Harvesting a Remote Renewable Resource

In standard models of spatial harvesting, the resource is distributed over the complete domain and the agent is able to control the harvesting activity everywhere all the time. In some cases though, it is more realistic to assume that the resource is located at a single point in space and that the agent is required to travel there in order to be able to harvest. In this case, the agent faces a combined travelling–and–harvesting problem. We scrutinize this type of a two–stage optimal control problem, and illuminate the interdependencies between the solution of travelling and that of the harvesting sub-problem. Since the model is parsimoniously parameterised, we are able to analytically characterise the optimal policy of the complete travelling–and–harvesting problem. In an appendix we show how bounds on either control, i. e. on acceleration and on the harvesting capacity, as well as a positive discount rate affect the solution of the travelling–and–harvesting problem