1.201 Introduction to Transportation Systems Transportation CostsTransportation CostsHigh Costs & Poor ProductivityHigh Costs & Poor Productivity: Capacity for Peak LoadsHigh Costs & Poor Productivity: Limits on Vehicle Size/WeightsImproving Costs & Productivity: Tailoring Services to DemandImproving Costs & Productivity: Information & ControlImproving Costs & Productivity: Increasing Vehicle Size/Weight Duality of Costs & Productivity Special Characteristics of Transportation CostsNet Present Value (NPV)AnnuityNetwork ConsiderationsEconomies of Scale Economies of DensityTriple transport tiers in a gorge – interstate plus bike path on opposite side of river from Amtrak (Colorado)Output is Complex – What Measures Are Needed?Example of the Accounting Approach D.L. Shrock, “The Functional Approach to Motor Carrier Costing: Application and LimitationTrucking Example, Continued Trucking Example: Significant Differences Depending Upon Method UsedSelected Cost & Productivity Issues: The Details are Critical!Vehicle CostsExample: Convert Life Cycle cost for A Truck to an Equivalent Truck Cost per Day (i = 10%)A More Expensive Vehicle May Have Better Operating CostA Larger Vehicle Can Earn More RevenueHorse-drawn Wagons competed successfully with Trucks into the 1930sWhen Is Equipment Obsolete?Vehicle Cost & Design IssuesVehicle ExamplesStructuring the Analysis of a Rail RouteFactors Influencing CostsFleet ManagementTerminal CostsClassic Problem of Terminal Management: Cost of Capacity vs. Cost of DelayClassic Problem of Terminal Management: Cost of Capacity vs. Cost of DelayClassic Problem of Terminal Management: Cost of Capacity vs. Cost of DelayTransportation Costs & Productivity1.201 Introduction to Transportation SystemsTransportation CostsCarl D. MartlandCourtesy of Carl D. Martland. Used with permission.Transportation Costs• Introduction & Motivation• Duality of Production Functions & Cost Functions• Types of Cost Functions• Engineering Cost FunctionsHigh Costs & Poor ProductivityPeak Traffic Demands Cause Delays at Bottlenecks Clark Junction, CTAPhoto: C.D. Martland, January 2003High Costs & Poor Productivity:Capacity for Peak LoadsTate Modern Subway Station, London Photo: C.D. Martland, October 2002)High Costs & Poor Productivity:Limits on Vehicle Size/WeightsPhotos: C.D. MartlandImproving Costs & Productivity:Tailoring Services to DemandSan Juan, Puerto Rico (Photo: C.D. Martland)Improving Costs & Productivity:Information & ControlPhoto: C.D. MartlandImproving Costs & Productivity:Increasing Vehicle Size/WeightPhotos: C.D. MartlandDuality of Costs & Productivity• Cost Function– Minimize cost of resources required to produce desired services • Production Function– Maximize value of output obtained from given resourcesBasic Economic Concepts- Differing Perspectives of Economists and Engineers Production functionsEconomists either assume this is known or try to estimate a very aggregate model based upon actual performanceEngineers are constantly trying to "improve productivity", i.e. find better ways to use resources to produce more or better goods and servicesCost functionsBoth use total, average, variable, and marginal costs; engineers go into much greater detail than economistsShort-run and long-run cost functionsEconomists typically focus on effects of volume and pricesEngineers typically focus on costs and capacityDuality of production and cost functionsUsing Average and Marginal CostsProfitability/Subsidy RequirementsComparison of average costs and average revenue Average revenue per trip is a natural way to look at revenue, so this becomes a useful way to look at costsProfitablity of a particular tripComparison of marginal cost and marginal revenueEconomic efficiency (or business common sense)Price = MC (Price > MC)Regulation of industries with declining costsMay need to segment markets and have differential pricing in order to cover total costsFixed vs. Variable CostsFixed CostsUnaffected by changes in activity level over a feasible range of operations for a given capacity or capability over a reasonable time periodFor greater changes in activity levels, or for shutdowns, the fixed cost can of course varyExamples: insurance, rent, CEO salaryVariable CostsVary with the level of activityExamples: construction labor, fuel costs, suppliesIncremental CostsAdded costs for increment of activityFixed, Variable, and Incremental CostsTotal Cost (V) = Fixed Cost + f(volume)Avg. Cost (V) = Fixed Cost/V + f(volume)/VIncremental Cost(V0,V1) = f(V1) - f(v0)Marginal Cost (V) = d(Total Cost)/dV = f'(V) (Assuming we in fact have a differentiable function for variable costs!)Long-Run & Short-Run CostsLong-run costsAll inputs can vary to get the optimal costBecause of time delays in reaching equilibrium and the high costs of changing transportation infrastructure, this may be a rather idealized concept in many systems!Short-run costsSome (possibly many) inputs are fixedThe short-run cost function assumes that the optimal combination of the optional inputs are used together with the fixed inputsA Simple, Linear Cost Function:TC = a + bV = 50 + V, 10 <V<100 TCVCFC10 20 30 40 50 60 70 80 90 100Volume050100150200CostFC VC TCA Simple, Linear Cost Function:Avg Cost = a/V + b = 50/V + 1Marginal Cost (V)= d(TC)dv = b = 1 Marginal CostAverage Cost10 20 30 40 50 60 70 80 90 100Volume 01234567CostAverage Cost Marginal CostClassic Tradeoff: Can we afford higher fixed costs in order to get lower variable costs? Breakeven point B is where TC1 = TC2TC2 = 95 + V/2 TC = 50 + VB10 20 30 40 50 60 70 80 90 100 110 120Volume406080100120140160180CostTC Base TC High TechMore Comments - CEE ProjectsTypical major projects reduce both marginal and average costs per unit of capacityWill there be sufficient demand to allow prices that cover average costs?In general, smaller projects will be better at low volumes until poor service and congestion hurt performanceVolume15202530354045CostBase Large ProjectSome Other Cost TerminologyOpportunity CostA key economic concept! What else could be done with these resources?Sunk CostExpenditures that cannot be recovered and that are common to all options and therefore can be ignored ("focus on the differences")Direct, Indirect, and Standard CostsDirect - easily related to a measurable activity or outputExcavation cost/cu. yd.Indirect (or overhead or burden) -ther costs related to