Optimal harvesting policy for stochastic Logistic population model

In this paper, we consider some optimal harvesting policies for single population models, in which the harvest effort and the intrinsic growth rate are disturbed by environment noises. We choose the maximum sustainable yield and the maximum retained profits as two management objectives, and obtain the optimal harvesting policies, respectively. For the two objectives, we give the optimal harvest effort that maximizes the sustainable yield (or retained profits), the maximum of expectation of sustainable yield (or retained profits) and the corresponding variance. Their explicit expressions are determined by the coefficients of equation and the disturbance intensity.     

A robust optimization approach to wine grape harvesting scheduling

Optimization models are increasingly being used in agricultural planning. However, the inherent uncertainties present in agriculture make it difficult. In recent years, robust optimization has emerged as a methodology that allows dealing with uncertainty in optimization models, even when probabilistic knowledge of the phenomenon is incomplete. In this paper, we consider a wine grape harvesting scheduling optimization problem subject to several uncertainties, such as the actual productivity that can be achieved when harvesting. We study how effective robust optimization is solving this problem in practice. We develop alternative robust models and show results for some test problems obtained from actual wine industry problems.     

Optimal impulsive harvesting policy for single population

In this paper, we established the exploitation of impulsive harvesting single autonomous population model by Logistic equation. By some special methods, we analysis the impulsive harvesting population equation and obtain existence, the explicit expression and global attractiveness of impulsive periodic solutions for constant yield harvest and proportional harvest. Then, we choose the maximum sustainable yield as management objective, and investigate the optimal impulsive harvesting policies respectively. The optimal harvest effort that maximizes the sustainable yield per unit time, the corresponding optimal population levels are determined. At last, we point out that the continuous harvesting policy is superior to the impulsive harvesting policy, however, the latter is more beneficial in realistic operation.     

DO ACCURATE STOCK ESTIMATES INCREASE HARVEST AND REDUCE VARIABILITY IN FISHERIES YIELDS?

Abstract Fisheries managers normally make decisions based on stock abundance estimates subject to process, observation, and model uncertainties. Considerable effort is invested in gathering information about stock size to decrease these uncertainties. However, few studies have evaluated benefits from collecting such information in terms of yield and stability of annual harvest. Here, we develop a strategic age‐structured population model for a long‐lived fish with stochastic recruitment, resembling the Norwegian spring‐spawning herring (NSSH, Clupea harengus L.). We evaluate how uncertainties in population estimates influence annual yield, spawning stock biomass (SSB), and variation in annual harvest, using both the proportional threshold harvesting (PTH) and the current harvest control rule for NSSH as harvest strategies. Results show that the consequences of a biased estimate are sensitive to the harvest strategy employed. If the harvest strategy is suitably chosen, the benefits of accurate information are low, and less information about the stock is necessary to maintain high average yield. Reduced harvest intensity effectively removes the need for accurate stock estimates. PTH (a variant of the constant escapement strategy) with low harvest ratio and the current NSSH harvest control rule both provide remarkable stability in yield and SSB. However, decreased uncertainty will often decrease year‐to‐year variation in harvest and the frequency of fishing moratoria.     

Optimal harvesting policy for general stochastic Logistic population model

We consider some optimal harvesting policies for a general stochastic Logistic population model. For two management objectives, that are maximum sustainable yield and the maximum retained profits, the optimal harvesting policies are obtained. Meanwhile, the optimal harvest effort, the maximum of expectation of sustainable yield (or retained profits) and the corresponding variance are given.     

周期Gompertz生态系统中的最优脉冲控制收获策略

以周期Gompertz系统为基础,讨论了周期变化的单种群生物资源的收获优化问题及种群的动力学性质.在单位收获努力量假设下,以最大可持续收获量为管理目标,确定了线性收获下的最优收获策略,获得了最优收获努力量、最大可持续收获及相应的最优种群水平的显示表达式,为自然资源的开发和利用提供了理论依据.     

Covering models and optimization techniques for emergency response facility location and planning: a review

With emergencies being, unfortunately, part of our lives, it is crucial to efficiently plan and allocate emergency response facilities that deliver effective and timely relief to people most in need. Emergency Medical Services (EMS) allocation problems deal with locating EMS facilities among potential sites to provide efficient and effective services over a wide area with spatially distributed demands. It is often problematic due to the intrinsic complexity of these problems. This paper reviews covering models and optimization techniques for emergency response facility location and planning in the literature from the past few decades, while emphasizing recent developments. We introduce several typical covering models and their extensions ordered from simple to complex, including Location Set Covering Problem (LSCP), Maximal Covering Location Problem (MCLP), Double Standard Model (DSM), Maximum Expected Covering Location Problem (MEXCLP), and Maximum Availability Location Problem (MALP) models. In addition, recent developments on hypercube queuing models, dynamic allocation models, gradual covering models, and cooperative covering models are also presented in this paper. The corresponding optimization techniques to solve these models, including heuristic algorithms, simulation, and exact methods, are summarized.     

