A Generic Model of Motor-A Generic Model of Motor-Carrier Fuel OptimizationCarrier Fuel Optimization

Yoshinori SuzukiYoshinori Suzuki

IntroductionIntroduction

Efficient management of fuel cost is an Efficient management of fuel cost is an important issue for carriersimportant issue for carriers Price is high and increasing Price is high and increasing Many carriers are going out of businessMany carriers are going out of business

Fuel optimizers are increasingly recognized as Fuel optimizers are increasingly recognized as efficient fuel management tool by TL carriersefficient fuel management tool by TL carriers

Fuel OptimizerFuel Optimizer

Step 1: Route optimization Step 1: Route optimization Shortest route between origin and Shortest route between origin and

destinationdestination Some products consider toll costsSome products consider toll costs

Step 2: Fuel optimizationStep 2: Fuel optimization Downloads fuel price of every truck stop Downloads fuel price of every truck stop

(U.S. and Canada)(U.S. and Canada) Determines which truck stop to use and how Determines which truck stop to use and how

many gallons to buymany gallons to buy ProMiles, Expert Fuel, Fuel & Route, Fuel ProMiles, Expert Fuel, Fuel & Route, Fuel

AdviceAdvice Cost savings = $1,200 per truck per yearCost savings = $1,200 per truck per year

LimitationsLimitations Considers only the fuel costConsiders only the fuel cost

The model’s DVs (decision variables) affect The model’s DVs (decision variables) affect other costs tooother costs too

Maintenance, depreciation, opportunity Maintenance, depreciation, opportunity costscosts

Carriers may be minimizing fuel costs at the Carriers may be minimizing fuel costs at the expense of increased costs for other elementsexpense of increased costs for other elements

Fuel optimizer may not provide the truly Fuel optimizer may not provide the truly optimal fueling solution from the overall cost-optimal fueling solution from the overall cost-minimization perspectiveminimization perspective

Study GoalStudy Goal Develop a now type of fuel optimizerDevelop a now type of fuel optimizer Considers not only the fuel cost but also other Considers not only the fuel cost but also other

costs that are:costs that are: Functions of fuel-optimizer DVsFunctions of fuel-optimizer DVs Not considered by commercial fuel optimizersNot considered by commercial fuel optimizers

A “generic” model that converges to the A “generic” model that converges to the standard form under certain conditionsstandard form under certain conditions

We show that, under the generic approach:We show that, under the generic approach: Fueling solution will be considerably differentFueling solution will be considerably different Overall cost may become noticeably lowerOverall cost may become noticeably lower

Product History & LiteratureProduct History & Literature Initial fuel optimizer developed in mid 1990s by a Initial fuel optimizer developed in mid 1990s by a

transportation consulting companytransportation consulting company Address concerns that fuel prices vary from on Address concerns that fuel prices vary from on

truck stop to the next within routestruck stop to the next within routes Buy more gallons at cheap truck stops and buy Buy more gallons at cheap truck stops and buy

fewer gallons at expensive truck stopsfewer gallons at expensive truck stops Limited literature and conducted only recentlyLimited literature and conducted only recently

Lin (2007) – fixed route fuel optimizationLin (2007) – fixed route fuel optimization Lin et al. (2007) – joint determination of route and Lin et al. (2007) – joint determination of route and

fuel decisionsfuel decisions Khuller et al. (2007) – fueling decisions in Khuller et al. (2007) – fueling decisions in

traveling salesman problemstraveling salesman problems

Literature (cont.)Literature (cont.) No studies have explicitly considered non-fuel costsNo studies have explicitly considered non-fuel costs Nor have they examined how the model with non-fuel costs Nor have they examined how the model with non-fuel costs

performs relative to the standard fuel optimizersperforms relative to the standard fuel optimizers In this study we:In this study we:

