informИнформатикаInformatics1816-03012617-6963UIIP NASBinform-65Research ArticleМАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕMATHEMATICAL MODELINGНИЖНИЕ ГРАНИЦЫ ЦЕЛЕВОЙ ФУНКЦИИ В ЗАДАЧE НАЗНАЧЕНИЯ ПОЕЗДОВ НА ВРЕМЕННЫЕ ИНТЕРВАЛЫLOWER BOUNDS OF THE CRITERIUM IN THE PROBLEM OF ASSIGNEMENT OF TRAINS ON THE TIME SLOTSБаркетовМ. С.BarketauM. S.barketau@mail.ruКопферХ.KopferH.ПешЕ.PeschE.Объединенный институт проблем информатики НАН БеларусиRussian FederationУниверситет Бремена, ГерманияRussian FederationУниверситет Зигена, ГерманияRussian Federation201330092016022229Copyright © Баркетов М.С., Копфер Х., Пеш Е., 20162016Баркетов М.С., Копфер Х., Пеш Е.Barketau M.S., Kopfer H., Pesch E.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://inf.grid.by/jour/article/view/65

Рассматривается задача оптимизации выполнения множества операций по перемещению контейнеров на железнодорожном узле. Разрабатываются нижняя граница, основанная на релакси-рованной задаче линейного программирования, и нижняя граница, полученная с помощью техники лагранжевой релаксации

In this paper we consider the container transshipment problem at a railway hub. New lowerbounds 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.

ReferencesBoysen, 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.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.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.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.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.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.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.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.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.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.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.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.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.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.Fisher, M.L. A dual algorithm for the one-machine scheduling problem / M.L. Fisher // Mathematical Programming. – 1976. – Vol. 11. – P. 229–251.Fisher, M.L. A dual algorithm for the one-machine scheduling problem / M.L. Fisher // Mathematical Programming. – 1976. – Vol. 11. – P. 229–251.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.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.Fischetti, M. An Additive Bounding Procedure for Combinatorial Optimization Problems /M. Fischetti, P. Toth // Operations Research. – 1989. – Vol. 37, № 2. – P. 319–328.Fischetti, M. An Additive Bounding Procedure for Combinatorial Optimization Problems /M. Fischetti, P. Toth // Operations Research. – 1989. – Vol. 37, № 2. – P. 319–328.

The authors declare that there are no conflicts of interest present.