Resource Allocation Logic Framework to Meet Highway Asset Preservation (2012)

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30 C h a p t e r 4 This chapter describes the mathematical general computational and optimization approaches employed in the proposed Resource Allocation Logic Framework. To begin with, the basic tax- onomy to describe, break down, and roll up allocations will ultimately be user defined as a basic starting point in applying the allocation logic framework. The research team has used several sample elements of such a taxonomy6 to describe and demonstrate the framework. Examples include bridge structures, pavements, signs, and guardrails. In this report and the demonstration model, we will refer to elements of the preservation program taxonomy with the following terms: Resource Allocation Logic Framework Development 6 Based on NCHRP research of widely used breakdowns of highway asset types and groupings (discussed later this chapter) as well as on case research that revealed significant variations in the taxonomy used for management of preservation programs. 7 This report employs sample units of measure such as lane-miles and numbers of bridge decks, but the computation model will permit user definition of these, as well. Term Application Text Shorthand Asset/Activity ID Identifies a grouping of asset inventory/preservation activities with an aggregated data set and allocation AAID Asset/Activity Group Refers to all physical inventory in the state or district with a common AAID AAG Asset/Activity Unit Refers to a typical single unit of measure7 of an Asset- Inventory Group AAU 4.1 Computational Logic Based on the requirements described in the previous chapter, the research team developed a computational solution that will work effectively for all AAGs for which preservation needs determination is adequately supported by necessary data or estimates. For AAGs that are not sup- ported by such data or estimates (usually non-bridge or pavement-related AAGs), alternate meth- ods are employed to approximate preservation needs. Preservation needs estimation is a starting point for the allocation solution, as shown in the following computational sequence overview: • Total preservation needs for each AAG based on programmatic performance goals • Preservation needs rolled up to total for all AAGs • Comparison of total needs to available preservation funds • If available funding exceeds total preservation needs, make the allocation based on (a) needs to meet stated performance/condition targets and to offset expected deterioration or (b) achiev- ing best performance/condition results with resources available • If available funding is short of total preservation needs, compute and optimize adjustments to approach performance/condition targets as closely as possible • Compute expected revised performance results expectations after optimized allocation adjustments

resource allocation Logic Framework Development 31 A linear programming approach is recommended to support resource allocation logic. This approach is advantageous for the following reasons: • Can be the basis for optimal solutions • Is commonly used by state DOTs for optimization problems • Is easy to understand and communicate compared with other optimization techniques • Is typically user- and data-friendly Linear programming uses mathematical functions that are available in Excel to solve the resource allocation optimization. 4.2 Solution Components 4.2.1 Decision Variables The research team identified potential quantifiable decisions that can be expected to be made in allocating resources for highway preservation needs. These decisions will be represented as decision variables whose respective values are to be determined. These decision variables rep- resent possible strategies and courses of action that state DOTs and other transportation and public agency managers can take in allocating the highway preservation resources. Examples of these decision variables are the amount of allocated funds to individual asset categories (i.e., dol- lar amount of allocated funds to an AAG). It is also possible that users will identify other kinds of decision variables for incorporation into the model, such as funding priorities for specific AAGs or specific asset preservation strategies. Certain AAGs could, for example, be designated specifically for light or heavy preservation treatment. Decision variables are expected to guide the highway preservation resource allocation pro- cess and include all relevant characteristics such as policy, organizational, programmatic, and performance that are expected to influence the resource allocation process (relevant research on multi-criteria decisionmaking is found in Reference 7). These may change given state DOT priorities for any given period. Figure 4-1 lists examples of decision variables. 4.2.2 Objective Functions The purpose of an objective function is to measure the composite effects of the decision vari- ables. Developing a clear, detailed, and quantifiable objective function is a fundamental element Policy State/DOT overarching goals: Safety Mobility Environmental stewardship Quality of life Economic competitiveness Fiscal responsibility Sustainability Organizational Regional priorities: Statewide Regional District Urban Rural Functional responsibilities: By DOT office Programmatic Investment priorities: By type of highway asset By tradition/culture By policy goals Funding process: Prioritization strategies (e.g., cost-benefit analysis) Performance State-adopted thresholds and objectives: Bridge rating Pavement rating Expected life of assets Tradeoffs among asset categories Traffic loads and use factors Locations, quantities, characteristics Figure 4-1. Decision variables for consideration in the resource allocation mathematical model.

