A Generic Model of Motor- Carrier Fuel Optimization Yoshinori Suzuki

Introduction  Efficient management of fuel cost is an important issue for carriers Price is high and increasing Price is high and increasing Many carriers are going out of business Many carriers are going out of business  Fuel optimizers are increasingly recognized as efficient fuel management tool by TL carriers

Fuel Optimizer  Step 1: Route optimization Shortest route between origin and destination Shortest route between origin and destination Some products consider toll costs Some products consider toll costs  Step 2: Fuel optimization Downloads fuel price of every truck stop (U.S. and Canada) Downloads fuel price of every truck stop (U.S. and Canada) Determines which truck stop to use and how many gallons to buy Determines which truck stop to use and how many gallons to buy  ProMiles, Expert Fuel, Fuel & Route, Fuel Advice  Cost savings = $1,200 per truck per year

Limitations  Considers only the fuel cost The model’s DVs (decision variables) affect other costs too The model’s DVs (decision variables) affect other costs too Maintenance, depreciation, opportunity costs Maintenance, depreciation, opportunity costs  Carriers may be minimizing fuel costs at the expense of increased costs for other elements  Fuel optimizer may not provide the truly optimal fueling solution from the overall cost- minimization perspective

Study Goal  Develop a now type of fuel optimizer  Considers not only the fuel cost but also other costs that are: Functions of fuel-optimizer DVs Functions of fuel-optimizer DVs Not considered by commercial fuel optimizers Not considered by commercial fuel optimizers  A “generic” model that converges to the standard form under certain conditions  We show that, under the generic approach: Fueling solution will be considerably different Fueling solution will be considerably different Overall cost may become noticeably lower Overall cost may become noticeably lower

Product History & Literature  Initial fuel optimizer developed in mid 1990s by a transportation consulting company Address concerns that fuel prices vary from on truck stop to the next within routes Address concerns that fuel prices vary from on truck stop to the next within routes Buy more gallons at cheap truck stops and buy fewer gallons at expensive truck stops Buy more gallons at cheap truck stops and buy fewer gallons at expensive truck stops  Limited literature and conducted only recently Lin (2007) – fixed route fuel optimization Lin (2007) – fixed route fuel optimization Lin et al. (2007) – joint determination of route and fuel decisions Lin et al. (2007) – joint determination of route and fuel decisions Khuller et al. (2007) – fueling decisions in traveling salesman problems Khuller et al. (2007) – fueling decisions in traveling salesman problems

Literature (cont.)  No studies have explicitly considered non-fuel costs  Nor have they examined how the model with non-fuel costs performs relative to the standard fuel optimizers  In this study we: Develop a model that mimics standard models Develop a model that mimics standard models Enhance the model by incorporating non- fuel cost elements Enhance the model by incorporating non- fuel cost elements Empirically investigate the performance of the enhanced model (relative to standard models) by using Monte-Carlo simulation Empirically investigate the performance of the enhanced model (relative to standard models) by using Monte-Carlo simulation

The Commercial Fuel Optimizers  Considers following factors while optimizing: Tank capacity Tank capacity Starting fuel Starting fuel Ending fuel Ending fuel MPG (fuel consumption rate) MPG (fuel consumption rate) Minimum gallons to maintain at all times Minimum gallons to maintain at all times Out-of-route (OOR) distance to each candidate truck stop Out-of-route (OOR) distance to each candidate truck stop  Customizable constraints (practical) Set of truck stops to be considered Set of truck stops to be considered Network truck stops Network truck stops Minimum purchase quantity Minimum purchase quantity

Mimic Standard Models  Model formulation shown in the manuscript  Mixed-Integer Liner Programming model  Easy to solve with standard Simplex and B&B algorithms  Verified the model solutions by using ProMiles  Will be used as a benchmark model during the simulation experiments

Costs Ignored by Standard Models  Based on interviews with 4 TL carriers, 3 drivers, 2 fuel-optimizer vendors, 2 truck-stop chains  Ignored costs Vehicle maintenance cost Vehicle maintenance cost Vehicle depreciation cost Vehicle depreciation cost Opportunity cost of OOR miles Opportunity cost of OOR miles Opportunity cost of fuel stops Opportunity cost of fuel stops  Underestimated cost Fuel cost (highway vs. OOR roads) Fuel cost (highway vs. OOR roads)  Implications May minimize fuel cost but not overall vehicle operating cost May minimize fuel cost but not overall vehicle operating cost

Proposed Model (Fuel Optimizer II)  Objective: Minimize the overall vehicle operating cost between origin and destination  Includes fuel cost, driver wage, depreciation cost, maintenance cost (over 95% of vehicle operating cost)  Plus the opportunity costs of OOR mils and fuel stops  Fuel cost is properly adjusted  Driver wage is not explicitly considered, as this cost is constant (from optimization standpoint)  Drivers are paid by “billed miles” rather than “odometer miles”

