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B. , L. , and N. , column generation algorithm for computing the dual bound at each node of the search tree when solving (22)-(27), Algorithm, vol.2

, Solve (M P (L R )) with additional branching constraints B and no-good cuts N R

. Let-(x-*, ? * ) be the optimal solution and ? * , µ * , ? * and ? * be the optimal dual variables associated with the constraints, vol.17

, Solve (P ricing (? * , µ * , ? * , ? * ))

, Let (y * , z * )

?. L-r-?-l-r-?-{|l-r-|-+-1} and . |l-r-|-?-y-*,

, L R ) if the pricing problem returns a column with a negative reduced cost. When Assumption 2.1 as well as Proposition 2.4 hold there is no need for Constraints (28), so that the pricing problem in Line 4 can be replaced with (P ricing(? * , µ * , ? * )). The left-hand-side of the tests, Line 5 of Algorithm 1. The loop 1-8 adds new columns to the restricted master M P (L R ) until no negative reduced cost column is found