32 resource allocation Logic Framework for highway asset preservation of the problem formulation and is essential for ensuring that state DOTs are allocating resources optimally and in a manner consistent with state policies, goals, and objectives. From this per- spective, the objective function can be quite specific, focusing on certain aspects of highway preservation. At the same time, to be successful, the application of operations research can seek solutions that are optimal for the overall organization rather than suboptimal solutions that are best for only one component. Given the nature of highway preservation resource allocation, decisionmakers may be expected to develop more than one objective function. Adding more than one objective to an optimization problem adds complexity. For example, if a state’s goals are to minimize the life-cycle cost of all asset categories and maximize overall safety benefits from investments in maintenance and rehabilitation, potential conflicts could transpire. In such an event, state DOTs are advised to consider tradeoffs and to combine the two objectives into one, loosening the requirements for each objective. An objective function in the Resource Allocation Logic Framework is used to determine opti- mal adjustments to computed preservation investment needs, optimized for a specific results objective. These adjustments to computed investment needs are necessitated by the unlikely case that funds available equal funds needed. Examples of potential definitions for objective functions include the following: • Maximize service life expectancy for the foreseeable future; in the allocation context, this trans- lates into maximizing performance/condition ratings for all AAGs in as short a period as practical • Maximize the performance/condition ratings of one or more AAGs while holding current per- formance condition ratings for other AAGs; this translates to maximizing the performance/ condition rating results for the selected AAGs at the end of the allocation cycle • Maximize benefits expressed as the sum performance/condition ratings for all AAGs; stated another way, all AAGs progress equally in terms of performance condition, given available funds • Minimize the differences in percentage progress for each AAG, from initial performance/ condition rating to target performance condition rating, expected at the end of the allocation cycle; this translates into all AAGs moving toward performance objectives at rates propor- tional to their respective performance gaps • Minimize the difference between desired cycle8 time (set for each AAG) and the expected actual cycle time (after allocation adjustment) to achieve performance targets for each AAG; if funds available are less than allocations needed, the time to reach performance targets will extend beyond the desired cycle times9 input by the framework user for each AAG The research team applied the last objective function to test the Resource Allocation Logic Framework computational model: Invest in maintenance and preservation projects so as to mini- mize the deviation between the desired and actual timelines to achieve recommended performance/ condition targets. Minimize: Differences for all AAGs between desired time and actual time to achieve performance targets∑ Readers will see that the use of this objective function works well to test all features of the computational approach. Desired and actual time cycles are also an excellent surrogate for rate of progress toward performance objectives, and they offer ways to set priorities. The other pos- 8 Allocation cycle. 9 A key presumption here is that small improvements are possible in a single cycle, but significant changes in average performance/condition rating for an entire AAG inventory will require multiple cycles.

resource allocation Logic Framework Development 33 sible objective functions can be tested reasonably well by manipulation of various input values and small adjustments in Excel model equations. 4.2.3 Constraints The purpose of the constraints is to define the “limits” or “boundaries” of certain aspects that agencies must conform to when they try to maximize overall network performance. The constraints can be broadly classified as policy, organizational, programmatic, or performance in nature. Figure 4-2 lists sample constraints for resource allocation. From a practical point of view, the constraints include possible restraints or restrictions that DOT managers face in preservation resource allocation. The following are examples: • Funding constraints on the total preservation program • Funding constraints on what should or should not be spent on specific AAGs • Any legislation or mandates directing specific highway preservation activities • Required interdependencies with investment in other programs • Limits on the time horizon because of the useful life expectations of specific AAGs Examples of common predetermined constraints that can be applied within the Resource Allocation Logic Framework include: • Total Funding Constraint. The summation of resources to be allocated should not exceed the funding available for preservation. • Minimum Funding Constraint. The resources allocated to certain asset groups should meet or exceed specific minimum funding amounts or funds needed to meet or exceed minimum performance thresholds. • Appropriation Constraint. The allocated resources must conform to appropriations that are predetermined or mandated by state legislation or agencies for specific programs or asset- preservation objectives. • Work-in-Process Constraint. The allocated resources must account for projects that have been committed to, where interruption or reduction of funding is not in the best interest of the state or network users. • Life-Cycle Constraint. The allocated resources should in some way account for the continued performance or the condition of assets in their near-term life cycle. Deferred maintenance/preservation from prior periods is sometimes treated as a constraint in deciding allocations, meaning that funds would need to be reserved to “pay back” on deferred needs. In the needs-based computation proposed here, deferred needs would show up in current performance/condition ratings. Policy Legislative mandates on highway preservation Organizational Minimum funding requirement by region or district Minimum funding requirement by function commitments “Fixed” Programmatic Total funds available for preservation Funding constraints on minimum and maximum funds available for individual preservation AAGs Performance Minimal acceptable or targeted level of service; usually mandated Minimal acceptable safety considerations Figure 4-2. Sample constraints for resource allocation.

