Optimizing Fueling Decisions for Locomotives in Railroad Networks

Even though rail transportation is one of the most fuel efficient forms of surface transportation, fueling costs are one of the highest operating cost head for railroad companies. In US, unlike Europe, fueling costs are indeed, by far, the single highest operating cost. For larger companies with several thousands of miles of rail network, the fuel bills often run into several billions of dollars annually. The railroad fueling problem considered in this paper has three distinct cost components. Fueling stations charge a location dependent price for the fuel in addition to a fixed contracting fee over the entire planning horizon. In addition, the railroad company must also bear incidental and notional costs for each fuelling stop. It is imperative that the number of fueling stops between an origin and destination should be restricted to avoid unnecessary delays. This paper proposes a mixed integer linear program model that determines the optimal strategy for contracting and fuel purchase schedule decisions that minimizes overall costs under certain reasonable assumptions. This model is tested on a large, real-life problem instances. This mathematical model is further enhanced by introducing several feasible MIP cuts. This paper compares the efficiency of different MIP cuts in order to reduce the run-time. Lastly, the paper concludes with an observation that even though the problem scale was expected to diminish the model performance, it was indeed noted that run-time and memory requirements are fairly reasonable. It thus establishes that this problem must be looked beyond the prism of heuristics and other approximate algorithms for actual implementation at railroad companies.