Benefit-Cost

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Benefit-Cost

This software supports the cost-effectiveness analysis procedure outlined in Chapter 2 of the 2011 Roadside Design Guide.   Cost-effectiveness is assessed using a benefit/cost (B/C) ratio.   Any reduction in annualized crash costs is considered a benefit while direct costs (i.e., maintenance, construction, right-of-way acquisition, etc.) are considered the "cost," that is, the denominator in the ratio.   The B/C ratio is calculated as follows:

BCRj/i=(CCi - CCj )/(DCj - DCi )

where:

BCRj/i= Incremental B/C ratio of Alternative j with respect to Alternative i,

CCi, CCj= Annualized crash cost for Alternatives i and j and

DCi, DCj= Annualized direct cost for Alternatives i and j.

Calculating the direct costs is relatively straight forward and has been part of publicly funded infrastructure projects since their inception. Calculating the crash costs can be complicated and relies on predictive models and crash data. RSAPv3 supports the tasks necessary to calculate the crash costs using the Encroachment conditional probability model. This model includes a series of conditional probabilities as follows:

<p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;line-height: normal;mso-pagination:none;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:10.0pt;font-family:"Arial","sans-serif"">E <span style="font-size:10.0pt;font-family:"Arial","sans-serif"">(CC)N,M = ADT ∙ LN ∙ P(Encr) ∙ P(Cr|Encr) ∙ P(Sev|Cr) ∙ E(CCs|Sevs)

<p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;line-height: normal;mso-pagination:none;mso-layout-grid-align:none;text-autospace:none">where:

<p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;line-height: normal;mso-pagination:none;tab-stops:1.25in1.5in;mso-layout-grid-align:none; text-autospace:none"><span style="font-size:10.0pt;font-family:"Arial","sans-serif"">  E <span style="font-size:10.0pt; font-family:"Arial","sans-serif"">(CC)N,M =undefinedExpected annual crash cost on segment N for alternative M,

<p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;line-height: normal;mso-pagination:none;tab-stops:1.25in1.5in;mso-layout-grid-align:none; text-autospace:none"><span style="font-size:10.0pt;font-family:"Arial","sans-serif"">  ADT =  <span style="font-size:10.0pt;font-family:"Arial","sans-serif"">Average Daily Traffic in vehicles/day,

<p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;line-height: normal;mso-pagination:none;tab-stops:1.25in1.5in;mso-layout-grid-align:none; text-autospace:none"><span style="font-size:10.0pt;font-family:"Arial","sans-serif"">  LN= Length of segment N in miles,

<p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;line-height: normal;mso-pagination:none;tab-stops:1.25in1.5in;mso-layout-grid-align:none; text-autospace:none"><span style="font-size:10.0pt;font-family:"Arial","sans-serif"">  P <span style="font-size:10.0pt; font-family:"Arial","sans-serif"">(Encr) = The probability a vehicle will Encroachment on the segment,

<p class="MsoNormal" style="margin-top:0in;margin-right:0in;margin-bottom:0in; margin-left:2.0in;margin-bottom:.0001pt;text-indent:-2.0in;line-height:normal; mso-pagination:none;tab-stops:1.25in1.5in;mso-layout-grid-align:none; text-autospace:none"><span style="font-size:10.0pt;font-family:"Arial","sans-serif"">  P <span style="font-size:10.0pt; font-family:"Arial","sans-serif"">(Cr|Encr) = The probability a crash will occur on the segment given that an Encroachment has occurred,

<p class="MsoNormal" style="margin-top:0in;margin-right:0in;margin-bottom:0in; margin-left:2.0in;margin-bottom:.0001pt;text-indent:-138.0pt;line-height:normal; mso-pagination:none;tab-stops:1.25in1.5in;mso-layout-grid-align:none; text-autospace:none"><span style="font-size:10.0pt;font-family:"Arial","sans-serif"">P <span style="font-size:10.0pt;font-family:"Arial","sans-serif"">(Sevs|Cr) = The probability that an crash of severity s occurs given that a crash has occurred and

<p class="MsoNormal" style="margin-top:0in;margin-right:0in;margin-bottom:0in; margin-left:2.0in;margin-bottom:.0001pt;text-indent:-138.0pt;line-height:normal; mso-pagination:none;tab-stops:1.25in1.5in;mso-layout-grid-align:none; text-autospace:none"><span style="font-size:10.0pt;font-family:"Arial","sans-serif"">E(CCs|Sevs)  <span style="font-size: 10.0pt;font-family:"Arial","sans-serif""> = The expected crash cost of a crash of severity s in dollars.