34 resource allocation Logic Framework for highway asset preservation The research team considered how the computational model would take into account resource allocation impact on the future asset preservation life-cycle costs (LCC). This pre- sents difficulties, mainly because resource allocation is typically a “static” process bounded by the current-year funding constraints, while the life-cycle view is on medium- and long- range timelines. The research team suggests that LCC considerations be addressed or accommodated in several ways in the logic framework: • In asset management practices, LCC analysis typically addresses optimal intervention tactics to improve asset performance through replacement, repair, preservation projects, or mainte- nance. Preservation practices and policies would be influenced by LCC findings. For example, pavements can be addressed frequently by light overlay tactics to extend time between more costly surface rehabilitation. Or certain pavement groupings may benefit most from one of these strategies alone, with attendant specific effects on unit cost estimates. The computation could consider multiple AAGs to account for these variations, each with a unique set of inven- tory, deterioration, condition, and unit cost data in support. • “Needs” could be determined either as current cycle needs only or include projected needs over a specified future time horizon. In practice, by determining total need and timeline to achieve performance/condition targets, the needs typically extend over a longer time span than the usual allocation cycle. • To the extent desired, agencies could apply this model to develop a first cut on resource allocation for a range of years (e.g., the next 5 years). Further resource allocation can then be refined year by year. The key point here is that to take into account life-cycle considerations, the yearly resource allocation process would be performed in the context of both current and future needs over longer allocation cycles. The constraints to be considered are Xij ijP≤∑ where Pij is the minimum/maximum value to be allocated for a given combination of AAG and preservation needs. 4.3 Data Needs The data needs for the allocation solution, along with the role played in the computational logic by each data set, are shown in Table 4-1. The first column lists the different user data ele- ments; the second column identifies the terminology used to define the data type (i.e., AAG, AAU). Columns 3, 4, and 5 identify whether the particular data element is used to estimate User Data Requirements Apply To Role in the Model Need Optimize Constraint AAG taxonomy AAG N O C AAG inventory AAG N C AAG units of measure AAG N O AAG ranking and allowable adjustment AAG O Average unit costs to restore AAUs AAG N Ideal performance/condition rating AAU N Current average performance/condition rating AAG N O C Target average performance/condition ratings AAG N O Timelines for target rating achievement AAG N C Available total funding for preservation Total N O C Table 4-1. Key data inputs for allocating resources for preservation.

resource allocation Logic Framework Development 35 resource needs, optimize allocation, or calculate constraints for allocating resources, respec- tively. A value of N in the third column (Need) indicates that the particular data element is used in the logic framework to estimate resource need. A value of “Oh” in column 4 indicates that the data is used in optimization procedure, and a value of C in the Constraint column indicates that the data is used to determine lower and upper bounds (constraints) for allocating resources. The key data inputs used for allocating resources all have an impact on the allocation results. However, the final results are more sensitive to a few input values as compared with the others. Table 4-2 flags the sensitivity of the different variables as High, Medium, and Low. Table 4-3 summarizes the availability of key allocation inputs in state DOT data management systems. 4.3.1 Asset Activity Groups and Inventory The AAGs that served as examples for developing the allocation solution were chosen as a result of an extensive literature review and discussions and interviews with panel members and state DOT agencies. State DOTs and other transportation agencies typically manage 11 asset groups that require preservation activities: • Bridges • Pavement • Drainage • Culverts • Signal systems • Signs and marking User Data Requirements Apply To Sensitivity of Result to the Variable Need AAG inventory AAG High AAG units of measure AAG Low AAG ranking and allowable adjustment AAG Low Average unit costs to restore AAUs AAG High Ideal performance/condition rating AAU Low Current average performance/condition rating AAG High Target average performance/condition ratings AAG High Timelines for target rating achievement AAG Medium Available total funding for preservation Total High Table 4-2. Key data inputs for allocating resources for preservation. Key Data Elements for Needs-Based Allocation Bridge and Pavement Assets Non-Bridge/Pavement Assets Inventory data for AAGs Most Many, for some assets Performance/condition data for AAGs Most Many survey some assets Average deterioration rates for AAG inventories Many Few Average unit costs to restore a single asset unit (AAU) to condition standard Many Few Historical data on work done and expenditure by AAGs Most Most Table 4-3. Key data inputs for allocating resources for preservation.

