Real-life locomotive planning: New formulations and computational results

In this paper, we develop new formulations for the locomotive planning problem (LPP) which is one of the most important railroad optimization problems. The objective of the LPP is to assign a consist (a set of locomotives) to each train in a pre-planned train schedule so as to provide sufficient power to pull the trains from their origins to their respective destinations at minimal cost. This assignment plan should be repeatable every week. In an earlier paper, we developed a formulation for locomotive planning and proposed a novel two-phase solution approach using linear, integer, and network programming. However, that formulation did not incorporate all the real-world constraints needed to generate a fully implementable solution. In this paper, we extend that approach on several dimensions by adding new constraints to the planning problem desired by locomotive directors, and by developing additional formulations necessary to transition solutions of our models to practice. We propose two formulations for this generalized LPP: consist formulation, and hybrid formulation. Finally, we present detailed computational tests that demonstrate the efficacy of models and conduct case studies on a number of instances to obtain several insights.