Implementation of a three-stage approach for the dynamic resource-constrained shortest-path sub-problem in branch-and-price

The resource-constrained shortest-path problem (RCSP) is often used as a sub-problem in branch-and-price because it can model the complex logic by which many actual systems operate. This paper addresses two special issues that arise in such an application. First, RCSP in this context is dynamic in t...

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Veröffentlicht in:Computers & operations research Jg. 40; H. 1; S. 385 - 394
Hauptverfasser: Zhu, Xiaoyan, Wilhelm, Wilbert E.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Kidlington Elsevier Ltd 01.01.2013
Elsevier
Pergamon Press Inc
Schlagworte:
Algorithms
Applied sciences
Branch & bound algorithms
Branch-and-price
Column generation
Cost estimates
Costs
Dealing
Dynamics
Exact sciences and technology
Fixed arcs
Flows in networks. Combinatorial problems
Iterative methods
Mathematical analysis
Mathematical models
Operational research and scientific management
Operational research. Management science
Optimization algorithms
Re-optimization
Resource-constrained shortest-path problem
Shortest path algorithms
Shortest-path problems
Studies
Three-stage approach
Resource-constrained shortest-path problem
Column generation
Fixed arcs
Branch-and-price
Three-stage approach
Re-optimization
Branching
Costs
Branch and bound method
Shortest path
Optimization
Resource management
Logic model
ISSN:0305-0548, 1873-765X, 0305-0548
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:The resource-constrained shortest-path problem (RCSP) is often used as a sub-problem in branch-and-price because it can model the complex logic by which many actual systems operate. This paper addresses two special issues that arise in such an application. First, RCSP in this context is dynamic in the sense that arc costs are updated at each column-generation iteration, but constraints are not changed. Often, only a few arc costs are updated at an iteration. Second, RCSP must be solved subject to arcs that are forbidden or prescribed as corresponding binary variables are fixed to 0 or 1 by the branching rule. A reoptimizing algorithm for dealing with a few arc-cost changes and a method for dealing with fixed arcs are proposed and incorporated into a three-stage approach, specializing it for repeatedly solving the dynamic RCSP as a sub-problem in branch-and-price. Computational tests evaluate the effectiveness of the proposed algorithms.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2012.07.007