typically not included in the sector's account, therefore the overall transportation sector's impact is even higher (Chester andHorvath 2009, Revi et al 2014).
In 2014, there were over 4.8 trillion vehicle kilometers traveled (VKT) on 14 million lane kilometers of roads (Census Bureau 2014, Federal Highway Administration 2014) in the United States. The agencies responsible for the care and maintenance of the most traveled roads, state departments of transportation, are being urged to reduce their carbon footprints. This is driven by desire to assist with reaching the national target, public pressure to be more sustainable, and state emissions goals set into law (e.g., Assembly Bill 32 in California) (Air Resources Board 2014). There is untapped potential within an agencies' scope, which could bring additional significant reductions (Horvath and Hendrickson 1998, Cicas et al 2007, Sathaye et al 2010, Santero et al 2011a, 2011b. In this letter, the focus is on the potential GHG emission reductions from new rehabilitation policies. Transportation agencies have two options for each road segment at any given point in time: they can elect to do nothing, or they can perform a rehabilitation action. If they elect to do nothing, the pavement condition worsens. Roughness has been identified as the most important indicator of performance and will be used as the measure of pavement condition in this letter (Federal Highway Administration 2012). It is a measure of the unevenness of the road along the longitudinal profile in the wheelpath and is measured by the international roughness index (IRI) in m/km. As roughness increases, fuel consumption also increases, resulting in greater emissions from the tailpipes of vehicles (Watanatada et al 1987). To keep the user emissions down, agencies can perform a rehabilitation action such as a resurfacing, which improves the condition of the road. While effective in reducing user emissions, rehabilitation actions result in large quantities of GHG emissions being released into the atmosphere from the manufacturing and transporting of the materials and the construction stage (Santero and Horvath 2009). There is optimal timing to perform rehabilitation where the combined user and agency emissions for that segment are minimized (Reger et al 2014). In theory, an agency would always choose to rehabilitate at that timing, but in practice, there are other factors that can interfere. The agency chooses the action and time, but the total budget they have is beyond their control. A binding financial budget can force the agency to rehabilitate the roads in the network with less frequency than would be optimal.
Multi-objective optimization has been identified as an effective technique for infrastructure management problems (Wu 2012). In Reger et al (2014), we solved a multi-facility, continuous time, continuous state, infinite horizon problem for a heterogeneous pavement network. We sought to minimize total societal costs (user and agency combined) subject to an emissions constraint, giving a range of potentially optimal policies that could be applied by the agency. For this range of potentially optimal solutions, an agency cannot reduce total costs without increasing GHG emissions, nor reduce GHG emissions without increasing costs, creating a Pareto frontier. Networklevel Pareto-optimal solutions have been applied to pavement management previously, but have focused on aspects such as cost, performance, condition, and work production (Fwa et al 2000, Bai 2011, Sathaye and Madanat 2012, Bryce et al 2014, Bai 2015. Wang et al (2012) and Wang et al (2014) examined the case of optimizing with respect to environmental considerations and energy at a network level. There has been research that has examined simultaneously optimizing costs and GHG emissions but did not include Pareto optimality (Zhang et al 2010) or focused on material comparison (Zhang et al 2013). At a single project level, the Pareto frontier between costs and GHG emissions was previously examined (Lidicker et al 2013). At a network level, Pareto optimality was examined by Gosse et al (2012), but did not include the GHG effects from user vehicles caused by changes in pavement condition.
The potentially optimal policies from Reger et al (2014) assumed unlimited financial resources for the agency. This is not typically the case in practice. In this letter we take a different perspective, examining the case of an agency which seeks to reduce its GHG emissions when the budget that can be spent on rehabilitation in a given year is limited. We show that achieving a financially sustainable and low-carbon pavement management system requires cooperation between legislators and transportation agencies. It is the responsibility of the agency to properly use the budget it is supplied with, but it is the responsibility of the legislation to provide the agency with sufficient funding to apply a policy which reduces its global warming impacts. There needs to be a combined effort to ensure that tax money is allocated properly to achieve the largest reductions in GHG emissions.
