Approximation schemes for the restricted shortest path problem
Mathematics of Operations Research
An incremental algorithm for a generalization of the shortest-path problem
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Constraint Programming Based Column Generation for Crew Assignment
Journal of Heuristics
A Space Saving Trick for Directed Dynamic Transitive Closure and Shortest Path Algorithms
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Resource Constrained Shortest Paths
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
A Set Partitioning Approach to the Crew Scheduling Problem
Operations Research
A Multicommodity Network-Flow Problem with Side Constraints on Paths Solved by Column Generation
INFORMS Journal on Computing
Computers and Operations Research
A model to optimize placement operations on dual-head placement machines
Discrete Optimization
A new algorithm for reoptimizing shortest paths when the arc costs change
Operations Research Letters
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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.