Constructing a more efficient railway stock planning

After a timetable has been made in which all trains run, enough seats need to be present for all travelers on each trip. We are interested in buying new train units and are therefore solving a train unit assignment problem (TUAP). This problem is NP-hard and therefore difficult to solve. We solve it by first constructing a lower bound to this problem using Cacchiani et al. (2010) and Cacchiani et al. (2019) by solving the problem to the peak period, a set of incompatible trips. Then, the heuristic based on Cacchiani et al. (2019) is used for finding a solution to the original problem using the found lower bound. The heuristic itself is also being modified to possibly improve their results and lower the computational time in three different ways. One is changing the way that train units are sorted. Another one is fixing the assignment of the train units of all trips in set S, a set which contains incompatible trips. The last modification also fixes the assignment of all trips in set S and also uses a tabu-search technique adapted from de Werra and Hertz (1989). In the results, four instances are used. In all instances, the lower bound is never found in one heuristic. However, good results are found in three instances. Moreover, two modifications lead to better results for three instances, while also having a lower computational time. And therefore, the two modifications can be used in real-world instances to lower the computational time of the existing algorithm by a lot while also obtaining better results than the original heuristic.