The methodology used in Reger et al (2014) is modified to become more applicable for real-life scenarios. That paper considered a single type of rehabilitation activity, but state agencies have many options at their disposal. We show how to compare these different rehabilitation options, while still maintaining the Lagrangian dual formulation which allows for efficient solutions for large-scale networks. Using this new approach, the optimal activity and the optimal timing are chosen for each road segment in the network. We show that the results are robust to uncertainty in the deterioration rate, best achievable roughness level, and effect of roughness on fuel consumption. We also examine the potential effects of using warm-mix asphalt (WMA) as a material in pavement resurfacing.

Problem formulation
As in Reger et al (2014), we use a continuous time, continuous state, infinite-horizon optimization formulation. The problem is formulated as an objective function subject to two constraints, as shown in equations (1)-(3). Equation (1), the objective function, is the sum of the total yearly emissions, Q jk , for all facilities j=1,K, J, choosing from potential rehabilitation actions, k=1,K, K. Q jk includes the user emissions, W jk , and the agency emissions associated with applying the rehabilitation action, A jk . W jk is an integral from 0 to τ and A jk is a function of the number of lanes of the roadway and the chosen action, k. jk t is the decision variable, and is the interval of action k for segment j. Emissions are annualized by dividing by τ, since there is no scientific consensus on a discount rate (Sedjo and Marland 2003). Equation (2) is the budget constraint, where M jk is the cost of action k for segment j and B is the annual budget. Budget values are not discounted as this is meant to represent the necessary budget per time and also helps to capture the idea of an agency having a multi-year budget. The final constraint bounds the potential solutions between 0 and jk e t (the optimal timing where total emissions are minimized). Note that τ cannot equal 0, as it would render the objective function undefined The scope of roughness considered for user emissions is shown in figure 1. The emissions associated with roughness below the best-achievable level after rehabilitation are beyond the control of the agency. Therefore, these emissions are not included in the optimization. However, different rehabilitation actions have different best-achievable levels of roughness. S 1 * is the best-achievable roughness level among all the potential actions. S k * is the best-achievable level after action k. Reaching S 1 * is still within the agency's control, so if they choose to apply action k, the emissions associated with the difference between S 1 * and S k * are included.

Solution methodology
In Reger et al (2014), we used a similar Lagrangian duality solution methodology to that developed by Sathaye and Madanat (2012). Here we maintain a Lagrangian dual methodology, but solve it in a different manner to allow for the addition of multiple rehabilitation activities. For a given budget at optimality, all facilities in the network will have the same value of L (the Lagrange multiplier), so the problem can be treated as separable. We solve for the optimal timing τ of action k on segment j, for all actions k=1, K, K. The optimally timed action which has the lowest value of D L ( ) is retained. The budget B is backcalculated by taking the sum of M jk for all j.