Model Features  Considers many other costs but: Retains the desirable linear form Retains the desirable linear form Same number of DVs and constraints Same number of DVs and constraints Solution time is similar Solution time is similar  Generic form of the standard model Reduces to the standard form if other costs = 0 Reduces to the standard form if other costs = 0 Allows users to choose the costs to minimize (depending on situation) Allows users to choose the costs to minimize (depending on situation)  Desirable solutions for drivers Less OOR miles Less OOR miles Less fuel stops Less fuel stops Driver compliance rate may become higher Driver compliance rate may become higher

Simulation Experiments  Compares Fuel Optimizer II with Fuel Optimizer I (standard fuel optimizer)  Data from 4 TL carriers, 3 drivers, 2 fuel- optimizer vendors, ProMiles  Simulation Procedure Truck refueling problems randomly generated Truck refueling problems randomly generated Each problem is solved by both Fuel Optimizers I and II (Simplex and B&B) Each problem is solved by both Fuel 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 experiment (solve 2,000 MILP problems)  3 experiments (medium, long, very long hauls)

Model Inputs (Selected)  Opportunity cost of OOR miles Calculate expected saved time per OOR mile Calculate 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 stop Calculate expected saved time per fuel stop (beyond the minimum stops) Calculate expected saved time per fuel stop (beyond the minimum stops) Expected profit per saved time (best alternative way) Expected profit per saved time (best alternative way)  Ending fuel Large value if the exp. fuel cost in the next route is higher than that in the current route Large value if the exp. fuel cost in the next route is higher than that in the current route Small value if the exp. fuel cost in the next route is lower than that in the current route Small value if the exp. fuel cost in the next route is lower than that in the current route

Simulation Results  OOR miles significantly lower for II than I May not make sense to go extra mile or two to reach cheap truck stops May not make sense to go extra mile or two to reach cheap truck stops  Fueling frequency significantly lower for II than I Should not fuel too frequently, but should not over-reduce frequency either Should not fuel too frequently, but should not over-reduce frequency either  Purchased fuel “per stop” is higher for II than I, but purchased fuel “per trip” is lower for II than I Intuitively sound results Intuitively sound results Fuel Optimizer II may provide “greener” or more “environmentally friendly” solutions Fuel Optimizer II may provide “greener” or more “environmentally friendly” solutions

Results (cont.)  Overall vehicle operating cost significantly lower for II than for I Fuel Optimizer II does a better job of reducing the overall cost (expected) Fuel Optimizer II does a better job of reducing the overall cost (expected)  Fuel cost lower for I than for II Fuel Optimizer I does a better job of reducing fuel cost (expected) Fuel Optimizer I does a better job of reducing fuel cost (expected) The difference is not always significant The difference is not always significant  The cost saving of II over I can be large Especially for large carriers Especially for large carriers II may outperform I by about 32% II may outperform I by about 32%

Implications  Fuel Optimizer vendors should consider modifying their models Minimize cost from overall perspective Minimize cost from overall perspective Fuel Optimizer II gives not only lower cost but also more desirable solutions for drivers Fuel Optimizer II gives not only lower cost but also more desirable solutions for drivers Interviews indicate that TL carriers will welcome this type of model Interviews indicate that TL carriers will welcome this type of model  Current users of Fuel Optimizer I may want to: Limit the candidates to those with small OOR Limit the candidates to those with small OOR Use large value for minimum purchase quantity Use large value for minimum purchase quantity May obtain solutions similar to II May obtain solutions similar to II

Summary & Future Research  Fuel Optimizer II is Capable of incorporating non-fuel costs that are ignored or underestimated currently Capable of incorporating non-fuel costs that are ignored or underestimated currently Better model that can lower overall cost Better model that can lower overall cost Flexible model that allows users to choose the costs to minimize Flexible model that allows users to choose the costs to minimize Attractive to drivers so that it may improve the driver compliance rates Attractive to drivers so that it may improve the driver compliance rates  Fuel Optimizer II limitation is It does not consider MPG by road class It does not consider MPG by road class Future research may incorporate GIS database to improve accuracy of fuel consumption calculation Future research may incorporate GIS database to improve accuracy of fuel consumption calculation

Discussion Questions  When is Fuel Optimizer II more beneficial than Fuel Optimizer I?  What are the main features of Fuel Optimizer II?  Is Fuel Optimizer II always better than Fuel Optimizer I? Why?  What type of carriers would benefit the most by using Fuel Optimizer I?  What other costs may be included in the model?