Some resources, especially renewable resources, are essentially heterogeneous. Thus biological resources (forests, fish etc.), for example, are structured by their size/age. Many studies have shown that the heterogeneity of biological resources should be taken into account for their optimal exploitation. Models of optimal control of heterogeneous resources are thus an important tool in advising policy on their management.
Methodologically, such models are expressed in the form of partial differential equations in which the exploitation rate becomes a control variable. A decision maker optimizes the economic profit from resource exploitation.
ASA recently started research on optimal management of heterogeneous resources. In 2013 Davydov and Platov  analyzed a model of two size-structured competing populations and proved the existence of sustainable (stationary) exploitation under several assumptions, most important being that intra-specific competition should dominate inter-specific competition.
Belyakovet al.  consider a model of optimal utilization of a spatially distributed renewable resource and prove that the sustainable (stationary) exploitation exists under the logistic law of population growth. This was found to become continuous (without stopping) if the resource growth rate sufficiently exceeds the search speed.
 Davydov A, Platov A (2013). Optimal exploitation of two size-structured competing populations.Workshop “Renewable resources, Sustainability, and Search”, Heidelberg, Germany, 12—14 December 2013.
 Belyakov AO, Davydov A, Veliov VM (under review). Optimal cyclic exploitation of renewable resources.Journal of Dynamical and Control Systems.
ASA’s main collaborators in the field of optimal management of heterogeneous resources include S. Behringer, Associate Professor, Universität Duisburg-Essen, Germany, H.M.Matos, Assistant Professor, Centro de Matemática da Universidade do Porto, Portugal; A. Platov, Assistant Professor, Vladimir State University, Russia; V. Veliov, Professor, Vienna University of Technology, Austria.
Last edited: 21 May 2014
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