Optimal fueling strategies for locomotive fleets in railroad networks

Railroad companies spend billions of dollars each year to purchase fuel for thousands of locomotives across the railroad network. Each fuel station 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 integrates not only fuel station location decisions but also locomotive fueling schedule decisions. The proposed model helps railroads decide which fuel stations to contract, and how each locomotive should purchase fuel along its predetermined shipment path, such that no locomotive runs out of fuel while the summation of fuel purchasing costs, shipment delay costs (due to fueling), and contracting charges is minimized. A Lagrangian relaxation framework is proposed to decompose the problem into fueling schedule and facility location selection sub-problems. A network shortest path formulation of the fueling schedule sub-problem is developed to obtain an exact optimal solution to the fueling schedule sub-problem. The proposed framework is applied to a large-scale empirical case and is shown to effectively reduce system costs.