HERS-ST Highway Economic Requirements System - State Version: Technical Report - Chapter 7: Evaluating Improvements
The HERS model applies a standard benefit-cost framework to the evaluation of improvement alternatives, but "standard" does not mean that the methods are cut-and-dried or necessarily obvious. Considerable distortions or bias can be introduced into the estimation of capital investment requirements by seemingly small errors or misconceptions in how the benefits and costs are discounted and summarized, and in how the BCRs/IBCRs are calculated and used.
This chapter describes the mechanics of how HERS summarizes and discounts benefits, and compares projects against a benefit-cost criterion or against each other. The concepts HERS is implementing are explained in Appendix D, "Basic Theory of Highway Project Evaluation" and Appendix B, "Induced Traffic and Induced Demand."
HERS recognizes four broad classes of costs:
- user costs, which are borne by the highway user;
- agency costs, such as maintenance, which are borne by the administrative agency responsible for the section;
- external costs, which are borne by non-users of the highway system (society at large); and
- capital improvement costs.
Benefits are reductions in costs as the result of an improvement, and are measured as the difference in costs between the base case and the improved case (the base case can be either the unimproved section or a less aggressive improvement). When performing benefit-cost analysis, HERS places the first three classes in the "benefit" category, with capital improvement costs being the "costs." Costs that increase as a result of an improvement (i.e., cost savings are negative) are labeled "disbenefits" and added to benefits with a minus sign. An improvement may produce both benefits and disbenefits, as when an improvement that increases average speed brings benefits resulting from the reduction in travel time, and disbenefits from an increase in vehicle operating costs and emissions.
In addition, there is an estimate of benefit from change in consumer surplus resulting from that change in travel that occurs from an improvement that changes the generalized price of travel for the user. This incremental consumer surplus only occurs if demand elasticity is not zero (perfectly inelastic); HERS does not accept elasticities of zero or greater.
Projects are selected using benefit-cost ratios (BCRs), and incremental benefit-cost ratios (IBCRs) relative to a less aggressive improvement alternative. Although the objective is to maximize net benefits (subject to constraints, if any), the procedures use ratios to achieve the goal rather than directly calculating net benefits.
After potential improvements have been identified, HERS evaluates them to gauge their economic attractiveness. HERS makes decisions about improvements on the basis of the ratio of the net present value of each improvement's incremental benefits to the present value of the incremental costs. This ratio is referred to as the incremental benefit-cost ratio, or IBCR. The decisions HERS makes based upon IBCR are:
- Does the section warrant improvement during this funding period?
- If so, which is the economically most attractive improvement for this section?
In a constrained scenario, HERS also asks:
- Among the potential improvements to all sections in the highway system under analysis, which are the economically most attractive?
This chapter first presents the steps HERS uses in determining the benefit-cost ratio (BCR, used interchangeably with IBCR). It then examines how HERS uses the BCR to answer the three questions.
The evaluation process consists of determining the benefit-cost ratio of each candidate improvement. This is accomplished in several steps:
- identifying the base case;
- determining the length of the analysis period;
- determining the user, agency, and external costs associated with the base case;
- determining the user, agency, and external costs associated with the candidate improvement;
- determining the capital cost of the improvement;
- determining the residual value of the improvement; and
- calculating the benefit-cost ratio.
This chapter addresses the process of determining the BCR for candidate improvements. The details of the calculations involved are discussed in Chapter 5, "Estimation of Impacts" (the forecast of traffic volume and pavement condition, and the calculation of user, agency, and external costs), and Chapter 6, "Capital Cost of Improvements."
In a typical HERS run, when the option to force the model to address unacceptable conditions has not been selected, the initial base case is the unimproved section. That is, the potential benefits of candidate improvements will be compared against the case in which no improvement is made to the section. HERS uses this base case when determining whether a section warrants improvement during the current funding period (see section 7.9, "Does a Section Warrant Improvement?"). However, if the option to force the model to make mandatory improvements to address unacceptable conditions has been selected, HERS uses the mandatory improvement as the base case.
HERS also uses a previously selected improvement as the base case when considering more aggressive improvements. This situation commonly arises in the selection process for constrained runs, and is also used to discover the economically most attractive improvement for a section during a minimum BCR run. Since the differences between the costs and benefits of the two improvements are used in calculating the benefit-cost ratio, the term ‘incremental benefit-cost ratio', or IBCR, is often used interchangeably with the term ‘benefit-cost ratio'.
Generally, when evaluating whether to improve the section during the current funding period, HERS uses a benefit-cost analysis period equal in length to the minimum number of funding periods that will encompass the lifetime of the least aggressive improvement. This might be as little as one or two periods, for example, with a simple resurfacing. The BCA period begins at the midpoint of the current funding period, and extends to the midpoint of the funding period during which the improvement would be "used up" (see Figure 2-8 "HERS Time Periods" on page 2-13).
