An extended branch-and-bound method for locomotive assignment

This paper considers the locomotive assignment problem encountered during the planning of the operations of a freight railroad, which consists of providing sufficient motive power to pull a set of scheduled trains at minimum cost while satisfying locomotive availability and maintenance requirements. In 1997, Ziarati et al. proposed for this problem a heuristic branch-and-price approach that relies on a simple depth-first search strategy without backtracking. In this paper, we present an efficient backtracking mechanism that can be added to this heuristic branch-and-price approach. To do so, we propose and evaluate different branching methods that impose multiple decisions on locomotive routes at each branching node, including one decision that forbids one such route. Finally, we introduce different ways of computing an estimate of the best integer solution value that can be obtained from a branch-and-bound node. These estimates can be used to guide the backtracking process of a two-phase search strategy.