Case study
The case study focuses on a 1600 lane-km sample of asphalt pavement segments in California over an infinite time horizon. This 1600 lane-km sample is made up of 311 different segments, including both urban and rural roads distributed across Northern California. The traffic data (AADT and AADTT) were obtained from the California Department of Transportation's (Caltrans) Division of Traffic Operations (Caltrans 2014). Data for rehabilitation actions were obtained from a study of Californian roads, which gives the best-achievable condition and the rate of deterioration after the activity is performed (Tseng 2012). The rehabilitation actions include five different thicknesses of overlays (3 cm, 4.5 cm, 7.5 cm, 10.5 cm, 15 cm). Although the only rehabilitation options shown for the case study are different resurfacing thicknesses, the methodology applies to other types of activities, such as seal coating or full-depth reconstruction. It is assumed that 80% of heavy vehicles will travel in the rightmost lane and that deterioration will primarily occur in this lane. Traffic is assumed to stay constant over time. Since rehabilitation is primarily performed overnight in California, the emissions from traffic delay are negligible. User emissions take into account the additional fuel burned because of the change in fuel consumption due to roughness. The effect of roughness on fuel consumption was determined by Zaabar and Chatti (2015), who found that an additional 1 m/km of IRI increases fuel consumption by 2%-3% for light vehicles and 1%-2% for heavy vehicles at highway speeds. We use the midpoints, 2.5% and 1.5%, respectively. The gasoline and diesel GHG emissions include emissions from combustion as well as supply chain emissions from extraction, refining, distribution, etc. Agency emissions are calculated using the PaLATE software (PaLATE 2013) and agency costs for resurfacing are taken from (Hand et al 1999). For agency actions, it is assumed that the agency will not deviate from its schedule if there are adjacent sections being rehabilitated in close timeframes.

Case study results
The methodology solves for the optimal action (and corresponding optimal timing) for each segment at each agency budget value. We find that the thinnest resurfacing option (3 cm) is always the optimal action for every 1.6 km long segment at every potential budget value. This is a different result than found in the literature, which states that it is always optimal to resurface to the best possible condition if the objective is to minimize total costs (Li and Madanat 2002, Ouyang and Madanat 2006, Gu et al 2012. For the case study, the best possible condition after resurfacing occurs after applying a 15 cm overlay, while the condition after applying a 3 cm overlay is the worst among the potential options. The result happens to be consistent with the practice of at least one US agency, the Washington State Department of Transportation.
In the roughness progression model, the 15 cm overlay will deteriorate 22% slower and have a 0.1 m/ km better condition after resurfacing, but will cost about twice as much and have 5 times the amount of GHG emissions as the 3 cm overlay. In this case, an agency can perform a 3 cm resurfacing on two segments for the same cost as a 15 cm resurfacing on one segment. This is important when the budget is low because keeping more roads in good condition reduces user emissions. When the budget is not binding, the 3 cm overlay remains optimal because now actions are being performed very frequently and the agency emissions from overlays are the controlling factor. Even going from a 3 cm overlay to a 4.5 cm overlay, costs per resurfacing increase by 14% and emissions increase by 50%. The benefit from slower deterioration does not offset these additional costs and emissions.
The results are shown in figure 2, with the x-axis representing the agency budget in millions of dollars and the y-axis representing the total GHG emissions in metric tons (mt). As the agency budget increases, total emissions decrease until the emissions-minimizing point is reached. When the budget is low, roads are allowed to deteriorate to poor condition, and the main contribution to emissions comes from the additional fuel consumed by the vehicles. Where budget values are high, the agency is rehabilitating frequently, so the majority of the emissions result from the materials and construction. The slope of the curve is the amount of GHG emissions that could be saved per additional dollar spent by the agency. The results exhibit diminishing returns. For example, an additional $1M/yr results in a reduction of 100 000 mtCO 2 e/yr when going from $1M/yr to $2M/yr, but only reduces the total emissions by 2500 mtCO 2 e/yr when going from $10M/yr to $11M/yr. Considering that vehicles emit a majority of the GHG emissions in the transportation sector and the roads which fall under Caltrans' jurisdiction carry over 80% of the VKT in California, scaling up to the entire network would have a significant statewide impact.
The agency is responsible for optimally using the budget it is allocated, but it does not control the size of that budget. A curve, like the one shown in figure 2, can help the agency and legislation work together to make budget decisions. Each point on the curve corresponds to a set of optimal actions and action intervals which the agency would apply under a potential budget value. This means that the entity assigning the budget is also choosing the corresponding yearly GHG emissions. The graph gives the agency a way to visualize and quantify the GHG emissions under a given budget as well as determine the potential reductions if additional funds are provided. One way to determine an appropriate budget would be to look at the price of carbon. It is given in the figure by taking the inverse of the slope. For example, if the societal value of carbon was $10/mt, the agency's budget should be $1.3M/yr. Since the cost of carbon changes along the curve, a lower budget would force the agency to operate where the value of carbon was lower than the societal value, while a higher budget would result in spending more than $10/mt for every dollar beyond $1.3M.
