A discrete optimality system for an optimal harvesting problem


Bakan H. O. , Yilmaz F., Weber G.

COMPUTATIONAL MANAGEMENT SCIENCE, cilt.14, ss.519-533, 2017 (ESCI İndekslerine Giren Dergi)

  • Cilt numarası: 14 Konu: 4
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s10287-017-0286-5
  • Dergi Adı: COMPUTATIONAL MANAGEMENT SCIENCE
  • Sayfa Sayısı: ss.519-533

Özet

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.