Exact algorithms for class-constrained packing problems

•Class constrained versions of the bin packing and knapsack problems are investigated.•A Branch-and-Price framework for class constrained bin packing problems is presented.•Branching schemes, heuristics and pricing algorithms are empirically evaluated.•Two generalizations of the class constrained knapsack problem are solved.•Solve 95% of proposed instances for class constrained bin packing in 15 min each.