The dynamic programming and branch-and-bound approaches are combined to produce a hybrid algorithm for separable discrete mathematical programs. The hybrid algorithm uses linear programming in a novel way to compute bounds and is readily extended to solve a family of parametric integer programs with related right-hand-sides. Computational experience is reported on a number of linear and nonlinear integer programs.Supported in part by the U.S. Army Research Office (Durham) under Contract DAHC04-73-C-0032.