Infinite horizon optimality criteria for equipment replacement under technological change

We consider the problem of optimally acquiring and retiring assets that are undergoing technological change over an unbounded horizon. The allowance for technological change prevents one from adopting the classic repeated-plant assumption that future replacements will be identical in costs to current asset contenders, thus confronting one with a non-stationary infinite horizon problem to solve. In this paper, we explore several variants of optimality criteria in this case where total costs diverge over the infinite horizon. In particular, we prove that under a mild condition, efficient solutions (i.e. replacement schedules that are least-cost to every replacement decision epoch) exist and are also average-cost optimal. Thus, the short-term optimality characteristics of efficient solutions are accompanied by the long-term prospect of being average-cost optimal as well. Moreover, in the case where discounted future per-period acquisition and maintenance costs go to zero, while total discounted costs diverge to infinity, we show that efficient solutions are overtaking optimal and, in particular, an overtaking optimal solution exists.