Railway Timetabling Using Lagrangian Relaxation
Published Online:1 Nov 1998https://doi.org/10.1287/trsc.32.4.358
References
- Network Flows: Theory, Algorithms, and Applications (1993) (Prentice Hall, Englewood Cliffs) Google Scholar
- On relaxation methods for nonsmooth convex optimization. (1993) . Ph.D. dissertation, Department of Mathematics, Royal Institute of Technology, Stockholm Google Scholar
- A descent proximal level bundle method for convex nondifferentiable optimization. Oper. Res. Lett. (1995) 17 121 126 Crossref, Google Scholar
- On improving relaxation methods by modified gradient techniques. Math. Programming Stud. (1975) 3 79 97 Google Scholar
- The Lagrangian relaxation method for solving integer programming problems. Management Sci. (1981) 27 1 18 Link, Google Scholar
- User's guide for LSSOL (Version 1.0): A Fortran package for constrained linear least-squares and convex quadratic programming. (1986) . Report SOL 86-1, Department of Operations Research, Stanford University Google Scholar
- Optimal dispatching under uncertainty: With application to railroad scheduling. (1993) . Ph.D. dissertation, Systems Engineering Department, University of Pennsylvania Google Scholar
- Experimental comparison of the first-price and second-price auctions—The case of track capacity allocation. (1996) . Working paper, Centre for Research in Transportation and Society, Dalarna University College, Borlänge, Sweden Google Scholar
- Tactical scheduling of rail operations: The SCAN I system. Transportation Sci. (1991) 25 46 64 Link, Google Scholar
- , Nemhauser G. L. , Rinnooy Kan A. H. G. , Todd M. J. Nondifferentiable optimization. Handbooks in Operations Research and Management Science, Vol. 1, Optimization (1989) (Elsevier Science, Amsterdam) 529 572 Google Scholar
- MathWorks Inc. Using MATLAB (1996) (The MathWorks Inc., Natick, MA. USA) Google Scholar
- Integer and Combinatorial Optimization (1988) (John Wiley & Sons, Inc., New York) Crossref, Google Scholar
- Allocation of track capacity. Experimental evidence on the use of priority auctioning in the railway industry. (1996) . Working paper, Centre for Research in Transportation and Society, Dalarna University College, Borlänge, Sweden Google Scholar
- Railway timetabling—Lagrangian heuristics. (1997) . Technical report, TRITA/MAT-97-OS12, Department of Mathematics, Royal Institute of Technology Google Scholar
- Computer aided train dispatching: Decision support through optimization. Interfaces (1983) 13 24 37 Link, Google Scholar
- Swedish State Railways, private communication. (1997) . SJ Google Scholar
- Routing trains through railway stations: Model formulation and algorithms. Transportation Sci. (1996) 30 181 194 Link, Google Scholar

