Linear and Lagrangean penalties for variable bounding in ILP: An application to a covering problem

Lagrangean and linear penalties can be used for variable bounding in ILP. Such penalties, embedded in a branch-and-bound algorithm, yield remarkable reductions in the search procedure effort for large scale problems. In this paper, four different ways of exploring this idea for a covering problem with integer variables are presented. Computing results taken from test problems have revealed the efficiency of the technique in reducing the amplitude of variable intervals, and even in fixing them at feasible values.