Many important economic problems concern an intertemporal choice between alternate dynamical systems. One example is determining the optimal management of alternative production technologies. This significance has motivated a substantial theoretical literature generalising the necessary conditions of Optimal Control Theory to multiple-phase problems. However, gaining detailed insight into their practical management is difficult because suitable numerical solution methods are not available. This paper resolves this deficiency through the development of a flexible and efficient computational algorithm based on a set of necessary conditions derived for finite-time multiple-phase systems. Its effectiveness is demonstrated in an application to a complex crop rotation problem.