Table 7-1 provides a brief summary of how the last funding period of a BCA period is determined. Benefit-cost analysis periods consist of an integral number of funding periods, and extend from the mid-point of the funding period in which the improvement is implemented to the midpoint of some subsequent funding period.
|Situation Being Analyzed||Funding Period in Which BCA Period Ends|
|a. Unacceptable conditions that cannot be corrected (e.g., those that require more widening than is feasible) are excluded from consideration in this test.|
|Section for which no improvement has yet been selected for the current funding period:|
|If current funding period is the last one in which resurfacing is practical;||Period in which condition first becomes unacceptablea, or maximum length of BCAP, or 15 years, whichever occurs first|
|Otherwise;||Next period in which pavement would "normally" be improved or period in which condition becomes unacceptablea after implementing the improvement, or maximum length of BCAP, whichever occurs first|
|Section for which an improvement has already been selected during the current funding period.||Next period in which pavement would "normally" be improved or period in which condition becomes unacceptablea after implementing the already selected improvement, or maximum length of BCAP, whichever occurs first|
In highway management, the improvement question is often viewed not as whether a section should be improved, but when? In many cases, the two most serious alternatives are "improve during the current funding period" and "improve during the next funding period." HERS does not attempt to optimize over time, and only evaluates whether an improvement might be justified during the current funding period.1 This is accomplished by comparing it to a "base case" in which no improvement is implemented during the current funding period. Use of such a base case against a simple resurfacing means that the improvement will be made if the benefits of the resurfacing over its lifetime (compared to letting the pavement deteriorate from its existing condition) exceed the costs of the resurfacing. If the improvement fails the BC test, the question of whether to resurface in the next funding period is postponed until that period becomes the current period. When comparing more aggressive improvements to an acceptable initial improvement, the benefits include a residual value from the most aggressive of the two candidates (see section 7.7 below).section 5.6 "The Travel Forecast Model" on page 5-51) and pavement condition (see section 5.1 "The Pavement Deterioration Model" on page 5-1) at the end of the funding period. It then calls upon the routines which calculate the operating costs, travel time costs, safety costs, maintenance costs, and emissions costs. The costs are calculated for the end of the funding period. This process of prediction and cost calculation is repeated for each funding period in the BCA period.
The process of calculating the costs associated with the potential improvement is similar to that for the base case. The model first simulates the effect of the improvement on the section (see section 4.2.4 "Effects of HERS Improvements" on page 4-20). This establishes the pavement condition at the time of the improvement, and HERS applies short-run elasticity to determine the new traffic volume (see section 5.6.3 "The Simultaneous Solution" on page 5-54). Traffic volume and pavement condition are then forecast for the end of the funding period, and the cost calculation routines are called upon to determine the user, agency, and external costs associated with the improved section at that time. The model then repeats the prediction and cost calculation for each funding period in the BCA period.
For most sections being improved, HERS calculates the capital cost by multiplying the cost per lane mile by the number of lanes and by the length of the section. The cost per lane mile depends upon the particular improvement, the section's functional class, and, for rural sections only, the prevailing terrain (flat, rolling, or mountainous). For sections receiving alignment improvements, HERS employs a more complex approach (including the cost of earthwork, clearing and grubbing, pavement, etc.) to determine the cost over the portion of the section being re-aligned. Portions of the section not being re-aligned are costed in the same manner as sections receiving no alignment improvements.
1. An analysis of the improve-now-or-later decision criterion is contained in the internal report "Build/NoBuild versus Now/Later" (US DOT/Volpe Center, June 2003). The conclusion is that applying a now-versus-later test produces muddled and misleading results, and adds nothing to the cross-sectional analysis (build-versus-no-build or now-versus-not-now) that HERS conducts.
See Chapter 6, "Capital Cost of Improvements" for the detailed presentation of how HERS calculates improvement costs.
Residual Value is the preferred concept for valuing an improvement after it has passed through its normal lifetime or through some phase of its life. Computation of this value, however, requires information and assumptions that are not currently contained in the HERS model. An expedient is used instead that provides a "refund" of a portion of the project's costs if the analysis period is truncated before the end of the improvement's normal lifetime. This concept is the Remaining Service Life (RSL).
The residual value of an improvement is the capital value remaining at the end of the analysis period. HERS uses RSL is a substitute for either residual value or salvage value, although it is not equivalent. Salvage value is applicable if the asset is being terminated and liquidated, which is not usually the case for highway sections. Residual Value (RV) is the capitalized net benefits of the asset in its current use in perpetuity.