Using this methodology, this agency would now have the potential to enter a modified cap-and-trade system. Another entity could purchase carbon credits by supplying the agency with the funds to use for rehabilitation. Standard cap-and-trade systems are typically for a one-time purchase, but what is proposed here is modified such that it could be sold as a contract to a particular entity or resold each year. As an example, if the agency currently has a budget of $5M/yr, each year they would be able to sell 8000 mtCO 2 e worth of credits for $1M since that would be the GHG reduction from increasing its budget to $6M/yr.
Another benefit of this curve is that it allows for comparisons of investments in rehabilitation policy with other alternatives within the agency's scope. As an example, if the agency received a grant for $5M/yr that it could spend on any activity with the goal of reducing emissions, it could either invest in pavement rehabilitation or in an alternative project such as replacing conventional roadway lighting with LEDs, incentivizing switching to alternative fuels, etc. The arrows in figure 3 are a graphical representation of an alternative project (in this case a project that would cost $5M/yr and reduce GHG emissions by 50 000 mtCO 2 e/yr). If the current rehabilitation budget was $2M/yr (blue arrow), the arrowhead would fall above the curve, so using the money for pavement resurfacing would result in larger emissions reductions. However, if the budget was $3M/yr (orange arrow), the arrowhead would fall below the curve, suggesting that the alternative project would be a better investment.
In addition to GHG emissions, the agency would want to look at the effects of budget values on road condition. Figure 4 shows a 'heat map' of the distribution of trigger roughness values for different agency budgets, where a trigger roughness is the level of roughness at which a rehabilitation action will be performed (i.e., the condition of segment j when exactly  (2014), which found that using a universal trigger roughness (i.e., applying the same trigger roughness value to every road in the network) is always suboptimal. In this case study, there are road segments which should be rehabilitated with very little frequency (e.g., τ≈50 years). However, the data collected to determine the rate of deterioration did not have a segment which was allowed to deteriorate for 50 years with no intervention. Weathering may prevent these long rehabilitation intervals from being feasible. More data are needed to determine how pavements would deteriorate if left without rehabilitation for long time periods and if there are minor treatments which can work as placeholders until it is time for a rehabilitation activity. The issue of condition may also become a factor for these segments since the roughness will surpass what is typically seen on paved roads in rich countries. In this case, the agency may have to allocate some of the budget to these roads suboptimally, but since only 2% of the case study roads fall into this category, it will not greatly affect the yearly emissions.

Uncertainty and sensitivity analysis
The parameters tested for sensitivity analysis were the deterioration rate, best achievable roughness level, and percentage change in fuel consumption. To represent uncertainty with respect to the best achievable roughness level and deterioration rate, we assume that each is normally distributed, with the mean being the value used earlier in the case study and the standard deviation being 25% of the mean value (25% was used such that there was a wide range of deterioration rates while also making sure that there is never a negative value). We then assume that the agency will use a predetermined policy, where they always apply the action and timing specified by the model. This means that if they are supposed to resurface at an interval of 10 years expecting the roughness to be 3.0 m/km, they will still resurface at 10 year intervals for that section even if the pavement condition is 2.0 m/km or 4.0 m/ km at that time. Figure 5 shows the results of the sensitivity analysis. The optimal policies are robust to the deterioration rate and the best achievable roughness level. The black line represents the predicted value of the GHG emissions, with the red lines representing the values of emissions for the simulations. The uncertainty affects the optimal policies when the budgets are high. Figure 6 shows a zoomed-in portion of figure 5 when the agency budget is between $15M/yr and $23M/yr. An agency may not be guaranteed to see the reductions they expect from spending more money in this range. For example, spending an additional $4M/yr, from $15M/yr to $19M/yr, would have an expected reduction of 1000 mtCO2e/yr, but the emissions from the simulations at $19M/yr had a range of 9000 mtCO 2 e/ yr. Therefore, the increased spending may lead to no reductions (or even increases) in GHG emissions.
