Abstract. We present how to apply Constraint Based Column Generation to a large class of subproblems, namely Constrained Knapsack Problems (CKP). They evolve e.g. from Cutting Stock Problems (see [7]) with additional constraints on the cutting patterns. Focussing on Constrained Knapsack Problems, we developed a new reduction algorithm for KP. It is being used as propagation routine for the CKP with O(n log n) preprocessing time and O(n) time per call. This sums up to an amortized time of O(n) for (log n) calls.
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