LOWER BOUNDS OF THE CRITERIUM IN THE PROBLEM OF ASSIGNEMENT OF TRAINS ON THE TIME SLOTS
Abstract
In this paper we consider the container transshipment problem at a railway hub. New lower
bounds are developed. One lower bound is based on the linear relaxation of the integer linear formulation, and the other lower bound is based on the Lagrangian relaxation technique.
bounds are developed. One lower bound is based on the linear relaxation of the integer linear formulation, and the other lower bound is based on the Lagrangian relaxation technique.
About the Authors
M. S. Barketau
Объединенный институт проблем информатики НАН Беларуси
Russian Federation
Russian Federation
H. Kopfer
Университет Бремена, Германия
Russian Federation
Russian Federation
E. Pesch
Университет Зигена, Германия
Russian Federation
Russian Federation
References
1. Boysen, N. New bounds and algorthms for the Transshipment Yard Scheduling Problem /N. Boysen, F. Jaehn, E. Pesch // Journal of Scheduling. – 2012. – Vol. 15, I. 4. – P. 499–511.
2. Boysen, N. Scheduling freight trains in rail-rail transshipment yards / N. Boysen, F. Jaehn, E. Pesch // Transportation Science. – 2011. – Vol. 45, I. 2. – P. 199–211.
3. Cordeau, J.F. A survey of optimization models for train routing and scheduling /J.F. Cordeau, P. Toth, D. Vigo // Transportation Science. – 1998. – Vol. 32. – P. 380–404.
4. Macharis, C. Opportunities for OR in intermodal freight transport research: A review /C. Macharis, Y.M. Bontekoning // European Journal of Operational Research. – 2004. – Vol. 153. –P. 400–416.
5. Bontekoning,Y.M. Is a new applied transportation research field emerging? A review of intermodal rail-truck freight transport literature / Y.M. Bontekoning, C. Macharis, J.J. Trip // Transportation Research Part A: Policy and Practice. – 2004. – Vol. 38. – P. 1–24.
6. Crainic, T.G. Intermodal transport / T.G. Crainic, K.H. Kim // In Transportation, Handbooks in Operations Research and Management Science 14, eds.: C. Barnhart, G. Laporte. – North-Holland, 2007. – P. 467–538.
7. Hoogeveen, J.A. Stronger Lagrangian bounds by use of slack variables: applications to machine scheduling problems / J.A. Hoogeveen, S.L. van de Velde // Mathematical Programming. – 1995. – Vol. 70. – P. 173–190.
8. Fisher, M.L. A dual algorithm for the one-machine scheduling problem / M.L. Fisher // Mathematical Programming. – 1976. – Vol. 11. – P. 229–251.
9. Van de Velde, S.L. Dual decomposition of a single-machine scheduling problem /S.L. van de Velde // Mathematical Programming . – 1995. – Vol. 69. – P. 413–428.
10. Fischetti, M. An Additive Bounding Procedure for Combinatorial Optimization Problems /M. Fischetti, P. Toth // Operations Research. – 1989. – Vol. 37, № 2. – P. 319–328.
Review
For citations:
Barketau M.S., Kopfer H., Pesch E. LOWER BOUNDS OF THE CRITERIUM IN THE PROBLEM OF ASSIGNEMENT OF TRAINS ON THE TIME SLOTS. Informatics. 2013;(2):22-29. (In Russ.)
Views: 815
Email this article 