We consider the problem of cost optimal railway line allocation for passenger trains for the Dutch railway system. At present, the allocation of passenger lines by Dutch Railways is based on maximizing the number of direct travelers. This paper develops an alternative approach that takes operating costs into account. A mathematical programming model is developed which minimizes the operating costs subject to service constraints and capacity requirements. The model optimizes on lines, line types, routes, frequencies and train lengths. First, the line allocation model is formulated as an integer nonlinear programming model. This model is transformed into an integer linear programming model with binary decision variables. An algorithm is presented which solves the problem to optimality. The algorithm is based upon constraint satisfaction and a Branch and Bound procedure. The algorithm is applied to a subnetwork of the Dutch railway system for which it shows a substantial cost reduction. Further application and extension seem promising. © 1998 Elsevier Science B.V. All rights reserved.
[1]
Martin W. P. Savelsbergh,et al.
Preprocessing and Probing Techniques for Mixed Integer Programming Problems
,
1994,
INFORMS J. Comput..
[2]
P. Kreuzer,et al.
Optimal lines for railway systems
,
1997
.
[3]
Ellis L. Johnson,et al.
Solving Large-Scale Zero-One Linear Programming Problems
,
1983,
Oper. Res..
[4]
David A. Kendrick,et al.
GAMS : a user's guide, Release 2.25
,
1992
.
[5]
A. Bouma,et al.
Linienplanung und Simulation für öffentliche Verkehrswege in Praxis und Theorie
,
1994
.
[6]
Edward Y. H. Lin,et al.
Multiple Choice Programming: A State‐of‐the‐Art Review
,
1994
.
[7]
David S. Johnson,et al.
Computers and Intractability: A Guide to the Theory of NP-Completeness
,
1978
.
[8]
M. Padberg,et al.
Lp-based combinatorial problem solving
,
1985
.