transportation cost estimation - purdue universitysrg/book/files/pdf/4. estimating age… · s =...
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Transportation Decision-makingPrinciples of Project Evaluation and Programming
Transportation Cost Estimation
Kumares C. Sinha and Samuel Labi1
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Transportation Costs
Classification of CostsAgency CostsUser Costs/Community CostsCost Functions
HighwayTransitAir
Issues in Cost Estimation
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Classification
By Incurring PartyAgencyUserNonuser or Community Costs
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Cost categories
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Cost Categories – Details of Agency Costs
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Cost Categories – Details of User Costs
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Cost Categories – Details of Community Costs
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Cost Variation with Output Volume
TC (V) = k + f(V)k = Fixed Costf (V) = Variable CostV = Output
Ratio of Variable Cost to Fixed Cost- Is an Indicator of Economy of Scale
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By the Expression of Unit Cost
Average Total Cost, ATC =
Average Fixed Cost =
Average Variable Cost =
Marginal Cost Vs. Average Cost
Ratio of Small Increment of Cost to a Small Increment of OutputMC =
VTC
VFC
VVC
VC
δδ
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MC and AC can differ significantly$10 million to build a 10-mile highway$10.5 million for 11-mile
AC’s are $1 million and $0.954 millionMC of additional 0.5 mile $0.5 million
• MVC =
• MTC =
VVCδδ
TC FC VC VC MVCV V V V
δ δ δ δδ δ δ δ
= + = =
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Table E4.1
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Example: Historical record of operating costs for a metropolitan bus system
Total Average and Marginal Costs
Significance of the interaction between AC and MC
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Illustration- Variation of Different Cost Types
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Illustration- Variation of Different Cost Types
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Illustration- Variation of Different Cost Types
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Solution: When MC < AC, scale economies
Revenue is maximum at the ridership level when MC = AC (@3.7 million)
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TC ($M) = 1.2 + 150V2 , V = monthly output in million of tons
AC =1.2/V + 150 V
MC = 300 V
Optimal Output = 0.09 million tons
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Illustration
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Cost classification by By Position in Facility Life Cycle
Initial or Construction Costs
Subsequent Costs e.g. Maintenance, Operation and Preservation Costs
Life Cycle Costs
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Other Classifications of Costs
In-House vs. Contract
Preventive vs. Corrective
Routine vs. Periodic
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Transportation Agency CostsFor Facilities
Advance PlanningPreliminary EngineeringFinal DesignR-O-W Acquisition and PreparationConstructionOperationsPreservation and MaintenanceSalvage or Disposal
For Rolling StocksAcquisitionOperationPreservationMaintenanceSalvage or disposal
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Techniques for Estimating Agency Costs
A. Disaggregate Approach• By Pay Items
• $ per length, area, or volume or weight of finished product, reported separately for materials, labor and supervision, and equipment use.
• At planning stages, level of identifying pay items and their costing is quite coarse.
• Cost models as a function of facility attributes.
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B. Aggregate Approach1. An average rate per unit output – for various subcategories.2. A statistical model.
Example: Unit cost per lane-mile-station in $M= 3.9 x L 0.702 x U 1.08 x ST -0.36
L = number of line-milesU = fraction underground
ST = number of stations
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Risk as an Element of Agency Cost
Is due to Uncertainties in Estimationpossible outcomesprobability of each outcomeconsequences of decisionsexpected valueMonte Carlo samplingdefined probability distribution
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Due to DisastersNatural or Man-madeVulnerability Cost =
(Pr )obability of Disaster Cost of Damage×∑
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User Costs
Travel TimeSafetyVehicle OperatingNoise, Air and Water Pollution
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Demand and User Cost Interaction
User Benefits DemandSupply Before Improvement
Supply After ImprovementUnitCost
Quantity
Demand is Inelastic27
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Figure 4.3
Elastic, Induced Trips 28
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Figure 4.4
Elastic Demand - Generated Trips29
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Figure 4.5
W
X
Y
K
Z
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Additional Consumer Surplus May Not be Equal to Change in User Cost
Change in (UC) > Change in (CS)
Change(UC) = (Y + Z) – (X + Y) = Z - X
Change(CS) = (K+X) - W
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Figure 4.6
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Table:
Possible Variables for Agency Cost Functions or Rate
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Highway Cost ModelsCont. Cost = F (Labor, Materials, Equipment Costs, Contract Characteristics, Environment)
VariablesNumber of CrossingsR-O-WEnvironmental ImpactsSoil and Site ConditionsProject SizeProject ComplexityConstruction Delivery MethodUrban/Rural Location
Historical Cost Database by Pay Items
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Transit Cost Models
High Speed RailHeavy RailCommuter RailLight RailMonorailBRTUrban Bus Transit
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Unit Cost of Heavy (Rapid) Rail Construction
UC = 3.906 * LM-0.702 * PU1.076 * ST-0.358
R2 = 0.94Where
UC = Cost Per Line-Mile-Station in $ M(2005)LM = number of Line-MilesPU = Percentage of System UndergroundST = Number of Stations
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Example 1: Heavy Rail
Given12 Line-Miles4 Stations85% Above Ground
Total Cost = (12)(4)[3.906(12-0.702)(151.076)(4-0.358]= $367.68 M
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Table 4.5Light Rail Construction Cost per Mile
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Guideways for Light Rail
Guideway construction accounts for 16-38% of overall capital costs of LRT
Guideway Cost= exp(-1997.92 + 1448.22*Length0.0005 + 553.55Stations0.0005)
R2 = 0.61
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Example 2: Light RailTwo Alternatives
Alternative 1: 21 Miles, 13 StationsAlternative 2: 38 Miles, 22 Stations
Total Guideway CostAlternative 1:
exp(-1997.92 + 1448.22*210.0005 + 553.55*130.0005)= $868.35 M
Alternative 2:exp(-1997.92 + 1448.22*380.0005 + 553.55*220.0005)= $1544.71 M
Average CostAlternative 1: $868.35 M / (21)(13) = $3.18 M / mile-stationAlternative 2: $1544.71 M / (38)(22) = $1.84 M / mile-station
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Stations and Yards for LRT
a. Passenger Station Costs per Station
b. Maintenance Yards and Shops per Unit of Capacity
c. Capacity = Max. Number of Vehicles that can be held in Maintenance Yard.
