Relaxations of an integer programming problem produce bounds on its optimal solution. The linear programming, Lagrangean, surrogate and combined Lagrangean-surrogate (L-S) relaxations are the most commonly used in the solution of an integer programming problem. We present a brief review of these relaxations, solution methods for the respective duals and theoretical relationships that exist among them. We give special emphasis to surrogate and combined L-S relaxations. The use of a combined L-S relaxation is illustrated through its application to a hierarchical covering location problem.
relaxations; surrogate and combined Lagrangean-surrogate; integer programming bounds
