We begin with a description of a general framework of subadditive lifting methods for partitioning, covering, and packing problems. For the special case of one equation, three different implementations are given. Then, we relate these methods to several existing methods: linear programming using the dual simplex method over the (usually unknown) facets of the convex hull of solutions, the group method, branch-and-bound, shortest paths, and dynamic programming. All except dynamic programming are shown to be within the class of dual feasible subadditive lifting methods. © 1980.