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Example: Subway LRT
Given: 20 Passenger Stations; 60 Vehicle Capacity
Average Cost of Passenger Station for Subway LRT= $26,982,000
Cost of Stations = 20 x 26,982,000 = $539,640,000
Average Cost of Maintenance Yard = $600,000 per unit capacity
Cost of 60 Capacity Yard = 60 x 600,000 = 36,000,000
Total Capital Cost for Stations and Yards = $575,640,000 42
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Rolling Stock Capital Costs for Rail Transit
Avg. Cost/Car ($ Millions)
Heavy Rail 2.3
LRT 2.6
Commuter Rail 2.4
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Rolling Stock Rehabilitation
Avg. Cost/Car ($ Millions)
Heavy Rail 0.84
Commuter Rail 0.99
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BRT Capital Costs
Depend on Location, Type, and Complexity of Construction
Independent at-grade 7.5 million/mileArterial Busways on Median $6.6 Mixed Traffic and/or Curb Bus lanes 1.0
Many Times Higher When Tunnels and Other Features for Exclusive Guideways are involved
See Table 4.11
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Rail Transit Operating Costs
As a Function of Supply-Based Measures Op. cost per mile, per vehicle, per expected VMT
As a Function of Demand-Based Measures Op. cost per passenger, per passenger-hour or passenger-mile
Personnel cost is 70 – 80%
Heavy Rail has the Lowest Op. Cost per Passenger-mile
See Tables 4.12 and 4.1346
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Example:
A LRT with 20 cars @ 330 miles/day
From Table 4.12, Avg. Op. Cost/Revenue Vehicle-Mile = $11.02
Expected Revenue Vehicle-Miles / Year = (330)(365)(20)
Estimated Total Op. Cost / Year = (2,409,000) (11.02) = $26,547,000
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Bus Transit Capital Costs
Acquisition and Rehabilitation of Buses
Construction and Preservation of Terminals, Stations and Maintenance Facilities
Bus Acquisition Costs – Table 4.14
Bus Rehabilitation Costs – Table 4.15
Facilities - $120-140/sq. ft.
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Bus Transit Operating Costs
Cost per Vehicle-Mile = 2.625S0.184 PBR0.029
S = Number of Buses in Maximum Service.PBR = Peak Buses/Off-peak Buses
Unit Op. Cost by System Size and PBR – Table 4.16
Average Capital and Operating Costs by City Size –Tables 4.17 – 4.19
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How to Update Costs?
Use of Price IndicesFHWA Federal-Aid Highway Price IndexFHWA Highway Maintenance and Operating Cost IndexFTA Cost Adjustment Factors
FHWA State Cost Factors (Table 4.20)
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Cost Adjustments for Economies of Scale
The Greater the Project Size, the Lower is the Unit Cost (e.g. Cost per Lane-Mile)
Adjustment for Economics of Scale on the Basis of Unit Aggregate Cost of a Project and Unit Aggregate Cost Function for all Projects of Same Type
Unit Cost Function can be Developed from Historical Contract Data
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Example:
Two Alternative Types, A & B
40-Mile Transit System
CA = -1.05 ln(x) + 5.2
CB = 30/x0.95
where, x = number of line-miles
$207,000 /Ac mile=
$285,000 /Bc mile=
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Figure E4.11 p. 92
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From Cost Function, Unit Cost to be Used Instead of Given Average Cost Values.
System A = $133,000/mile
System B = $90,000/mile
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Problem of Cost Overruns5-14% Underestimation at Planning StageDesign RevisionsUnexpected Site ConditionsConstruction ErrorsWeak Estimates of Inflation
Include a Realistic Contingency Amount
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