Numerical Optimisation of Multiple-Phase Systems Incorporating Transition Costs

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.