The computation of RSL is given by the formula:
|RSLt = C0 ×||n ∠ t|
|t||=||length of the benefit-cost analysis period (BCAP);|
|C0||=||initial cost of the improvement at time 0;|
|n||=||the normal or expected lifetime of the improvement, and t < n.|
This RSL is the value at time t, which must be discounted to time 0 for evaluation of benefits and costs:
|RSL0 = RSLt ×||1|
|(1 + r)t|
|RSL0||=||Remaining Service Life in present value terms at time 0; and|
The effect of the RSL is to give the improvement a "credit" for the unused portion of the investment, scaled proportionately to the percentage of the lifetime that has not already passed. Use of the RSL introduces some qualifying considerations to the analysis:
- If the improvement is worthwhile, benefits after the end of the BCAP are likely to occur at a greater rate per year than the comparable rate that costs would be "spread" over the life of the improvement. Since truncating the analysis period treats these net benefits as zero (i.e., benefits are equal to costs), improvements with long lifetimes suffer a bias against them.
- Truncating the benefits and rebating a portion of costs yields a different project than the one specified: a shorter lifetime with shorter benefit period, and lower costs. It is likely that such an improvement does not exist, e.g., it is not possible to add half a lane and get whole-lane benefits for half as long.
- For the RSL algorithm to yield reasonable results in HERS, the BCAP must be equal to or less than the life of the shortest-lifetime improvement. If not, the more aggressive alternative is being compared to a base case that has been allowed to deteriorate to unrealistic levels. The proper base case would be repetition of a less aggressive improvement (e.g., resurfacing), until the lifetime of the more aggressive improvement or until the BCAP. HERS does not implement subsequent improvements, so it is necessary that the BCAP be no longer than the lifetime of the least durable improvement being evaluated. As long as more aggressive improvements have longer lifetimes, this condition is satisfied.
In the following numerical example, a more aggressive improvement project (B) is compared to another improvement (A). Both projects are measured against a do-nothing base case. The assumed data are given in Table 7-2. HERS selects the lifetime of the least aggressive improvement as the BCAP.
|initial cost (Co)||10||30|
|begin benefits (yr)||1||1|
|analysis period (BCAP)||10|
Diagrammatically, the projects can be represented as shown in Figure 7-1, with the BCAP and project lifetimes indicated.
Benefits and costs for each improvement can be calculated relative to the do-nothing base, with the results shown in Table 7-3. Improvement A has no RSL because the BCAP coincides with the life of the improvement. The more aggressive improvement receives a benefit in the form of a share of its initial cost (½ in this instance), discounted to year 0.
|present worth||fixed BCA period|
|remaining service life||-||9.21|
The formal HERS benefit-cost ratio, as shown in Equation 7.3 below, compares a base case to a potential improvement. The base case may be the unimproved section or a previously identified improvement, in which case all potential improvements will be more aggressive than the base case improvement. The HERS procedure includes estimation of the incremental costs and benefits of each potential improvement for each period of the benefit-cost analysis period, as well as estimation of the improvement's residual value at the end of the analysis period. The residual value of the improvement is discounted back to the initial year of the analysis period and treated as a benefit of the improvement.
|IBCR =||(TotCostB) ∠ (TotCostI) + RV|
|ImpCostI ∠ ImpCostB|
|IBCR||=||incremental benefit-cost ratio;|
|TotCost||=||Ucost + Acost + Ecost for either the base case B or the improved case I;|
|UCost||=||user costs (travel time costs, operating costs, and safety costs) for either the base case B or the improved case I;|
|ACost||=||agency costs (maintenance costs) for either the base case B or the improved case I;|
|ECost||=||external costs (emissions costs) for either the base case B or the improved case I;|
|RV||=||residual value of the improvement relative to the base case; and|
|ImpCost||=||the capital cost of either the base case B or the improved case I, or zero when the base case is unimproved.|
The actual process is slightly more complex. When the benefit-cost analysis period is longer than one funding period in length, benefits must be calculated and accrued for each period. These accruing benefits are then discounted back to the time of implementation.
The introduction of demand elasticity results in different traffic volumes for the base and improved case in each subsequent period. This yields an incremental consumer surplus that must be included in the IBCR calculations for benefit components that are dependent upon VMT (HERS calculates consumer surplus for operating cost benefits, safety benefits, travel time benefits, and user charges that are included in the generalized price; the last portion does not reflect a cost saving but, rather, a willingness to pay for the added or deterred travel).
In Figure 7-1 the base case is represented by the price p0 and the volume q0, which intersect on the demand curve. In HERS, the "price" is a generalized price or cost to the user that includes travel time, vehicle operating costs, accident risk, and user charges (emissions and agency costs are omitted from the price). The price to the user after improvement is represented by p1, and results in movement along the demand curve to yield the increased volume q1. The rectangle labeled "user benefits" represents lower user costs on trips which would have been made had the improvement not changed the price to the user. The triangle labeled "incremental consumer surplus" represents benefits from the additional trips that result from the lower price.