Develop a model that mimics standard modelsDevelop a model that mimics standard models Enhance the model by incorporating non-fuel cost Enhance the model by incorporating non-fuel cost

elementselements Empirically investigate the performance of the enhanced Empirically investigate the performance of the enhanced

model (relative to standard models) by using Monte-Carlo model (relative to standard models) by using Monte-Carlo simulationsimulation

The Commercial Fuel OptimizersThe Commercial Fuel Optimizers Considers following factors while optimizing:Considers following factors while optimizing:

Tank capacity Tank capacity Starting fuelStarting fuel Ending fuelEnding fuel MPG (fuel consumption rate)MPG (fuel consumption rate) Minimum gallons to maintain at all timesMinimum gallons to maintain at all times Out-of-route (OOR) distance to each candidate truck Out-of-route (OOR) distance to each candidate truck

stopstop Customizable constraints (practical)Customizable constraints (practical)

Set of truck stops to be consideredSet of truck stops to be considered Network truck stopsNetwork truck stops Minimum purchase quantityMinimum purchase quantity

Mimic Standard ModelsMimic Standard Models

Model formulation shown in the manuscriptModel formulation shown in the manuscript Mixed-Integer Liner Programming modelMixed-Integer Liner Programming model Easy to solve with standard Simplex and B&B Easy to solve with standard Simplex and B&B

algorithmsalgorithms Verified the model solutions by using ProMilesVerified the model solutions by using ProMiles Will be used as a benchmark model during the Will be used as a benchmark model during the

simulation experimentssimulation experiments

Costs Ignored by Standard ModelsCosts Ignored by Standard Models

Based on interviews with 4 TL carriers, 3 drivers, Based on interviews with 4 TL carriers, 3 drivers, 2 fuel-optimizer vendors, 2 truck-stop chains2 fuel-optimizer vendors, 2 truck-stop chains

Ignored costsIgnored costs Vehicle maintenance cost Vehicle maintenance cost Vehicle depreciation costVehicle depreciation cost Opportunity cost of OOR milesOpportunity cost of OOR miles Opportunity cost of fuel stopsOpportunity cost of fuel stops

Underestimated costUnderestimated cost Fuel cost (highway vs. OOR roads)Fuel cost (highway vs. OOR roads)

ImplicationsImplications May minimize fuel cost but not overall vehicle May minimize fuel cost but not overall vehicle

operating costoperating cost

Proposed ModelProposed Model(Fuel Optimizer II)(Fuel Optimizer II)

Objective: Minimize the overall vehicle operating Objective: Minimize the overall vehicle operating cost between origin and destinationcost between origin and destination

Includes fuel cost, driver wage, depreciation cost, Includes fuel cost, driver wage, depreciation cost, maintenance cost (over 95% of vehicle operating maintenance cost (over 95% of vehicle operating cost)cost)

Plus the opportunity costs of OOR mils and fuel Plus the opportunity costs of OOR mils and fuel stopsstops

Fuel cost is properly adjustedFuel cost is properly adjusted Driver wage is not explicitly considered, as this cost Driver wage is not explicitly considered, as this cost

is constant (from optimization standpoint)is constant (from optimization standpoint) Drivers are paid by “billed miles” rather than Drivers are paid by “billed miles” rather than

“odometer miles”“odometer miles”

Model FeaturesModel Features Considers many other costs but: Considers many other costs but:

Retains the desirable linear formRetains the desirable linear form Same number of DVs and constraintsSame number of DVs and constraints Solution time is similarSolution time is similar

Generic form of the standard modelGeneric form of the standard model Reduces to the standard form if other costs = 0Reduces to the standard form if other costs = 0 Allows users to choose the costs to minimize Allows users to choose the costs to minimize

(depending on situation)(depending on situation) Desirable solutions for driversDesirable solutions for drivers

Less OOR milesLess OOR miles Less fuel stopsLess fuel stops Driver compliance rate may become higherDriver compliance rate may become higher

Simulation ExperimentsSimulation Experiments Compares Fuel Optimizer II with Fuel Compares Fuel Optimizer II with Fuel

