Revisiting surrogate relaxation for the multidimensional knapsack problem

The multidimensional knapsack problem (MKP) is a classic in combinatorial optimisation. Several authors have proposed to use surrogate relaxation compute upper bounds for the MKP. In their papers, dual solved heuristically. We show that, using modern simplex solver as subroutine, one can solve exactly reasonable computing times. On other hand, resulting bound tends be strong only relatively small MKP instances.