For each funding period, HERS first determines the gross benefit for each of the benefit components: travel time benefits, safety benefits, and operating cost benefits (grouped as user benefits); maintenance cost benefits (agency benefits); and emission cost benefits (external benefits). Maintenance costs are calculated per lane mile; all other components are per vehicle mile traveled. For each of the components, the benefit is:
|BEN = COSTB ∠ COSTI|
|BEN||=||the benefit for a specific cost component;|
|COSTB||=||the base case cost for a specific cost component; and|
|COSTI||=||the improvement case cost for a specific cost component.|
HERS also computes a discount factor based upon the user-specified discount rate:
|DFACTR = DRATE(LFP × (FPC ∠ 0.5))|
|DRATE||=||1 + the user-specified discount rate divided by 100;|
|LFP||=||length of a funding period in years; and|
|FPC||=||funding period counter pointing to funding period under analysis.|
The discount factor is calculated separately for each funding period in the analysis period. HERS next calculates the "per-vehicle" benefit for user and external benefits:
|BENPV =||LFP × 365 × SLEN × (OPBEN + SAFBEN|
|+ TTBEN + EMBEN)/DFACTR|
|BENPV||=||discounted benefit per vehicle trip;|
|SLEN||=||the section length in miles;|
|OPBEN||=||operating cost benefits per VMT;|
|SAFBEN||=||safety benefits per VMT;|
|TTBEN||=||travel time benefit per VMT; and|
|EMBEN||=||emission cost benefit per VMT.|
The interim total in Equation 7.6 includes the discounted benefits for each mile traveled over the section for each day of the funding period for the benefit components expressed by VMT. However, it does not include traffic volume, neither the "old trips", or the "new trips" which result from the change in user price. HERS calculates the total benefit to include the benefits from "old trips", the consumer surplus, and the discounted maintenance cost savings:
|TOTBEN =||BENPV × AADTB + BENPV|
|×||AADTI ∠ AADTB||+ MNCBEN/DFACTR|
|TOTBEN||=||discounted total benefits for the funding period;|
|AADTB||=||AADT for the base case B;|
|AADTI||=||AADT for the improved case I; and|
|MNCBEN||=||maintenance cost benefit for the period.|
This total, TOTBEN, is calculated for each funding period of the benefit-cost analysis period. When benefits have been calculated for all periods of the benefit-cost analysis period, HERS calculates the IBCR for the improvement:
|IBCR =||TOTBENSUM + RV|
|(IMPCOSTI ∠ IMPCOSTB)|
|IBCR||=||the incremental benefit-cost ratio for the improvement;|
|TOTBENSUM||=||the sum of the discounted total benefits for all funding periods in the benefit cost analysis period;|
|RV||=||the discounted residual value of the improvement;|
|IMPCOSTI||=||the capital cost of the improvement being analyzed; and|
|IMPCOSTB||=||the capital cost of the base case improvement (zero when the base case is "no improvement.")|
When considering one or more candidate improvements for a section, HERS calculates the BCR for each of them relative to the same base case and for the same evaluation period. When the user has not requested mandatory improvements HERS will decide whether or not the section warrants improvement based upon the highest BCR relative to the unimproved base case. HERS will not improve the section if the highest BCR is less than the qualifying threshold. For constrained runs, the threshold is set at 1.0. For minimum BCR runs, the user specifies the minimum BCR in the specification file (the term "economic efficiency run" is used for a minimum BCR run with a minimum BCR of 1.0).
The case of a section where improvement is not warranted by benefit-cost analysis is shown in Figure 7-3. Three potential improvements have been identified for the section, numbered 10, 20, and 30. The cost of each improvement is shown on the x-axis (shown as c10, c20, and c30), and the benefits of each improvement during the benefit-cost analysis period are plotted on the y-axis (b10, b20, and b30). For each improvement, a dotted line is drawn from the origin through the intersection of its costs and benefits depicting the improvement's benefit-cost ratio. These are labeled r100, r200, and r300 (the "r" is for ratio, and the subscript zero indicates that the ratio is relative to improvement zero, the unimproved base case). The dashed line drawn at 45° represents a benefit-cost ratio of 1.0. Potential improvement 10 has the highest benefit-cost ratio, as it is closest to 45°; however, as in the other two cases, the potential benefits are less than the capital costs, and the section will not be improved.
Figure 7-4 illustrates the case of a section where two of the potential improvements have benefit-cost ratios greater than 1.0. In this case, potential improvement 10 has the highest benefit-cost ratio. In a minimum BCR run, either improvement 10 or 20 will be implemented; in a constrained run, improvements 10 and 20 will be eligible for implementation.
When the user has specified mandatory improvements, all sections for which mandatory improvements have been identified are deemed to justify improvement and- unless the funding limits are reached in a constrained fund run- will be improved. Thus, if improvement 10 in Figure 7-3 were a mandatory improvement, it would be implemented even though its benefit-cost ratio is less than 1.0. A discussion of the selection of more aggressive improvements, including the replacement of mandatory improvements, is contained in the next section.