Optimizer I (standard fuel optimizer) Optimizer I (standard fuel optimizer) Data from 4 TL carriers, 3 drivers, 2 fuel-Data from 4 TL carriers, 3 drivers, 2 fuel-

optimizer vendors, ProMilesoptimizer vendors, ProMiles Simulation ProcedureSimulation Procedure

Truck refueling problems randomly generatedTruck refueling problems randomly generated Each problem is solved by both Fuel Each problem is solved by both Fuel

Optimizers I and II (Simplex and B&B)Optimizers I and II (Simplex and B&B) Compare solutions (fuel cost & overall cost)Compare solutions (fuel cost & overall cost)

Repeat the procedure 1,000 times for each Repeat the procedure 1,000 times for each experiment (solve 2,000 MILP problems)experiment (solve 2,000 MILP problems)

3 experiments (medium, long, very long hauls)3 experiments (medium, long, very long hauls)

Model Inputs (Selected)Model Inputs (Selected) Opportunity cost of OOR miles Opportunity cost of OOR miles

Calculate expected saved time per OOR mileCalculate expected saved time per OOR mile Expected profit per saved time (best alternative way)Expected profit per saved time (best alternative way)

Opportunity cost of fuel stopOpportunity cost of fuel stop Calculate expected saved time per fuel stop (beyond Calculate expected saved time per fuel stop (beyond

the minimum stops)the minimum stops) Expected profit per saved time (best alternative way)Expected profit per saved time (best alternative way)

Ending fuelEnding fuel Large value if the exp. fuel cost in the next route is Large value if the exp. fuel cost in the next route is

higher than that in the current routehigher than that in the current route Small value if the exp. fuel cost in the next route is Small value if the exp. fuel cost in the next route is

lower than that in the current routelower than that in the current route

Simulation ResultsSimulation Results

OOR miles significantly lower for II than I OOR miles significantly lower for II than I May not make sense to go extra mile or two May not make sense to go extra mile or two

to reach cheap truck stopsto reach cheap truck stops Fueling frequency significantly lower for II than IFueling frequency significantly lower for II than I

Should not fuel too frequently, but should not Should not fuel too frequently, but should not over-reduce frequency either over-reduce frequency either

Purchased fuel “per stop” is higher for II than I, Purchased fuel “per stop” is higher for II than I, but purchased fuel “per trip” is lower for II than I but purchased fuel “per trip” is lower for II than I Intuitively sound resultsIntuitively sound results Fuel Optimizer II may provide “greener” or Fuel Optimizer II may provide “greener” or

more “environmentally friendly” solutionsmore “environmentally friendly” solutions

Fuel Optimizer I Fuel Optimizer II

Experiment 1 (500 - 1,000 miles)Number of fuel stops per tripa 1.55 1.30 - 0.25 ***Out-of-route miles per trip 0.57 0.41 - 0.16 ***Purchased fuel per stop (gal.) 75.67 89.75 14.08 ***Total purchased fuel per trip (gal.) 117.01 116.49 - 0.51 *Fuel purchasing cost per trip 285.66 285.82 0.16Total vehicle cost per trip 513.32 510.60 - 2.73 ***

Experiment 2 (1,000 - 2,000 miles)Number of fuel stops per tripa 2.80 2.27 - 0.53 ***Out-of-route miles per trip 1.00 0.68 - 0.32 ***Purchased fuel per stop (gal.) 83.64 102.72 19.08 ***Total purchased fuel per trip (gal.) 234.03 233.27 - 0.76 *Fuel purchasing cost per trip 568.74 569.01 0.27Total vehicle cost per trip 1,032.35 1,027.22 - 5.13 ***

Experiment 3 (2,000 - 3,000 miles)Number of fuel stops per tripa 4.57 3.64 - 0.93 ***Out-of-route miles per trip 1.65 1.11 - 0.54 ***Purchased fuel per stop (gal.) 87.80 110.12 22.32 ***Total purchased fuel per trip (gal.) 401.51 401.26 - 0.25 ***Fuel purchasing cost per trip 972.44 975.41 2.97 ***Total vehicle cost per trip 1,755.69 1,749.21 - 6.47 ***

* p - value < 0.05, ** p - value < 0.01, ***p - value < 0.001 (paired t - test).a Average MRS (minimum required stops) were 1.215, 1.974, and 3.022, for experiments 1, 2, and 3, respectively.

