Optimal Cyclic Exploitation of Renewable Resources
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The paper contributes to the topic of optimal utilization of spatially distributed renewable resources. Namely, a problem of “sustainable” optimal cyclic exploitation of a renewable resource with logistic law of recovery is investigated. The resource is distributed on a circle and is collected by a single harvester moving along the circle. The recovering and harvesting rates are position dependent, and the latter depends also on the velocity of the harvester, which is considered as a control. The existence of an optimal solution is proved, as well as necessary optimality conditions for the velocity of the harvester. On this base, a numerical approach is proposed, and some qualitative properties of the optimal solutions are established. The results are illustrated by numerical examples, which reveal some economically meaningful features of the optimal harvesting.
KeywordsSpacial heterogeneity Optimal harvesting Averaged functional
Mathematics Subject Classification (2010)49J15 34H05 93C10
This research financed by a joint project of the Austrian Science Foundation (FWF) and Russian Foundation for Basic Research (RFBR) under grant No I 476-N13 and 10-01-91004 AИΦ_a, respectively .
- 7.Ekeland I, Temam R. Convex analysis and variational problems. Classics in Mathematics Society for Industrial and Applied Mathematics. Philadelphia; 1999.Google Scholar
- 10.Repetto R, Gillis M. Public policies and misuse of forest resources: Cambridge University Press; 1990.Google Scholar
- 13.Undersander D J, Albert B, Porter P, Crossley A. Pastures for profit: a hands on guide to rotational grazing. University of Wisconsin Cooperative Extension Publication A3529, Madison. WL 1994:26.Google Scholar
- 14.Warga J. Optimal control of differential and functional equations: Academic Press; 1972.Google Scholar