In the case of the crew pairing problem, negative
reduced cost columns are identified without explicitly considering each pairing. Instead, all columns
are implicitly considered by solving a pricing problem, often formulated as a multilabel, shortest path
problem in which some paths correspond to pairings.
By exploiting dominance, shortest paths—and hence
minimum reduced cost pairings—are identified without examining all paths, or pairings. For a detailed
exposition of multilabel, shortest path problems, see
Desrochers and Soumis (1988).
In the case of the crew pairing problem, negativereduced cost columns are identified without explicitly considering each pairing. Instead, all columnsare implicitly considered by solving a pricing problem, often formulated as a multilabel, shortest pathproblem in which some paths correspond to pairings.By exploiting dominance, shortest paths—and henceminimum reduced cost pairings—are identified without examining all paths, or pairings. For a detailedexposition of multilabel, shortest path problems, seeDesrochers and Soumis (1988).
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