Optimizing regular symmetric timetables: a method to reach the best modal split for railway

A regular timetable is a collection of events that repeat themselves every specific time span. This even structure, whenever applied at a whole network, leads to several benefits both for users and the company, although some issues are introduced, especially about dimensioning the service. It is therefore fundamental to properly consider the interaction between the transport demand and supply, to create an effective network timetable. In this paper, a specific cycle base to solve the Cycle Periodicity Formulation (CPF) of a symmetric timetable is proposed. This is combined with a modal choice model, adding the possibility to disable stops along lines for further increasing the transportation demand acquired by the railway system. The problem is modeled as a Mixed-Integer Linear Program (MILP) and solved through a state of the art MILP solver (CPLEX). Computational results regard a case study about a railway network in a northern Italy region.


CASCETTA, E., 2009. Transportation Systems Analysis: Models and Applications. Springer US. CHIERICI, A., CORDONE, R. and MAJA, R., 2004. The demand-dependent optimization of regular train timetables. CORDONE, R. and REDAELLI, F., 2011. Optimizing the demand captured by a railway system with a regular timetable. Transportation Research Part B: Methodological, 45(2), pp. 430-446. GOOSSENS, J., VAN HOESEL, S. and KROON, L., 2004. A branch-and-cut approach for solving railway line-planning problems. Transportation Science, 38(3), pp. 379-393. GOOSSENS, J., VAN HOESEL, S. and KROON, L., 2006. On solving multi-type railway line planning problems. European Journal of Operational Research, 168(2), pp. 403-424. KROON, L.G. and PEETERS, L.W.P., 2003. A Variable Trip Time Model for Cyclic Railway Timetabling. Transportation Science, 37(2), pp. 198-212. LIEBCHEN, C., 2004. Symmetry for Periodic Railway Timetables. Electronic Notes in Theoretical Computer Science, 92, pp. 34-51. LIEBCHEN, C. and PEETERS, L., 2009. Integral cycle bases for cyclic timetabling. Discrete Optimization, 6(1), pp. 98-109. MAJA, R., 1999. Accordo di programma per la riqualificazione e il potenziamento della linea ferroviaria Milano-Mortara. Technical Report, Politecnico di Milano MCCORMICK, G.P., 1972. Converting general nonlinear programming problems to separable nonlinear programming problems. NACHTIGALL, K., 1994. A Branch and Cut Approach for Periodic Network Programming. Univ., Inst. fur Mathematik. SERAFINI, P. and UKOVICH, W., 1989. A Mathematical Model for Periodic Scheduling Problems. SIAM Journal on Discrete Mathematics, 2(4), pp. 550-581. VOORHOEVE, M., 1993. Rail scheduling with discrete sets. Unpublished report, Eindhoven University of Technology, The Netherlands.



View Optimizing regular symmetric timetables: a method to reach the best modal split for railway