Journal of Applied Mathematics & Decision Sciences, 2(1), 3-21 (1998) Reprints Available directly from the Editor. Printed in New Zealand. OPTIMAL INVESTMENT STRATEGIES FOR RENEWABLE FACILITIES JOE FLOOD Australian Housing and Urban Research Institute, Level 7, 20 Queen St Melbourne 3000, A USTRALIA. Abstract. Although a large literature exists on the repair and deterioration of machines, the associated problem of maintenance schedules for deteriorating renewable facilities has been little studied. These facilities include all those which can be restored to a near-new state by renovation or rebuilding, so that the market value and performance of the facility depends on the current state of repair rather than on the time since initial construction. This paper solves the general deterministic problem of finding the optimal repair strategy for a depreciating renewable facility. It is shown that the value of the facility should approach the level where a function defined as the "nett internal return" is greatest. If the facility has a finite life before sale or demolition, an adjustment to repair strategies should be made as the facility approaches this time, increasing repairs where this permits a better sale price to be obtained, or discontinuing repairs if they are not justified by scrap or market value. Solutions for a range of common depreciation functions and for linear and quadratic repair cost functions are obtained. The optimal life of the facility is determined at the time when nett "external" marginal return, which includes potential capital gain or loss and opportunity cost of capital, falls to zero. Keywords: Replacement strategies, renewable facilities, depreciation, optimal control 1. Introduction A very large literature has developed around the problem of determining optimal maintenance and replacement strategies for deteriorating facilities, as the review articles by Pierskalla and Voelker (1976) and Pintolon and Golders (1992) relate, or as detailed in texts such as Jardine (1970, 1973), Rapp (1974), Gertsbakh (1979), and Newnan (1983). A range of techniques has been developed for examining the economic lifetimes of machines in particular, ranging from the deterministic analyses of Hotelling (1925), Naslund (1966), Thompson (1968) and Hartl (1981), through statistical control (Kamien and Schwartz 1971, Virtanen 1982, Hopp and Wu 1990, Cho 1993, Tang 1993, Mehrez and Bernan 1994), to reliability theory (Barlow and Proschan 1975, Gertsbakh 1989, Chand and Sethi 1982). The problem of deteriorating built facilities or infrasmacture is rather different from deterioration of a machine, in that many facilities may be restored to near-new state by rebuilding or renovation. The value and performance of these facilities depend on their current state of repair rather than on the time since initial construction, as with a machine. Those facilities which have a large number of small components which can be regularly