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Excerpt from A Composite Algorithm for the Concave-Cost Ltl Consolidation Problem The concave - cost network flow problem (abbreviated as ccnfp) that we consider involves routing multiple commodities on a given network. We define each commodity by its origin node-and its destination node, and by the flow amount required to be routed from the origin to the destination. The commodities can be routed via any number of intermediate transshipment nodes. The cost of flow along each arc is a concave piecewise - linear function. Therefore, for each arc (i, j) of the network, the set of all possible flows on that arc is partitioned into several prespecified 'cost ranges'. The incremental cost per unit of flow on the arc is constant within each of these ranges, and this per unit cost is lower for higher ranges. Figure 1 shows a typical total cost curve for flow along arc (the notation in the figure will be defined in the next section.) The objective of the ccnfp is to find the flow pattern that satisfies the commodity requirements at minimum total cost. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com 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.

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