Lagrangean dual ascent algorithms for computing bounds in capacitated plant location problems

Given a mixed-integer programming problem, if one dualizes all linking constraints and the constraints containing only integer variables, the optimum of the Lagrangean dual is equal to the optimum of the LP relaxation. If one strengthens this dual by adding valid inequalities such that the problem still decomposes into a continuous and a pure integer problem and is relatively easy to solve due to some special structure, one may be able to devise dual ascent steps for the Lagrangean dual. This is investigated for the capacitated plant location problem, whose strengthened Lagrangean relaxed problem decomposes into a transportation problem and a knapsack problem. Computational experiments are reported based on some very simple ascent steps.