Abstract
This study proposes a new framework to tackle the uncertainty that prevails in the exploitation of renewable resources. It deals with the question of how to guarantee both a minimum multi-species harvest and the renewal of resources when their evolutions are uncertain. The problem is twofold: to decentralize a global constraint (on a multi-species harvest) into local constraints (on the resources of the different species) and, then, to use a “tychastic” approach necessitating only the forecasts of the lowers bounds of the resource growth rates. This study, formulated as a “tychastic” regulated system with viability constraints, departs from stochastic approaches generally used to deal with uncertain situations. It provides the time dependent harvesting rule allowing to always comply with a minimum harvest objective and resources replenishment thresholds whatever happens and a tychastic measure of risk viability in terms of minimum resources initially required. To solve this problem involving global and local constraints a new method that decentralizes the constraints has been devised. An example is presented whose numerical results are obtained thanks to a dedicated software using mathematical and algorithmic tools of viability theory.
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Acknowledgments
This work was supported by the program Agrobiosphere of the French agency ANR (Agence Nationale de la Recherche) through the funded research project Gaia-Trop. Jean-Pierre Aubin has been partially supported by the Commission of the European Communities under the 7th Framework Programme Marie Curie Initial Training network (FP7-PEOPLE-2010-ITN), project SADCO, contract number 264735.
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Aubin, JP., Chen, L. & Durand, MH. Dynamic decentralization of harvesting constraints in the management of tychastic evolution of renewable resources. Comput Manag Sci 10, 281–298 (2013). https://doi.org/10.1007/s10287-013-0192-4
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DOI: https://doi.org/10.1007/s10287-013-0192-4