The Zaabar and Chatti (2014) study found that the effect of change in fuel consumption due to roughness is between 2%-3% and 1%-2% for light and heavy vehicles, respectively, so for sensitivity analysis we assumed that the effect of roughness on fuel consumption is uniformly distributed in these ranges. Again, we assumed that the agency applies the predetermined intervals chosen by the model. The model is robust to fuel consumption as 95% of the simulations resulted in GHG emissions within 500 mtCO 2 e/yr of the predicted value from the optimization.

Sensitivity to changes in pavement technology
New pavement technologies, such as WMA, could affect rehabilitation policy. WMA uses a lower mixing temperature than traditional hot-mix asphalt, and in a best case scenario has the potential to reduce GHG emissions from an asphalt mix by up to 20% (Rodríguez-Alloza et al 2015). Figure 7 shows the effect of using WMA for rehabilitation on the case results, assuming a 20% reduction in GHG emissions from asphalt and no change in pavement performance or unit price. There is almost no benefit until the agency budget is greater than $10M/yr. This is because when the budget is low, there are few rehabilitations performed each year, so the user emissions are the main contributors to the total. Near the emissions minimizing point, using WMA can result in savings of up to 3000 mtCO 2 e/yr, since there will be a sufficient number of rehabilitations performed each year. However, it is unlikely that an agency will be operating at this point on the curve. Beyond an agency budget of $10M/yr, the cost of saving an additional metric ton of carbon is upwards of $700/mtCO 2 e, which is higher than carbon has ever been traded on the market. There may be other benefits to WMA, such as improved workability and laborer safety, but with respect to GHG reductions in pavement rehabilitation policies, it will provide little benefit unless it brings significant improvements in performance.
The cost of asphalt may change with the recent drop in oil prices. Bitumen is a product of petroleum refining and is also the most expensive part of the asphalt mix. Figure 8 shows the results assuming a 20% reduction in rehabilitation costs. The effect is significant for low budget values, but is less noticeable as the agency budget increases. At a budget of $1M/yr,  the 20% reduction in costs would reduce the GHG emissions by 50 000 mtCO2e/yr. When the budget is $15M/yr or higher, the effect is negligible. This occurs because a reduction in costs stretches the budget farther, allowing more roads to receive rehabilitation and overall reducing GHG emissions. It is equivalent to increasing the budget.

Conclusion
This letter presents an approach that can be followed by a road agency to minimize its GHG emissions from rehabilitation while operating under a constrained financial budget. A Lagrangian dual solution methodology is used to efficiently solve for the optimal resurfacing policies in a large-scale network. The results provide the optimal timing along with the optimal actions for every road segment in the network. An agency can use these results to make the case for a higher rehabilitation budget to achieve its emissions reduction target. It is also possible to implement a system where the agency could sell carbon credits by quantifying the emissions reductions from increasing its operating budget and price accordingly. This methodology also allows the agency to compare spending money on pavement rehabilitation or another project within its scope (e.g., roadway lighting) to determine which is a better investment.
A case study of Californian roads was examined and it was found that it is optimal to apply frequent, thin resurfacings, which is contrary to the less frequent, thick overlays specified in the literature for minimizing costs. Sensitivity analyses showed that the solutions are robust with respect to the deterioration rate, best achievable roughness level, and effect of roughness on fuel consumption. The effect of using WMA was determined to only be significant when agency budgets are high since at low budget values rehabilitation is infrequent. However, if asphalt prices fall or the agency finds a way to reduce costs, the