As first presented in Chapter 2, "An Outline of the Model Structure" the HERS process has several variants depending upon the analytical objective and whether the user has stipulated that mandatory improvements must be made to correct unacceptable conditions. Previous sections in this chapter presented the steps HERS uses to calculate an improvement's BCR and to determine whether a section warranted improvement during the current funding period. This section examines the HERS methods for deciding which improvement to implement on sections warranting improvement and, during a constrained run, which of the sections warranting improvement will be improved and which will not be improved. The first part of this section examines the process when no mandatory improvements have been specified by the user, first for minimum BCR runs, followed by the process for constrained runs. The second portion of this section contains a discussion of how mandatory improvements are involved in the selection process for each of the three analytical objectives.
In most cases, the HERS model is run without the specification of mandatory improvements (this includes runs used in preparation of the 1995, 1997, 1999 and 2002 C&P Reports). As shown in Figure 2-4 "HERS Process Flow Without Mandatory Improvements" on page 2-8, HERS uses either of two logic flows when selecting improvements without mandatory improvements. When conducting a minimum BCR analysis, HERS is able to select an improvement for each section immediately after evaluating its potential improvements and determining that it warrants improvement during the current funding period. During a constrained run, HERS "pre-selects" a list of improvements for those sections warranting improvement, and, after processing all sections, selects from that list until the specified constraint has been satisfied. These two processes are presented below in more detail.
When the analytic objective stipulates a minimum BCR run, every section which warrants improvement will be improved. For these sections, then, the question HERS asks is: What is the economically most attractive improvement for this section?
To determine that a section warrants improvement during the current funding period, HERS calculates BCRs for all the potential improvements and identifies the improvement with the highest BCR. This improvement is designated the base case improvement. This base case improvement might not be the most desirable improvement to implement during this period. It may be that an improvement that costs more and generates more benefits is more desirable.
In the example shown in Figure 7-5, the length of the benefit-cost analysis period is set to encompass the life of improvement 10. Of the various options, improvement 20 has the highest initial benefit-cost ratio relative to the unimproved base case: it's benefit-cost line (labeled "r20") lies above those for improvements 10 and 30. Improvement 20 has qualified the section for improvement, as its BCR is greater than the minimum threshold of 1.0 (also shown in the figure). Improvements 10 and 30 would also have justified improvement in this funding period. Improvement 20 thus becomes the new base case improvement against which the BCRs of more aggressive improvements will be calculated.
To determine whether a more desirable improvement exists, HERS next identifies all more aggressive improvements worth analyzing. HERS numbers improvements in order of increasing aggressiveness; in the example, Improvement 20 is more aggressive than Improvement 10, but less aggressive than Improvement 30. HERS then estimates the incremental benefits and costs of implementing each more aggressive improvement relative to the new base case improvement.
In general, the more aggressive improvement will incorporate some widening and/or alignment option not included in the base case improvement. If this option is not implemented in the current funding period, it is not likely to be implemented until the section is next resurfaced. Accordingly, the incremental benefits and costs of immediately implementing the more aggressive improvement are analyzed over a time frame that ends when the section would normally next be resurfaced following the implementation of the provisionally selected improvement.
The example continues in Figure 7-6. Here, the new base case is improvement 20, so the model calculates an incremental benefit-cost ratio for improvement 30 relative to improvement 20. The length of the benefit-cost analysis period is determined by the life of improvement 20. When the life of improvement 20 is longer than the life of improvement 10, additional benefits accrue to improvement 30 due to the longer period. In the diagram, the increased benefit level for improvement 30 is labeled "b30lp" and the recalculated BCR (relative to improvement 20) is labeled "r30lp." As the longer-period BCR for improvement 30 is greater than the minimum BCR (MINBCR) specified by the user (the default value is 1.0), improvement 30 will be selected for implementation.
The diagram also shows the BCR for improvement 30 ("r30") calculated without the lengthening of the benefit-cost analysis period. This case would apply when the life of improvements 10 and 20 are the same1. This BCR is also greater than MINBCR, with the result that improvement 30 would be selected for implementation. Note that the two BCRs for improvement 30 are drawn as originating from the intersection of improvement 20's costs and benefits. This is because the BCRs are calculated relative to the "base case" of improvement 20. The line representing the minimum BCR threshold of 1.0 also originates from this point.
In a constrained run, whether the constraint is a performance goal or a funding limit, it is possible that not all sections warranting improvement will actually be improved. HERS uses benefit-cost analysis to identify the most attractive set of improvements to meet the analytical objective. If the constraint is a funding limit, the model chooses the set of improvements that will return the greatest net benefit for the capital investment. When the constraint is the attainment of a specified level of highway system performance, the model chooses the set of improvements that will meet the goal with the least expenditure of capital.
