A Generic Model of Motor-Carrier Fuel Optimization

1. A Generic Model of Motor-Carrier Fuel Optimization Yoshinori Suzuki

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

3. Fuel Optimizer • Step 1: Route optimization • Shortest route between origin and destination • Some products consider toll costs • Step 2: Fuel optimization • Downloads fuel price of every truck stop (U.S. and Canada) • 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

4. Limitations • Considers only the fuel cost • The model’s DVs (decision variables) affect other costs too • 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

5. 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 • 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 • Overall cost may become noticeably lower

6. 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 • 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 et al. (2007) – joint determination of route and fuel decisions • Khuller et al. (2007) – fueling decisions in traveling salesman problems

7. 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 • 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

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

9. 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

10. 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 depreciation cost • Opportunity cost of OOR miles • Opportunity cost of fuel stops • Underestimated cost • Fuel cost (highway vs. OOR roads) • Implications • May minimize fuel cost but not overall vehicle operating cost

11. 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”

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

13. 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 • Each problem is solved by both Fuel Optimizers I and II (Simplex and B&B) • 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)

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

15. 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 • Fueling frequency significantly lower for II than I • 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 • Fuel Optimizer II may provide “greener” or more “environmentally friendly” solutions

17. 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 cost lower for I than for II • Fuel Optimizer I does a better job of reducing fuel cost (expected) • The difference is not always significant • The cost saving of II over I can be large • Especially for large carriers • II may outperform I by about 32%

19. Implications • Fuel Optimizer vendors should consider modifying their models • Minimize cost from overall perspective • 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 • Current users of Fuel Optimizer I may want to: • Limit the candidates to those with small OOR • Use large value for minimum purchase quantity • May obtain solutions similar to II

20. Summary & Future Research • Fuel Optimizer II is • Capable of incorporating non-fuel costs that are ignored or underestimated currently • Better model that can lower overall cost • Flexible model that allows users to choose the costs to minimize • 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 • Future research may incorporate GIS database to improve accuracy of fuel consumption calculation

21. 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?