AbstractThe Donaldson model for inventory replenishment is investigated for a general class of increasing demands. In particular, it is shown that the system of reorder times is uniquely specified and well-behaved when the demandf(t) is log-concave, i.e. the derivative of logf(t) is a decreasing function of time. In addition, a numerical procedure is outlined which will produce the set of optimal times at which to re-order, provided the demandf(t) is of sufficiently simple form, for example a simple power law or exponential demand.