36 resource allocation Logic Framework for highway asset preservation • Guardrails • Safety structures • Lighting • Roadside • Landscaping Table 4-4 shows a sample asset management taxonomy used by Virginia DOT. There are two things to bear in mind on the topic of AAGs: • The allocation logic framework will be applicable for any realistic set of highway AAGs. • Performance/condition rating indicators to represent an AAG can be assessed and set for specific elements or asset types within an asset group (e.g., bridge deck rating) as an indicator for the entire AAG. For better precision in estimating average deterioration rates and preservation unit costs, sepa- rate AAGs can be used to address wide variations in these factors. For example, rigid and flexible pavements could be handled separately as distinct AAG inventories. The research team notes that the allocation framework is meant to be high level, and its value will reach a point of diminishing return as detail and required effort increase to develop and feed input data for more AAGs. It is noted that for high-level allocation decisions, it may be useful and simpler to adopt a spe- cific asset type (e.g., bridge decks) as an indicator of preservation needs for an entire asset group. Most state DOTs maintain detailed asset inventories for bridge and pavement asset groups. Although some states do not maintain any data for NBP assets, many states maintain this data for at least some assets, such as signage, signals, guardrail, and culverts. Source: Review of Virginia Department of Transportation’s Administration of the Interstate Asset Management Contract, Joint Legislative Audit and Review Commission of the Virginia General Assembly. Table 4-4. Typical asset groups and asset types.

resource allocation Logic Framework Development 37 Because we are determining high-level statewide and districtwide estimates to set overall allo- cations (and not work planning or project selection), coming up with best estimates of the required data will be sufficient. If the asset inventory information is not available for NBP assets, the data can be synthesized using a variety of means to get a rough estimate of the asset inven- tory and conditions. For example, to get the asset inventory, agencies may survey samples of asset counts in areas with different road densities (by classification) and use that information to build the systemwide estimates of assets and conditions. For instance, linear quantity could be surveyed or sampled and prorated to support the estimation of guardrail quantities. 4.3.2 Performance/Condition Ratings Most state DOTs maintain detailed asset condition data for bridge and pavement asset types. NBP asset condition assessment can be determined by trained survey teams applying condition standards and conducting district surveys every 1 or 2 years to assess conditions. Simple mea- sures such as pass/fail on key roadside assets can be used to assess conditions when no detailed procedures are in place. Definitions of the performance condition ratings used in the allocation solution are shown in Table 4-5. By way of illustration, an example of performance ratings used by the Virginia DOT is pre- sented in Table 4-6. 4.3.3 Deterioration Rates The asset deterioration rates and unit costs can be determined for bridges and pavement reasonably well, because most states use the historical expenditure, condition data, and asset inventory data. However, estimating the unit costs and deterioration rates for NBP assets is a bit more challenging because of a lack of detailed condition and inventory information. NBP asset deterioration rates can be determined by engineering estimation of useful service life with (or without) long-term data on work done to check and correlate. In general, the deterioration rate would be the number of units (e.g., miles, feet, count) divided by expected life. For instance, an asset type with a 20-year expected life would be expected to have its inventory deteriorate to below a set condition standard at 5 percent per year (average). Deterioration rates can also be estimated based on the asset age and known or estimated asset decay rates in particular regions or under known wear-and-tear conditions. An example is sign retro-reflectivity performance under various climate conditions. 4.3.4 Unit Costs Unit costs can be determined for bridges and pavement reasonably well in most states using the historical expenditure, condition data, and asset inventory data. However, estimating the Rating Type Meaning Ideal Expected performance/condition rating of a single unit of an AAG (an AAU10) when a preservation project is completed Target Desired average performance/condition rating of an entire AAG inventory Current Current actual average performance/condition rating of an entire AAG inventory Table 4-5. Resource allocation model—performance/condition rating. 10 Such as a specific lane-mile of pavement, a bridge deck, or a sign.

38 resource allocation Logic Framework for highway asset preservation unit costs for NBP assets is a bit more challenging because of the lack of detailed condition and inventory information. Average unit cost to restore to an as-new or nearly new condition standard can be estimated based on quantities restored and material/labor cost estimates or on-average costs of projects divided by units (e.g., miles, feet, count) done. Published material/labor cost indices can be used to address near-term escalation. It is noted that several types of treatments can be used to preserve an asset (e.g., thin overlay or chip seal in pavements) depending on the condition and available resources. However, the cost Source: Review of Virginia Department of Transportation’s Administration of the Interstate Asset Management Contract, Joint Legislative Audit and Review Commission of the Virginia General Assembly. Table 4-6. Virginia DOT target asset maintenance and rehabilitation rating schema.