Table 2: Comparisons of Fuel Optimizer I and Fuel Optimizer II

Difference (II - I)

Results (cont.)Results (cont.)

Overall vehicle operating cost significantly Overall vehicle operating cost significantly lower for II than for I lower for II than for I Fuel Optimizer II does a better job of Fuel Optimizer II does a better job of

reducing the overall cost (expected)reducing the overall cost (expected) Fuel cost lower for I than for IIFuel cost lower for I than for II

Fuel Optimizer I does a better job of reducing Fuel Optimizer I does a better job of reducing fuel cost (expected)fuel cost (expected)

The difference is not always significant The difference is not always significant The cost saving of II over I can be largeThe cost saving of II over I can be large

Especially for large carriersEspecially for large carriers II may outperform I by about 32%II may outperform I by about 32%

Medium Carrier Large Carrier Very-Large Carrier(1,000 trucks) (5,000 trucks) (10,000 trucks)

Exp. cost saving per mile ($) a 0.00321 0.00321 0.00321

Exp. saving per truck per year ($) b 385.74 385.74 385.74

Overall cost saving per year ($) 385,741 1,928,704 3,857,408

a Average of three simulation experimentsb Annual mileage of 120,000 per truck (class-8 tractors) is assumed (see, e.g., ActionLine [1]).

Table 3: Annual cost savings of Fuel Optimizer II (over Fuel Optimizer I) by carrier size

ImplicationsImplications Fuel Optimizer vendors should consider Fuel Optimizer vendors should consider

modifying their models modifying their models Minimize cost from overall perspectiveMinimize cost from overall perspective Fuel Optimizer II gives not only lower cost but Fuel Optimizer II gives not only lower cost but

also more desirable solutions for driversalso more desirable solutions for drivers Interviews indicate that TL carriers will Interviews indicate that TL carriers will

welcome this type of modelwelcome this type of model Current users of Fuel Optimizer I may want to:Current users of Fuel Optimizer I may want to:

Limit the candidates to those with small OORLimit the candidates to those with small OOR Use large value for minimum purchase Use large value for minimum purchase

quantityquantity May obtain solutions similar to IIMay obtain solutions similar to II

Summary & Future ResearchSummary & Future Research

Fuel Optimizer II is Fuel Optimizer II is Capable of incorporating non-fuel costs that Capable of incorporating non-fuel costs that

are ignored or underestimated currentlyare ignored or underestimated currently Better model that can lower overall costBetter model that can lower overall cost Flexible model that allows users to choose the Flexible model that allows users to choose the

costs to minimizecosts to minimize Attractive to drivers so that it may improve the Attractive to drivers so that it may improve the

driver compliance ratesdriver compliance rates Fuel Optimizer II limitation isFuel Optimizer II limitation is

It does not consider MPG by road classIt does not consider MPG by road class Future research may incorporate GIS Future research may incorporate GIS

database to improve accuracy of fuel database to improve accuracy of fuel consumption calculationconsumption calculation

Discussion QuestionsDiscussion Questions

When is Fuel Optimizer II more beneficial When is Fuel Optimizer II more beneficial than Fuel Optimizer I?than Fuel Optimizer I?

What are the main features of Fuel What are the main features of Fuel Optimizer II?Optimizer II?

Is Fuel Optimizer II always better than Is Fuel Optimizer II always better than Fuel Optimizer I? Why?Fuel Optimizer I? Why?

What type of carriers would benefit the What type of carriers would benefit the most by using Fuel Optimizer I?most by using Fuel Optimizer I?

What other costs may be included in the What other costs may be included in the model?model?