Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
The probability of occurrence of two hurricanes is highest as shown by the
Gumbel Distribution in Step 1 C
For x = 2
1 π ⎛ π 1⎞
2r
β = − +
2 ⎜ −
2 ⎟ +
2
2 s ⎝s 2⎠
s
2
2
1 0.05 ⎛0.05 1 ⎞ 2×
0.09
= − +
2 ⎜ −
2 ⎟ +
2
2 0.1 ⎝ 0.1 2 ⎠ 0.1
= 1.68
* 101×
1.68
V = = $719 million
−( 2−1.67)
⎛ −e
0.88
−(2−1.67)
⎞
⎜
⎟
0.88
⎜e
⎟(1.68 −1)
⎜
⎟
⎝
⎠
*
Since V
< V
−(2−1.67)
( 2 1.67)
1.68
⎛
0.88 −e
⎞ ⎛101×
1.68 ⎞
F( 100,101,2,0.05,0.1 ) = (2× 100) e e
0.88
1.68
Gumbel
⎜ ⎟ ⎜ ⎟
⎝
⎠ ⎝ 1.68 −1
⎠
= $17.09 million
− − 1.68−1
Step 3 – Perform analysis to decide if it is worth implementing the strategy/policy
A. Calculate the total cost of implementing the strategy/policy.
B. Calculate the total benefits as a result of implementing the strategy/policy.
C. Perform the analysis to decide if it is worth implementing the strategy/policy.
Step 3 – Perform analysis to decide if it is worth implementing the strategy/policy
A. Total cost of installing the pumping system = $101 million
B. The present value of the damage per hurricane event calculated using the
capital planning methods = $100 million
Option value of the investment opportunity associated with the occurrence of 2
hurricane events per year = $17.09 million
Total benefits = 2 × 100 + 17.09 = $217.09 million
C. Because the benefits are more than the cost in the case of two hurricanes,
which is most likely, it is worth the investment to install the pumping system.
VALUATION OF TRAVEL-TIME RELIABILITY FOR RARE EVENTS Page C-17