Applying simulation optimization to the asset allocation of a property–casualty insurer

Proper asset allocations are vital for property–casualty insurers to be competitive and solvent. Theories of finance offer little practical guidance in constructing such asset allocations however. This research integrates simulation models with a newly developed evolutionary algorithm for the multi-period asset allocation problem of a property–casualty insurer. We first construct a simulation model to simulate operations of a property–casualty insurer. Then we develop multi-phase evolution strategies (MPES) to be used with the simulation model to search for promising asset allocations for the insurer. A thorough experiment is conducted to evaluate the performance of our simulation optimization approach. Computational results show that MPES is an effective search algorithm. It dominates the grid search method by a significant margin. The re-allocation strategy resulting from MPES outperforms re-balancing strategies significantly. This research further demonstrates that the simulation optimization approach can be used to study economic issues related to multi-period asset allocation problems in practical settings.     

The optimal harvesting problem under price uncertainty

In this paper we study the exploitation of a one species forest plantation when timber price is governed by a stochastic process. The work focuses on providing closed expressions for the optimal harvesting policy in terms of the parameters of the price process and the discount factor, with finite and infinite time horizon. We assume that harvest is restricted to mature trees older than a certain age and that growth and natural mortality after maturity are neglected. We use stochastic dynamic programming techniques to characterize the optimal policy and we model price using a geometric Brownian motion and an Ornstein–Uhlenbeck process. In the first case we completely characterize the optimal policy for all possible choices of the parameters. In the second case we provide sufficient conditions, based on explicit expressions for reservation prices, assuring that harvesting everything available is optimal. In addition, for the Ornstein–Uhlenbeck case we propose a policy based on a reservation price that performs well in numerical simulations. In both cases we solve the problem for every initial condition and the best policy is obtained endogenously, that is, without imposing any ad hoc restrictions such as maximum sustained yield or convergence to a predefined final state.     

Bionomic exploitation of a ratio-dependent predator–prey system

The present article deals with the problem of combined harvesting of a Michaelis–Menten-type ratio-dependent predator–prey system. The problem of determining the optimal harvest policy is solved by invoking Pontryagin's Maximum Principle. Dynamic optimization of the harvest policy is studied by taking the combined harvest effort as a dynamic variable. Computer simulations are carried out to illustrate our analytical findings. Biological and bioeconomical interpretations of the results are explained critically.     

AN OPTIMIZATION APPROACH TO IDENTIFYING TIMBER SUPPLY FUNCTION COEFFICIENTS

This paper examines an optimization approach to identifying short-run timber supply function coefficients when the form of the supply function is known. By definition, a short-run timber supply function is a functional relationship between the optimal harvest level in each period (e.g., each year) and the actual forest-market state in the same period. The short-run timber supply function represents the optimal harvest decision policy, and therefore, the problem of optimal harvesting can be formulated as a problem of determining this function. When the form of the supply function is known, the problem becomes one of identifying the coefficients of the supply function. If the management objective is to maximize the expected present value of net revenues from timber harvesting over an infinite time horizon, and the timber price process is, in a sense, stationary, the supply function coefficients correspond to the optimal solution to an anticipative optimization problem. In this case, the supply function coefficients can be determined by maximizing the expected present value of the net revenues from timber harvesting, where periodic harvest levels are determined using the supply function. Numerical results show that the short-run supply functions determined using this approach gives good approximations of the true supply function.     

Simulation models to support the preliminary electoral results program for the Mexican Electoral Institute

On July 1st, 2018, federal elections for president, senators and deputies took place in Mexico. In most states, elections for state governors and representatives took also place in the same polling booths. The Technical Unit for Information Services (UNICOM) of the National Electoral Institute (INE) of Mexico has the responsibility for planning and implementation of the Preliminary Electoral Results Program (PREP) for federal elections. For the 2018 elections UNICOM developed forecasting models for the performance of PREP based on simulation models that were developed using a special purpose simulation software and C++ subroutines for fast simulation of queues. These simulation models were a valuable tool for planning, scheduling and allocation of the main resources that participated in the operational process of the PREP. In this article we report the main features, applications and results obtained by using these simulation models.

     

OPTIMAL DYNAMIC HARVEST OF A MOBILE RENEWABLE RESOURCE

Abstract We present a mathematical model for the growth, movement, and harvesting of a renewable resource, and characterize the spatiotemporal distribution of harvest effort which maximizes the present value of harvest (yield) over a finite time horizon. We derive the optimality system for this model and show that the yield‐maximizing solution often includes one or more no‐take reserves that change in size over time. We explore how the results change with varying parameter values. The results inform ongoing debate about the use of reserves, and are increasingly relevant as technology enables enforcement of spatially structured harvest constraints.     