Conceptually, the method is easily visualized: calculate BCRs for all possible improvements for all sections, order them by BCR, and select them for implementation in order of economic attractiveness until the constraint/goal is reached. The process is the same for the two types of constraints: the difference is in determining that the constraint has been reached, either (a) all the funds have been expended, or (b) enough improvements have been implemented to satisfy the performance goal.
In practice, HERS uses a ‘two-listed' approach which avoids calculating incremental BCRs for more aggressive improvements until they are actually candidates for selection. As with the minimum BCR option, HERS calculates BCRs for all candidate improvements to determine whether the section warrants improvement during the current funding period. Having identified the candidate improvement with the highest initial BCR, that improvement is placed on a list of improvements for potential selection.
Only sections which warrant improvement during the current funding period are represented with an improvement on the potential list. The improvement specified for a section is the one with the highest BCR relative to the unimproved base case. Figure 7-7 diagrams the benefits, costs, and BCRs for three potential improvements to a section. The diagram shows the benefit-cost ratios for improvements 10, 20, and 30, all relative to the unimproved base case (indicated by the subscript 0), as being above the minimum BCR requirement. Of these, the ratio for improvement 10 (labeled "r100") is the highest; the model will put improvement 10 on the list of potential improvements representing this section.
After HERS has processed all the sections in the highway system, it has a list of potential improvements. Each list entry consists of:
- a section number,
- an improvement number,
- and the improvement's BR.
The second list, that of selected improvements, is ordered by section number and contains the number of the improvement selected for implementation on the section. If no improvement has been selected for a section, zero is used as the improvement number. Initially, all list entries are set to zero.
HERS proceeds by sorting the potential improvement list by BCR. The list is processed in order of descending BCR. HERS takes the number of the improvement on the top of the potential list and places it on the list of selected improvements. The model then checks whether implementing this improvement violates the funding constraint or satisfies the performance goal.1
If not, it examines any more aggressive improvements which may have been identified for the section. HERS calculates incremental BCRs for all more aggressive improvements using a benefit-cost analysis period that corresponds to the life of the base case improvement. The "most recently selected" improvement (the one just moved to the selected list) is used as the base case.
This step is illustrated in Figure 7-8. In this diagram the BCRs for improvements 20 and 30 and the minimum BCR of 1.0 are redrawn to be relative to improvement 10. The length of the benefit-cost analysis period is set to the life of improvement 10 (which was also the time period used in the initial calculations as shown in Figure 7-7). The BCR for improvement 20 is greater than the threshold of 1.0. HERS adds improvement 20 to the list of potential improvements; its placement on the list depends upon its BCR. For this section, improvement 10 is now entered on the list of selected improvements, and improvement 20 is on the list of potential improvements.
1. In order to guarantee that net benefits are maximized given the constraint, some special code is required when full implementation of either improvement results in exceeding a funding constraint or a benefits goal. In this situation, the more aggressive improvement is implemented on some of the mileage represented by the sample section, and no improvement is implemented on the remaining mileage; the number of miles to be improved is determined so that the specified objective is just reached.
The model continues the process of moving improvements from the potential list to the selected list. Should the constraints permit, it will eventually come to the example section's improvement 20 on the potential list. HERS repeats the process, as shown in Figure 7-9.
At this point, improvement 20 represents the most economically attractive improvement option available within the system. HERS moves improvement 20 from the potential list to the selected list and improvement 20 becomes the base case for analyzing subsequent improvements; HERS will now use the expected life of improvement 20 as the length of the benefit-cost analysis period. Figure 7-9 illustrates the case when the life of improvement 20 is the same length as the previously selected improvement. Improvement 30's BCR relative to improvement 20 (represented by "r3020") lies below the minimum BCR threshold of 1.0, and therefore it will not be considered a candidate for potential implementation.
It is possible that the expected life of improvement 20 is longer than that of improvement 10. When this is the case, the benefit-cost analysis period (BCAP) for improvement 30 (and other more aggressive improvements, should they exist) is extended to the funding period in which improvement 20 would next be improved. Figure 7-10 presents an illustration of this analysis.
The label "b3020" on the Benefits axis represents the additional benefits which accrue to improvement 30 as a result of the extended BCAP. The capital cost of improvement 30 does not change. The additional benefits are sufficient to raise improvement 30's BCR above the 1.0 threshold, so HERS adds improvement 30 to the list of potential improvements, with its placement in the list determined by its BCR. Should the constraints permit, it will be implemented in its turn.
Note that had sufficient additional benefits accrued to improvement 30, its BCR ("r3020") could have exceeded improvement 20's BCR ("r2010"). If this were the case, improvement 30 would immediately supplant improvement 20 on the list of selected improvements, thus skipping the potential list entirely.
