In many mixed integer programs there is some embedded problem structure which can be exploited, often by a decomposition. When the relaxation in each node of a branch-and-bound tree is solved by column generation, one speaks of branch-and-price. Optionally, cutting planes can be added in order to strengthen the relaxation, and this is called branch-price-and-cut.
Desrosiers, J., & Lübbecke, M. E. (2011). Branch-price-and-cut algorithms. Encyclopedia of Operations Research and Management Science. John Wiley & Sons, Chichester, 109-131.