AbstractIt is observed that sample cost functions for the pipeline problem [1] are discretely convex, i.e., their graphs are discrete subsets of graphs of convex functions. As a result, it is shown that the pipeline problem may be attacked by using either a minimum cost flow approach, or a combination of dynamic programming and sorting. Problems with concave cost functions are shown to be relatively easy. Even for problems which are neither convex nor concave, it is shown that in certain instances, only a subset of the data for each cost function is relevant. Error bounds are presented when approximations to the original cost functions are used. Results obtained in [4]for a related problem are summarized.