The HERS process for identifying mandatory improvements is presented in section 220.127.116.11 "Addressing Unacceptable Conditions: the Optional First Pass" on page 4-15. Typically, all mandatory improvements will be selected for implementation. The two exceptions are when there are insufficient funds to implement all mandatory improvements (this applies to fund-constrained runs only), and when a selected mandatory improvement is replaced by a more aggressive improvement.
When a mandatory improvement has been identified for a section during the first processing pass, it is subsequently identified as the base case improvement during analysis of more aggressive improvements (when mandatory improvements are not being considered, the unimproved case is used as the base case). This may result in the implementation of an improvement with a BCR below the usual threshold of 1.0. While this may seem anomalous in an economic model, the mandatory improvement feature is provided to allow the user to ensure that highways in unacceptably poor condition are improved regardless of whether the improvements can be justified economically.
Figure 7-11 presents an example. During the initial pass, improvement 10 was selected as a mandatory improvement for the section. As a mandatory improvement, its BCR (designated r10) does not have to meet a minimum threshold. Improvement 20 was identified during the second pass, and its incremental BCR (shown as r2010) was calculated using improvement 10 as the base case with the length of the analysis period set to the life of improvement 10.
While improvement 20 is certainly more attractive than the mandatory improvement 10 (r20 lies above r10), neither would have been selected had the user not specified the correction of unacceptable conditions, as both of their BCRs are less than 1.0 relative to an unimproved base case (both r10 and r20 lie below the threshold designated 1.0.). Because the mandatory improvement 10 was used as the base case, however, the model calculates improvement 20's BCR relative to improvement 10, shown in Figure 7-11 as r2010. This BCR lies above the threshold 1.010, which is relative to improvement 10. The model therefore replaces improvement 10 with improvement 20.
The case illustrated represents a possibility which can occur in both constrained and minimum BCR runs when mandatory improvements are specified, and results from the use of the mandatory improvement as the base case. Note that the objective of the mandatory improvement of unacceptable conditions is still achieved: unacceptable conditions are corrected. And while the replacement improvement (improvement 20 in the example) is not in itself attractive, it is an economically more attractive improvement than the one it replaces.
During a constrained fund run, HERS uses benefit-cost analysis to select among potential improvements until the available funds are expended. The user electing to have unacceptable conditions identified and corrected during a constrained fund run will designate a portion of the total funds for this purpose. If the designated funds are sufficient to implement all mandatory improvements identified in the first pass, the remaining funds are available for the correction of other deficiencies during the second pass.
If the designated funds are insufficient, then benefit-cost analysis is used to select the most economically attractive of the mandatory improvements for implementation. The procedure used is the same as presented above for constrained runs (see section 7.11.2), except that the universe of potential improvements consists only of the mandatory improvements identified during the first pass through the sections. Those mandatory improvements not selected at this point are placed on the list of potential improvements and will be evaluated for implementation during the second pass, competing (on the basis of their relative BCR values) with non-mandatory improvements for the non-reserved funds.
During the second pass, improvements selected as mandatory may be replaced by a more aggressive improvement on that section if it presents a more economically attractive alternative.
It is important to consider carefully the designation of funds for the correction of unacceptable conditions. Consider the case where, during the initial funding period of a run, a large number of unacceptable conditions may be identified, and funds remaining for use during the second pass may be very limited. In the case of a section with two deficiencies, including one that is unacceptable, only the unacceptable deficiency would be corrected during the initial funding period. The other deficiency would frequently be corrected with a separate improvement selected during a subsequent funding period - an inefficient means of correcting the two deficiencies. For this reason, when the option of correcting unacceptable conditions is exercised, it is desirable that at least some funds be reserved in each period for implementing more aggressive improvements. HERS allows the user to specify either (a) specific funding levels for the correction of unacceptable conditions, or (b) a maximum percentage of available funds that can be allocated for mandatory improvements for each combination of functional classes during any funding period (see section 2.10, "Functional Classes," page 2-13, for the combinations of functional classes recognized by HERS).
During a performance constrained run, HERS uses benefit-cost analysis to select among potential improvements until designated system performance levels are met. The user may either specify explicit levels of performance or require that the program maintain the current level of system performance. If the user selects to have unacceptable conditions identified and corrected during such a run, the program executes the first loop to identify sections with unacceptable conditions and improvements for their correction. If implementing all such improvements would improve the system beyond the specified level, all the mandatory improvements are implemented, and no more aggressive improvements are identified. In this case, unlike the constrained fund run, HERS does not use benefit-cost analysis to select the smallest (and most economically attractive) set of mandatory improvements which meet the specified goal.
Should the implementation of all identified improvements not bring the system performance level to the desired goal, the second pass procedures are exercised to identify deficiencies and improvements. As in the case of the Constrained Fund run, a more aggressive improvement may be selected to replace an improvement originally selected to correct an unacceptable condition.
