Optimal Exploitation of Nonrenewable Resources

Kunow, Angela; Rosche, Sandy; Tammer, Christiane; Weiser, Christoph

doi:10.1007/s10957-013-0429-y

Cited by 1 publication

(2 citation statements)

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“…Blanchard et al [36] and Yu and Leung [37] considered impulsive harvesting strategies of aquacultured organisms with density-dependent growth. Kunow et al [38] analyzed a cost-effective optimal exploitation strategy of non-renewable resources subject to a prescribed demand rate. Although not the research on aquaculture, Alshamary and Calin [39,40] presented simple and tractable applications of the theory of stochastic optimal stopping to industrial problems.…”

Section: Introductionmentioning

confidence: 99%

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Optimization model to start harvesting in stochastic aquaculture system

Yoshioka

Yaegashi

2017

Appl Stoch Models Bus & Ind

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Establishment of cost-effective management strategy of aquaculture is one of the most important issues in fishery science, which can be addressed with bio-economic mathematical modeling. This paper deals with the aforementioned issue using a stochastic process model for aquacultured non-renewable fishery resources from the viewpoint of an optimal stopping (timing) problem. The goal of operating the model is to find the optimal criteria to start harvesting the resources under stochastic environment, which turns out to be determined from the Bellman equation (BE). The BE has a separation of variables type structure and can be simplified to a reduced BE with a fewer degrees of freedom. Dependence of solutions to the original and reduced BEs on parameters and independent variables is analyzed from both analytical and numerical standpoints. Implications of the analysis results to management of aquaculture systems are presented as well. Numerical simulation focusing on aquacultured Plecoglossus altivelis in Japan validates the mathematical analysis results. Bus. Ind. 2017, 33 476-493 The quantity W * is related to Ψ that solves the reduced BE (12), and therefore, Ψ and W * have to be simultaneously solved. The curve C is therefore a free boundary. Assuming the unique existence of such C, the one-dimensional domain 0 < w < +∞ for each t < T can be separated into the two regions: the waiting region S 1 (t) = {w; Ψ (t, w) > w} and the Appl. Stochastic Models Bus. Ind. 2017, 33 476-493 Appl. Stochastic ModelsProof of Proposition 3.3 J ,t with p = ( p) i (i = 1, 2) is denoted as J ,t,i . For each ∈ t,T , the inequalitydirectly follows from (5). This leads to

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Section: Introductionmentioning

confidence: 99%

“…Kunow et al . analyzed a cost‐effective optimal exploitation strategy of non‐renewable resources subject to a prescribed demand rate. Although not the research on aquaculture, Alshamary and Calin presented simple and tractable applications of the theory of stochastic optimal stopping to industrial problems.…”

Section: Introductionmentioning

confidence: 99%

Optimization model to start harvesting in stochastic aquaculture system

Yoshioka

Yaegashi

2017

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

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Optimal Exploitation of Nonrenewable Resources

Cited by 1 publication

References 3 publications

Optimization model to start harvesting in stochastic aquaculture system

Optimization model to start harvesting in stochastic aquaculture system

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