A Stochastic Constrained Optimal Replacement Model: The Case of Ship Replacement

This paper formulates a stochastically constrained equipment replacement model. Its aim is to determine a sequence of replacement dates such that the total “current account” cost of all future costs and capital expenditures over an infinite time horizon for the n initial incumbent machines is minimized subject to the constraints that, at each point in time, the expected number of machines in each of several “utility classes” has a prescribed value. The theoretical model is then solved under a set of simplifying assumptions and applied to the problem of ship replacement.