On implicit versus explicit max-plus modeling for the rescheduling of trains

Reference:
B. Kersbergen, T. van den Boom, and B. De Schutter, "On implicit versus explicit max-plus modeling for the rescheduling of trains," Proceedings of the 5th International Seminar on Railway Operations Modelling and Analysis (RailCopenhagen), Copenhagen, Denmark, 15 pp., May 2013.

Abstract:
In this paper a new railway traffic model is introduced. This model is determined by rewriting the model introduced in the papers "A permutation-based algorithm to optimally reschedule trains in a railway traffic network" by T.J.J. van den Boom, N. Weiss, W. Leune, R.M.P. Goverde, and B. De Schutter (Proceedings of the 18th IFAC World Congress, pages 9537–9542, Milan, Italy, August–September 2011) and "Structured modeling, analysis, and control of complex railway operations." by T.J.J. van den Boom, B. Kersbergen, and B. De Schutter (Proceedings of the 51st IEEE Conference on Decision and Control, pages 7366–7371, Maui, Hawaii, December 2012). The models are both macroscopic, contain the same level of details, allow the rescheduling of trains, and are formulated as Switching Max-Plus-Linear (SMPL) models, the difference being that the first model is an implicit SMPL model and the second one is an explicit SMPL model. In this paper a method is detailed for rewriting an implicit SMPL model into an explicit SMPL. Both models are used to solve the rescheduling problem. By solving the rescheduling problem a schedule for all trains in the network is found that minimizes the total delay. The rescheduling problem will be written as a Mixed Integer Linear Programming (MILP) problem and solved using the standard solver available in the Multi-Parametric Toolbox for Matlab. The time needed to solve the rescheduling problem using either the implicit and explicit model is compared.