Optimal Locomotive Fueling Schedule and Location in Railroad Networks

Railroad companies spend billions of dollars each year to purchase fuels for thousands of locomotives across the railroad network. Each fuel station normally charges a site-dependent fuel price, and the railroad companies must pay an additional flat contracting fee in order to use it. This paper presents a linear mixed-integer mathematical model that minimizes the summation of fuel purchasing costs, shipment delay costs (due to fueling), and contracting charges, while ensuring that no locomotives run out of fuel along their predetermined shipment paths. A Lagrangian relaxation framework is proposed to decompose the problem into fueling schedule and facility location selection subproblems. A network shortest path formulation of the fueling schedule subproblem is developed to obtain an exact optimal solution to the fueling schedule subproblem. The proposed framework is applied to a large-scale empirical case and is shown to effectively reduce system costs.