During a minimum BCR run, HERS evaluates potential improvements for all deficient sections and selects the most aggressive improvement with an incremental BCR above the user-specified minimum. If the user opts to have unacceptable conditions identified and corrected during such a run, the program executes the first loop to identify sections with unacceptable conditions and improvements for their correction. The model then executes the second loop to identify improvements to correct "normal" deficiencies and to identify more aggressive improvements.
Each section found to be in unacceptable condition by the first processing loop will be improved, either with the improvement which corrects the unacceptable condition or by a more aggressive improvement. In this case, as with constrained runs, improvements originally selected to correct unacceptable conditions are implemented regardless of their BCR unless superseded by a more aggressive improvement. As depicted in Figure 7-11, the more aggressive improvement which replaces a mandatory improvement may not in itself have qualified for implementation had its incremental BCR not been calculated against the mandatory improvement.
As in a minimum BCR run in which the option to correct unacceptable conditions was not exercised, economically attractive improvements from the second processing loop will be implemented if their incremental BCRs are above the specified threshold.
This section details how HERS-ST estimates the user benefits and improvement costs of user-specified improvements and also the corresponding incremental benefits and incremental costs of replacing a user-specified improvement by a more aggressive improvement.
If the cost of any user-specified improvement is provided, HERS-ST uses that cost as the cost of the improvement. Otherwise, if the improvement is a HERS-type improvement, the cost is estimated using the HERS-ST procedure for estimating improvement costs. If no cost is provided for a special improvement, HERS-ST prints a warning message and sets the improvement cost to a default value.
When evaluating the possibility of replacing a HERS-type user-specified improvement (e.g., resurfacing, as identified by a State's Pavement Management System) by a more aggressive improvement (e.g., resurface and add lanes), HERS-ST estimates the incremental cost of replacing the former improvement by the latter one. This incremental cost is estimated as the difference between estimates of the costs of the two improvements that are both obtained using HERS' procedure for estimating improvement costs (regardless of whether the user has provided an exogenous cost estimate for the user-specified improvement).
Consider the possibility of replacing a non-HERS-type user-specified improvement (Type divisible by 20) by a combination of that improvement and a HERS-type of improvement. The cost of the combined improvement is estimated by using the HERS-ST procedure for estimating improvement costs to estimate the cost of the HERS-type of improvement, and adding this cost to the cost of the original user-specified improvement. Thus, the resulting estimate of the incremental cost of adding the HERS-type improvement ignores any efficiencies obtained by implementing both improvements simultaneously; and so there may be a tendency to overestimate the incremental cost.
If the first improvement applies only to an intersection or interchange and the second applies to an entire section, this effect is likely to be fairly small and so may be ignored. However, if both improvements apply to the entire section, the effect may be more significant. For this reason, HERS-ST will tend to overestimate the incremental cost of adding a HERS-type improvement to a user-specified improvement that affects an entire section. Also for this reason, HERS-ST requires that the override flag be set to one for user-specified improvements that combine HERS-type and non- HERS-type improvements.
HERS-ST estimates the user benefits of an improvement as the net reduction in user costs resulting from changes in the physical characteristics of the improved section (including increases in the number of lanes) and from the resulting increases in capacity and average speed.
In the case of user-specified improvements, the user specifies any increase in the number of lanes and any increase in capacity of the section. The user benefits of a non-HERS-type improvement (Type divisible by 20) are estimated entirely from these two increases. For such improvements, if both fields are zero, estimated benefits will be zero. (However, if only the second field is zero, increased capacity will be estimated from the increase in the number of lanes.)
User-specified improvements that either are purely HERS-type (Type < 20) or are a combination of HERS-type and non-HERS-type (Type not divisible by 20), may produce other changes in the physical characteristics of the section. These are simulated by HERS-ST, and thus they provide another potential source of information for estimating user benefits. For these sections, the estimates of user benefits reflect any non-capacity effects of these changes plus either the user-coded change in capacity or, if the capacity change is not coded, the HERS-ST estimate of change in capacity.
When evaluating the possibility of replacing a user-specified improvement by a more aggressive improvement, HERS-ST estimates the incremental user benefits of the replacement by analyzing the effects of the replacement on the physical characteristics of the section and the resulting effects on user benefits. This process is straight-forward when the capacity effects of the user-specified improvement are not supplied by the user (but calculated by HERS-ST), but it requires some clarification for the case in which the user specifies these effects. In the latter case, HERS-ST distinguishes several different estimates of capacity:
- Estimated capacity before implementation of the user-specified improvement.
- Estimated capacity after implementation of this improvement - obtained by adding the user-coded capacity effect of the improvement to .
- A separate estimate of capacity after implementation of the improvement that is produced by HERS-ST entirely from the physical characteristics of the section after improvement (ignoring the user-coded capacity effect).
- HERS-ST's estimate of capacity after implementation of the more aggressive improvement (obtained entirely from the physical characteristics of the section without reference to the user-specified capacity effect of the original improvement).