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Loop 3-19 processes the open nodes. The solution of the relaxation at the current node is computed in Line 5. If the solution satisfies the integrality requirements (Line 10), we check whether it satisfies constraints (22) (Line 11-12). Note that this is always the case when Assumption 2.1 and the conditions of Proposition 2.4 hold, so that Lines 11-16 can be replaced by line 13 only, where PrimalBound and S * are updated. If the current second-stage solution y * is not compatible with the current first-stage solution x *, best feasible solution found, S * , and the subset of no-good cuts, vol.66, pp.1086-1100, 2018. ,

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

? * ) 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 ) 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