resource allocation Logic Framework Development 39 of treatments can vary significantly among available options. Similarly, the deterioration rates and unit costs can vary significantly based on the asset type or category (e.g., asphalt vs. concrete vs. bituminous surface treatment pavement). To account for these major differences, the user needs to define each asset as a different AAG with a different unit cost and deterioration rate assumption. For example, asphalt and concrete pavement types can be defined as two different AAGs to capture the variation in unit costs. 4.3.5 Priority-Setting and Ranking Priority-setting and ranking of AAGs in the preservation context represent an organization’s strategic direction and emphasis in resource allocation as indicated here: • From the operations research point of view, the priorities and ranking are used as the “bal- ancing” factors to integrate multiple competing objectives into a practical application of a “collective” representation of factors influencing allocation results. • AAG priorities and ranks can be determined by agencies from many perspectives. They can be linked to policy, organization, programmatic mandates, asset LCC, or network performance goals. Two (of many) examples of the logic processes that can influence priority-setting and ranking are: – An agency can use engineering tools to calculate LCCs for individual asset types, groups, and programs. By comparing these LCCs, the agency can obtain an objective view of the relative importance or criticality of preserving specific AAGs based on long-term cost, which contributes to the determination of priorities. – An agency can analyze customer service requests for recent years to rank the AAGs and specific performance objectives or programs in terms of their importance to customers (or in the example shown in Chapter 5, asset leverage on program objectives). This ranking influences the optimization solution. Priority-setting and ranking is not necessarily based on engineering or math; rather, it is strategic and addresses questions like, “What service or objective should be our emphasis this cycle?” • Agency consensus on AAG preservation priority influences, but does not of itself drive allocation results a great deal, unless there is a large mismatch between resources needed and resources available. First and foremost, preservation needs drive the distribution of resources across AAGs. Priorities are incorporated into the computational model in several ways: – AAG allocation needs are influenced strongly by performance/condition targets and the user-set desired time to reach the targets (urgency of the need). For an AAG, the preserva- tion need in an allocation cycle is controlled by [cost of deterioration during the cycle] + [cost of performance improvement needed + desired years to achieve this]. All other things being equal, a 2-year desired timeline for one AAG reflects twice the improvement urgency of a 4-year desired timeline for another AAG. – Users rank AAGs sequentially. They can be 1, 2, 3, 4, etc., or they can be 1, 1, 2, 3, 4, 4, etc. The allocation model will not depend on the “true” or “absolute” values of these rankings. What will affect the outcome of the allocation model are the relative ranks among AAGs. – Next, assuming that AAG allocation needs have to be reduced because of a shortfall11 in available funding, users set adjustment limits commensurate with each rank assigned to an AAG. Doing so results in low-priority AAGs taking a bigger percentage “hit” than high- priority AAGs. 11 If there is no shortfall, no adjustment priority is needed. Either the process is complete, or performance goals driving needs would be re-evaluated (see also Section 4.1).

40 resource allocation Logic Framework for highway asset preservation 4.3.6 Historical Data Most state agencies maintain a detailed log of the historical expenditures. The data is readily available for bridges and pavement, in particular. However, assembling the data accurately for NBP assets in some situations might be a bit more difficult, as the preservation and maintenance expenditures for NBP assets are sometimes rolled into major road or bridge project works and not tracked individually. 4.4 Allocation Logic The ultimate goal of the Resource Allocation Logic Framework and supporting mathematical model is to determine the optimal investment allocations by AAG for specific allocation cycles and specific regions or districts given statewide goals and objectives, available funding con- straints, and performance thresholds (see Figure 4-3). Other valuable outputs from the resource allocation model include realistic performance/condition expectations (both conditions and timelines to achieve targets) by AAG after allocations are adjusted to conform to funding limita- tions and other strategic variables. Once the strategic inputs and targeted performance/condition (left side of the diagram), and the data inputs (top right side of the diagram) are introduced, the computations and objective function optimize and compute allocations to match available resources, as well as achievable performance results that are accountable to the investments (unshaded blocks). If the perfor- mance and timeline results are unacceptable to decisionmakers, adjustments to AAG perfor- mance goals or to the overall funding commitment can be made, resulting in new allocation and performance results. AAG Data and Estimates Compute Preservation Needs for all AAGs Inventories Average Performance/Condition Rating Average Unit Cost Average Deterioration Rate Strategic Decisions and Goals: Priorities AAG Rank Timelines Constraints, Funding Decisions Performance and Condition Targets Compare to Available Preservation Funding and Constraints Optimize AAG Allocation Adjustments Compute Expected Performance and Timeline Results NO NOYES YES DONE Funding & Constraints Met? Adjust Funding or Goals? Figure 4-3. Allocation logic overview.