A Fast Heuristic Algorithm for the Train Unit Assignment Problem

In this paper we study a railway optimization problem known as the Train Unit Assignment Problem. A train unit consists of a self-contained train with an engine and a set of wagons with passenger seats. Given a set of timetabled train trips, each with a required number of passenger seats, and a set of train units, each with a given number of available seats, the problem calls for the best assignment of the train units to the trips, possibly combining more than one train unit for a given trip, that fulfills the seat requests. We propose a heuristic algorithm based on the computation of a lower bound obtained by solving an Integer Linear Programming model that gives the optimal solution in a "peak period" of the day. The performance of the heuristic algorithm is computationally evaluated on real-world instances provided by a regional Italian Train Operator. The results are compared with those of existing methods from the literature, showing that the new method is able to obtain solutions of good quality in much shorter computing times

A Heuristic Algorithm for the Train-Unit Assignment Problem

The Train-Unit Assignment Problem calls for an optimal assignment of train units (which are self-contained trains with an engine and passenger seats) to a given set of timetabled trips. The goal is to minimize the number of train units globally used, while satisfying the seat requests, the sequencing constraints and the maintenance constraints. We propose an Integer Linear Programming model and a heuristic alcorithm, based on the Lagrangian Relaxation of the model. Computational results on real-world instances show the effectiveness of the proposed algorithm