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A discrete optimality system for an optimal harvesting problem

Author

Listed:
  • Hacer Öz Bakan

    (Atılım University)

  • Fikriye Yılmaz

    (Gazi University)

  • Gerhard-Wilhelm Weber

    (Middle East Technical University)

Abstract

In this paper, we obtain the discrete optimality system of an optimal harvesting problem. While maximizing a combination of the total expected utility of the consumption and of the terminal size of a population, as a dynamic constraint, we assume that the density of the population is modeled by a stochastic quasi-linear heat equation. Finite-difference and symplectic partitioned Runge–Kutta (SPRK) schemes are used for space and time discretizations, respectively. It is the first time that a SPRK scheme is employed for the optimal control of stochastic partial differential equations. Monte-Carlo simulation is applied to handle expectation appearing in the cost functional. We present our results together with a numerical example. The paper ends with a conclusion and an outlook to future studies, on further research questions and applications.

Suggested Citation

  • Hacer Öz Bakan & Fikriye Yılmaz & Gerhard-Wilhelm Weber, 2017. "A discrete optimality system for an optimal harvesting problem," Computational Management Science, Springer, vol. 14(4), pages 519-533, October.
    • Handle: RePEc:spr:comgts:v:14:y:2017:i:4:d:10.1007_s10287-017-0286-5
    DOI: 10.1007/s10287-017-0286-5
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    Cited by:

    1. Hidekazu Yoshioka & Yuta Yaegashi, 2020. "A growth rate control problem of harmful species population and its application to algae bloom," Environment Systems and Decisions, Springer, vol. 40(1), pages 107-124, March.
    2. Gomes, Vanessa de Souza & Monti, Cássio Augusto Ussi & Silva, Carolina Souza Jarochinski e & Gomide, Lucas Rezende, 2021. "Operational harvest planning under forest road maintenance uncertainty," Forest Policy and Economics, Elsevier, vol. 131(C).

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