Graphs, Maneuvers and Turnpikes

We address the problem of moving a collection of objects from one subset of Z^m to another at minimum cost. We show that under fairly natural rules for movement assumptions, if the origin and destination are far enough apart, then a near optimal solution with special structure exists: Our trajectory from the origin to the destination accrues almost all of its cost repeating at most m different patterns of movement. Directions for related research are identified.