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  • 2020-2022  (2)
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  • 1
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    Harvesting a remote renewable resource (2020)
    SPRINGER HEIDELBERG
    In:  EPIC3Theoretical Ecology, SPRINGER HEIDELBERG, ISSN: 1874-1738
    Details
    Publication Date: 2020-09-21
    Description: In standard models of spatial harvesting, a resource is distributed over a continuous domain with an agent who may harvest everywhere all the time. For some cases though (e.g., fruits, mushrooms, algae), it is more realistic to assume that the resource is located at a fixed point within that domain so that an agent has to travel in order to be able to harvest. This creates a combined travelling–and–harvesting problem where slower travel implies a lower travelling cost and, due to a later arrival, a higher abundance of the resource at the beginning of the harvesting period; this, though, has to be traded off against less time left for harvesting, given a fixed planning horizon. Possible bounds on the controls render the problem even more intricate. We scrutinise this bioeconomic setting using a two-stage optimal control approach, and find that the agent economises on the travelling cost and thus avoids to arrive at the location of the resource too early. More specifically, the agent adjusts the travelling time so as to be able to harvest with maximum intensity at the beginning and the end of the harvesting period, but may also find it optimal to harvest at a sustainable level, where the harvesting and the growth rate of the stock coincide, in an intermediate time interval.
    Repository Name: EPIC Alfred Wegener Institut
    Type: Article , isiRev
    Format: application/pdf
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  • 2
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    Optimal stock–enhancement of a spatially distributed renewable resource (2021)
    In:  EPIC3Journal of Economic Dynamics and Control, 123, pp. 104060, ISSN: 01651889
    Details
    Publication Date: 2021-01-20
    Description: We study the economic management of a renewable resource, the stock of which is spatially distributed and moves over a discrete or continuous spatial domain. In contrast to standard harvesting models where the agent can control the take-out from the stock, we consider the case of optimal stock enhancement. In other words, we model an agent who is, either because of ecological concerns or because of economic incentives, interested in the conservation and enhancement of the abundance of the resource, and who may foster its growth by some costly stock–enhancement activity (e.g., cultivation, breeding, fertilizing, or nourishment). By investigating the optimal control problem with infinite time horizon in both spatially discrete and spatially continuous (1D and 2D) domains, we show that the optimal stock–enhancement policy may feature spatially heterogeneous (or patterned) steady states. We numerically compute the global bifurcation structure and optimal time-dependent paths to govern the system from some initial state to a patterned optimal steady state. Our findings extend the previous results on patterned optimal control to a class of ecological systems with important ecological applications, such as the optimal design of restoration areas.
    Repository Name: EPIC Alfred Wegener Institut
    Type: Article , isiRev , info:eu-repo/semantics/article
    Format: application/pdf
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    PAPER (OA)
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