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Optimality of greedy and sustainable policies in the management of renewable resources
Author(s) -
Rapaport A.,
Sraidi S.,
Terreaux J.P.
Publication year - 2003
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.718
Subject(s) - bellman equation , mathematical optimization , function (biology) , economics , class (philosophy) , time horizon , greedy algorithm , mathematical economics , marginal value , value (mathematics) , mathematics , computer science , microeconomics , statistics , evolutionary biology , artificial intelligence , biology
We consider a discrete‐time modelling of renewable resources, which regenerate after a delay once harvested. We study the qualitative behaviour of harvesting policies, which are optimal with respect to a discounted utility function over infinite horizon. Using Bellman's equation, we derive analytically conditions under which two types of policies (greedy and sustainable) are optimal, depending on the discount rate and the marginal utility. For this particular class of problems, we show also that the greedy policy is attractive in a certain sense. The techniques of proof lie on concavity, comparison of value functions and Lyapunov‐like functions. Copyright © 2003 John Wiley & Sons, Ltd.