Advances in Solving the Multicommodity-Flow Problem

McBride, Richard D.; Carrizosa, Emilio; Conde, Eduardo; Munõz-Márquez, Manuel

doi:10.1287/inte.28.2.32

Cited by 37 publications

(14 citation statements)

References 23 publications

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“…Furthermore, the available algorithms usually assume that variables may have fractional values (Ahuja et al [2], McBride [12]). Solution approaches for integer multi-commodity flow problems were studied by Barnhart et al [4], based on branch-and-price techniques.…”

Section: Solution Approachmentioning

confidence: 99%

Efficient Circulation of Railway Rolling Stock

Alfieri

Groot

Kroon

et al. 2006

Transportation Science

124

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Railway rolling stock is one of the most significant cost sources for operators of passenger trains. The efficient circulation of rolling stock is therefore one of the main objectives pursued in practice. This paper focuses on the determination of appropriate numbers of train units of different types together with their efficient circulation on a single line. In order to utilize the train units on this line in an efficient way, they are coupled to or uncoupled from the trains in certain stations according to the passengers' seat demand in peak hours and off-peak hours. Since coupling and uncoupling train units has to respect specific rules related to the shunting possibilities in the stations, it is important to take into account the order of the train units in the trains. This aspect strongly increases the complexity of the rolling stock circulation problem. This paper presents a solution approach based on an Integer Programming model. The approach is applied to a real life case study based on the timetable of NS Reizigers, the main Dutch operator of passenger trains.

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Section: Solution Approachmentioning

confidence: 99%

Efficient Circulation of Railway Rolling Stock

Alfieri

Groot

Kroon

et al. 2006

Transportation Science

124

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“…A multi-commodity flow problem is a kind of network flow problem where multiple commodities are routed between different sources and sinks [29]. In STFN, we use different commodities to indicate the distinction between the topological relations of different connected S-T pairs (the term "A connect to B" is used for simplicity in a directed graph and means exactly that A can reach B or B can reach A).…”

Section: Modelling Long-term Transition As Multi-commodity Flowmentioning

confidence: 99%

An Efficient Graph-based Method for Long-term Land-use Change Statistics

Zhang

Gao

et al. 2015

Sustainability

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Statistical analysis of land-use change plays an important role in sustainable land management and has received increasing attention from scholars and administrative departments. However, the statistical process involving spatial overlay analysis remains difficult and needs improvement to deal with mass land-use data. In this paper, we introduce a spatio-temporal flow network model to reveal the hidden relational information among spatio-temporal entities. Based on graph theory, the constant condition of saturated multi-commodity flow is derived. A new method based on a network partition technique of spatio-temporal flow network are proposed to optimize the transition statistical process. The effectiveness and efficiency of the proposed method is verified through experiments using land-use data in Hunan from 2009 to 2014. In the comparison among three different land-use change statistical methods, the proposed method exhibits remarkable superiority in efficiency.

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“…The table clearly shows that (MMCF) instances with very many commodities cannot be solved in reasonable time by standard (LP) techniques, while a Lagrangian approach can be successfully used to compute an optimal solution to the problem. We should point out that specialized (LP) techniques, such as those of McBride (1998), Castro (2000, may be competitive with Lagrangian ones-but in fact the Lagrangian approach applied to this case is a specialized (LP) technique itself, namely a variant of the Dantzig-Wolfe decomposition algorithm. An interesting feature of the Lagrangian approach is that it can be more easily adapted to related but different problems (e.g.…”

Section: Enumerative Algorithmsmentioning

confidence: 99%

About Lagrangian Methods in Integer Optimization

Frangioni

2005

Ann Oper Res

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It is well-known that the Lagrangian dual of an Integer Linear Program (ILP) provides the same bound as a continuous relaxation involving the convex hull of all the optimal solutions of the Lagrangian relaxation. It is less often realized that this equivalence is effective, in that basically all known algorithms for solving the Lagrangian dual either naturally compute an (approximate) optimal solution of the "convexified relaxation", or can be modified to do so. After recalling these results we elaborate on the importance of the availability of primal information produced by the Lagrangian dual within both exact and approximate approaches to the original (ILP), using three optimization problems with different structure to illustrate some of the main points

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Advances in Solving the Multicommodity-Flow Problem

Cited by 37 publications

References 23 publications

Efficient Circulation of Railway Rolling Stock

Efficient Circulation of Railway Rolling Stock

An Efficient Graph-based Method for Long-term Land-use Change Statistics

About Lagrangian Methods in Integer Optimization

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