We consider a dynamic problem of an optimal sustainable exploitation of a renewable bioresource system that in equilibrium is equivalent to a mathematical programming problem. The latter, in the case of a system with a binary structure described by a nonlinear generalization of Leslie’s model, for a fixed value of some aggregated variable, turns into a linear program. A solution algorithm is proposed for the optimal sustainable exploitation problem. The algorithm employs the peculiarities of the constraint system of the problem dual to this linear program and reduces the original problem to a series of one-dimensional optimization problems.
Keywords: rational exploitation of ecosystems, optimal nondestructive controls, concave programming
Received May 18, 2021
Revised July 9, 2021
Accepted July 19, 2021
Aleksandr Ivanovich Smirnov, Cand. Sci. (Phys.-Math.), Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: asmi@imm.uran.ru
Vladimir Danilovich Mazurov, Dr. Phys.-Math. Sci. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: mazurov@imm.uran.ru
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Cite this article as: A.I. Smirnov, Vl.D. Mazurov. A solution algorithm for a problem of optimal exploitation of a system with a binary structure, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 4, pp. 142–160.
