Excerpt from Partitioning Algorithms for a Class of Knapsack Problems<br><br>In this paper algorithms are presented for evaluating the knapsack function for a class of two-dimensional knapsack problems such as arises, for example, in the solution of cutting stock problems in staged guillotine cutting operations. This class includes as a special case the classical one-dimensional knapsack problem. In each algorithm evaluation proceeds from the larger knapsack sizes to the smaller, exploiting for each size the optimality of all partitions or descendents of an optimal solution for a knapsack of that Size. All of the algorithms discussed are based on the methods of combinatorial programming and are reliable in the respect that if carried to completion they guarantee optimal evaluations for knapsacks.<br><br>About the Publisher<br><br>Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com<br><br>This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.