The Loading Problem

Two techniques, of lexicographic search and of bracketing bounds, are developed in the context of the loading or knapsack problem. Starting from an initial feasible selection, the first technique proceeds to an “intelligent enumeration” of all the exchanges possible and leads to a better selection, when one exists. The second technique sets upper bounds to feasible values (of the objective function) and allows us to take decisions about the selection of articles by employing a criterion involving conditional bounds. The techniques are easy to apply and allow of direct extension to the case of multiple criteria.