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Constant Versus Periodic Fishing: Age Structured OptimalControl Approach

Published online by Cambridge University Press:  20 June 2014

A.O. Belyakov  and
V.M. Veliov
A.O. Belyakov*
Affiliation:
ORCOS, Vienna University of Technology Institute of Mechanics, Lomonosov Moscow State University
V.M. Veliov
Affiliation:
ORCOS, Vienna University of Technology
*
⋆ Corresponding author. E-mail: anton.belyakov@tuwien.ac.at
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Abstract

The paper investigates an age-structured infinite-horizon optimal control model ofharvesting a biological resource, interpreted as fish. Time and age are considered ascontinuum variables. The main result shows that in case of selective fishing, where onlyfish of prescribed sizes is harvested, it may be advantageous in the log run to implementa periodic fishing effort, rather than constant (the latter suggested by single-fishmodels that disregard the age-heterogeneity). Thus taking into account the age-structureof the fish may qualitatively change the theoretically optimal fishing mode. This resultis obtained by developing a technique for reliable numerical verification of second ordernecessary optimality conditions for the considered problem. This technique could be usefulfor other optimal control problems of periodic age-structured systems.

Keywords

age-structured systemsperiodic controloptimal fishingproperness test
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 4: Optimal control , 2014 , pp. 20 - 37
Copyright
© EDP Sciences, 2014

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