Optimal harvesting of a renewable resource in a polluted environment: An allocation problem of the sole owner

2019 ◽  
Vol 32 (2) ◽  
pp. e12206
Author(s):  
Srinivasu D. N. Pichika ◽  
Simon D. Zawka
Keyword(s):  
Renewable Resource ◽  
Allocation Problem ◽  
Optimal Harvesting ◽  
Polluted Environment ◽  
Sole Owner

INFLUENCE OF INVESTING IN TREATING A POLLUTED ENVIRONMENT ON THE HARVEST: A PROBLEM OF OPTIMAL ALLOCATION

2019 ◽  
Vol 27 (02) ◽  
pp. 257-279
Author(s):  
P. D. N. SRINIVASU ◽  
SIMON D. ZAWKA
Keyword(s):  
Optimal Allocation ◽  
Infinite Horizon ◽  
Renewable Resource ◽  
Maximum Sustainable Yield ◽  
Allocation Problem ◽  
Sustainable Yield ◽  
Optimal Solutions ◽  
Polluted Environment ◽  
Sole Owner

This study is concerned with harvesting a renewable resource that is surviving in a polluted environment. Fall in the revenue from the resource due to presence of pollution in the environment drives the sole owner to allocate a part of the available effort towards treating the environment and the interest is to find the optimal allocation of the available effort towards harvesting the resource and treating the environment so that the revenue is maximized. Resource-pollution dynamics are studied, maximum sustainable yield and maximum sustainable revenue have been evaluated. Further, an optimal allocation problem has been formulated on infinite horizon and optimal solutions are obtained. Key results of the study are demonstrated through numerical illustrations.

scholarly journals Optimal Harvesting Effort for Nonlinear Predictive Control Model for a Single Species Fishery

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Messaoud Bounkhel ◽  
Lotfi Tadj
Keyword(s):  
Predictive Control ◽  
Renewable Resource ◽  
Single Species ◽  
State Equation ◽  
Control Model ◽  
Optimal Harvesting ◽  
Solution Approach ◽  
Nonlinear Predictive Control ◽  
Nonlinear State ◽  
Resource System

We use nonlinear model predictive control to find the optimal harvesting effort of a renewable resource system with a nonlinear state equation that maximizes a nonlinear profit function. A solution approach is proposed and discussed and satisfactory numerical illustrations are provided.

scholarly journals A Mathematical Model for Optimal Management and Utilization of a Renewable Resource by Population

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
B. Dubey ◽  
Atasi Patra
Keyword(s):  
Output Feedback ◽  
Output Feedback Control ◽  
Hamiltonian Function ◽  
Renewable Resource ◽  
Optimal Harvesting ◽  
Positive Equilibrium ◽  
Optimal Management ◽  
Crowding Effect ◽  
Stability Behavior ◽  
Theoretical Results

A dynamical model is proposed and analyzed to study the effect of the population on the resource biomass by taking into account the crowding effect. Biological and bionomical equilibria of the system are discussed. The global stability behavior of the positive equilibrium is studied via the output feedback control. An appropriate Hamiltonian function is formed for the discussion of optimal harvesting of resource which is utilized by the population using Pontryagin's Maximum Principal. A numerical simulation is performed on the model to analyze the theoretical results.

Optimization of discounted income for a structured population exposed to harvesting

2021 ◽  
pp. 15-25
Author(s):  
Anastasia V. Egorova
Keyword(s):  
Time Moment ◽  
Renewable Resource ◽  
Optimal Harvesting ◽  
Infinite Time ◽  
System Of Difference Equations ◽  
Time Intervals ◽  
Homogeneous Population ◽  
Structured Population ◽  
The Cost ◽  
Conventional Unit

A structured population the individuals of which are divided into n age or typical groups x_1,…,x_n. is considered. We assume that at any time moment k, k = 0,1,2… the size of the population x(k) is determined by the normal autonomous system of difference equations x(k+1)=F(x(k)), where F(x)=col(f_1 (x),…,〖 f〗_n (x) ) are given vector functions with real non-negative components f_i (x), i=1,…n. We investigate the case when it is possible to influence the population size by means of harvesting. The model of the exploited population under discussion has the form x(k+1)=F((1-u(k) )x(k) ), where u(k)= (u_1 (k),…,u_n (k))∈〖[0; 1]〗^n is a control vector, which can be varied to achieve the best result of harvesting the resource. We assume that the cost of a conventional unit of each of n classes is constant and equals to C_i≥0, i=1,…,n. To determine the cost of the resource obtained as the result of harvesting, the discounted income function is introduced into consideration. It has the form H_α (u ̅,x(0))=∑_(j=0)^∞▒〖∑_(i=1)^n▒〖C_i x_i (j) u_i (j) e^(-αj) 〗,〗 where α>0 is the discount coefficient. The problem of constructing controls on finite and infinite time intervals at which the discounted income from the extraction of a renewable resource reaches the maximal value is solved. As a corollary, the results on the construction of the optimal harvesting mode for a homogeneous population are obtained (that is, for n = 1).

scholarly journals Optimal harvesting of a spatial renewable resource

2014 ◽  
Vol 42 ◽  
pp. 105-120 ◽  
Author(s):  
Stefan Behringer ◽  
Thorsten Upmann
Keyword(s):  
Renewable Resource ◽  
Optimal Harvesting

scholarly journals Optimal control for a size-structured predator-prey model in a polluted environment

2021 ◽  
Vol 269 ◽  
pp. 01004
Author(s):  
Tainian Zhang ◽  
Zhixue Luo
Keyword(s):  
Size Structure ◽  
Necessary Optimality Conditions ◽  
Optimal Harvesting ◽  
Polluted Environment ◽  
Nonlinear Functional ◽  
Predator Prey ◽  
Optimal Harvesting Policy ◽  
Predator Prey Model ◽  
Dependent Model ◽  
The Fixed Point Theorem

In this paper, we deal with an optimal harvesting problem for a periodic predator-prey hybrid system dependent on size-structure in a polluted environment. In other words, a size-dependent model in an environment with a small toxicant content has been established. The well-posedness of state system is proved by using the fixed point theorem. The necessary optimality conditions are derived by tangent-normal cone technique in nonlinear functional analysis. The existence of a unique optimal harvesting policy is verified via the Ekeland’s variational principle. The optimal harvesting problem has an optimal harvesting policy, which has a Bang-Bang structure and provides a threshold for the optimal harvesting problem. Using the optimization theories and methods in mathematics to control phenomena of life. The objective function represents the total economic profit from the harvested population. Some theoretical results obtained in this paper provide a scientific theoretical basis for the practical application of the model.

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