OPTIMAL HARVESTING OF FISH POPULATIONS WITH NON-STATIONARY STOCK-RECRUITMENT RELATIONSHIPS

Optimal harvesting policies are commonly derived by assuming a time-invariant relationship between some productivity measure and the resource variable under control. Yet, long-term trends in the environment appear to induce persistent changes in spawning success in several fish stocks. I show that when predictable trends in environmental effects are incorporated into stock-recruitment models, optimal policies respond to changing environmental conditions in a way that depends very much on the management objective. When the goal is to maximize expected discounted yield, resulting risk-neutral policies computed for a model of a cyclic iteroparous population respond by continuously adjusting optimal spawning targets in phase with the environmental cycle: escapements are raised when favorable conditions are anticipated and they are lowered when poor environments are expected. These feedback responses reinforce recruitment fluctuations and lead to a sequence of boom and bust periods in the fishery. Policies shift diametrically when a risk-averse objective is pursued such as maximization of the expected sum of discounted logarithms of catches. Optimal escapements closely parallel fluctuations in population abundance, with harvest rates and catches much less variable than in the risk-neutral policy. Harvest rates respond in a compensatory way to changes in population abundance, anticipated environmental conditions, and expected strength of incoming year-classes. Depending on the specific model used, a constant harvest rate strategy may perform nearly as well as the optimal. Analytical results are provided that characterize risk-neutral optimal policies for stochastic delay-difference population models. Results show that knowledge of current environmental conditions can be used to construct harvest policies which are nearly as good as those “optimal” ones based on long-term environmental forecasts.     

Optimal harvesting policy for a stochastic predator–prey model

Optimal harvesting of a stochastic predator–prey model is considered in this paper. Sufficient and necessary criteria for the existence of optimal harvesting strategy are obtained. At the same time, the optimal harvest effort and the maximum of sustainable yield are given.     

Bioeconomic modelling of a three-species fishery with switching effect

This paper aims to study the problem of combined harvesting of a system involving one predator and two prey species fishery in which the predator feeds more intensively on the more abundant species. Mathematical formulation of the optimal harvest policy is given and its solution is derived in the equiblibrium case by using Pontryagin's Maximum principle. Dynamic optimization of the harvest policy is also discussed by takingE(t), the combined harvest effort, as a dynamic variable. Biological and bioeconomic interpretations of the results associated with the optimal equilibirum solution are explained. The significance of the constraints required for the existence of an optimal singular control are also given.     

Some Examples of the Use of Simulation in U.S. and Canadian Agriculture

Mathematical simulation is a technique widely used by agricultural engineers to determine systems interactions, to evaluate technical feasibility, to determine economic feasibility, to design complex structures and to help with managing production. In the past, simulation has been used one level removed from the farmers who manage operation on a day-to-day basis. This is changing.Three completely different types of simulations are presented: (1) a static and deterministic simulation of on-farm ethanol production that models the conversion process and determines economic feasibility; (2) a dynamic and deterministic simulation of maize production, including harvest and drying that is weather dependent; (3) a static and stochastic simulation that uses Monte Carlo techniques to obtain information about strength and performance of glued-laminated beams.We believe that inexpensive computing capability will tremendously increase the use of simulation models, such as the three described, that will help farmers better manage their production systems.     

Dynamics of the discrete Seno population model: Combined effects of harvest timing and intensity on population stability

The paper contains new results on the impact of harvesting times and intensities on the stability properties of Seno population models. It is proved that sufficiently high harvest intensities are stabilizing for any harvesting time in the sense that they create a positive equilibrium that attracts all positive solutions. Moreover, in the special case that the nonlinearity in the Seno model is a Ricker function, we derive a global stability result independent of timing and valid for low to medium harvesting efforts. The proof is based on a characterization of those harvesting intensities which guarantee a negative Schwarzian derivative for all harvesting times. Finally, we rigorously show that timing can be stabilizing as well as destabilizing by itself. In particular, a recent conjecture formulated by Cid et al. (2014) [1] is shown to be false.     

一类随机模型的最优捕获问题研究

在Volterra两种群竞争模型的基础上,构造了随机的具有捕获的两种群竞争模型,研究讨论了捕获对种群生长过程的影响和如何实现最优捕获等问题.从确定性模型入手,深入讨论随机竞争模型的收获最优问题.通过对捕获强度E和贴现率等的估计与讨论,计算出了最优捕获强度最优捕获量最优经济收益.     

Optimal impulsive harvesting on non-autonomous Beverton–Holt difference equations

Many recent advances in the theory of the optimal economic exploitation of renewable fish resources have been gained by applying optimal control theory. However, despite these successes, much less is known about how seasonal environments affect the maximum sustainable yield (MSY) (or population persistence) and any effects of relations between intensity and frequency of harvesting. Assuming that fish populations follow Beverton–Holt equations we investigated impulsive harvesting in seasonal environments, focusing on both economic aspects and resource sustainability. We first investigated the existence and stability of a periodic solution and its analytic formula, and then showed that the population persistence depends on the intensity and frequency of harvesting. With the MSY as a management objective, we investigated optimal impulsive harvesting policies. The optimal harvesting effort that maximizes the sustainable yield, the corresponding optimal population level, and the MSY are obtained by using discrete Euler–Lagrange equations and product formulae, and their explicit expressions were obtained in terms of the intrinsic growth rate, the carrying capacity, and the impulsive moments. These results imply that harvest timing is of crucial importance to the MSY. Since impulsive differential equations incorporate elements of continuous and discrete systems, we can apply all results obtained for Beverton–Holt equations with impulsive effects to periodic logistic equations with impulsive harvesting.