Turnpike Results for Single Location Capacity Expansion

We consider the problem of selecting capacity additions from a finite set of possible facility sizes to meet demand at a single location over an infinite horizon. The problem is motivated and illustrated by an application to the planning for the deployment of long haul transmission facilities in the nationwide intercity telephone network. Under the assumption that demand grows at an increasing rate, taken to be exponential for purposes of exposition, we prove a “turnpike theorem” which characterizes the optimal policy as one in which the least average cost facility is eventually the only optimal facility type installed over the infinite horizon. This structural result, together with an efficient algorithm for solving the finite horizon problem, which has been implemented in a facilities network planning tool known as OFNPS, leads to a constructive algorithm for finding the optimal first facility for the infinite horizon problem. The approach avoids the end of study effects inherent in a finite horizon approach to the problem.