Stabilizing management of fluctuating resources

We consider a resource management problem in which the management objective is to minimize fluctuations in resource stocks. Stabilizing management policies constitute the designing of memoryless state feedback control strategies for a discrete time resource model which contains unknown but bounded fluctuations. We also show that the problem of maximizing sustainable yield in an uncertain fishery can be considered as the problem of stabilizing of the stock level.The paper corresponds to an invited talk at the 14th Symposium on Operations Research, Ulm, September 6–8, 1989.The support by Yrjö Jahnsson Foundation is gratefully acknowledged.This work was supported by NSF and AFOSR under grant ECS 8602524.     

STEADY STATE AND INTERTEMPORAL MANAGEMENT MODELS FOR MARINE FISHERIES

Abstract Steady state and dynamic management models are developed for analyzing the Malaysian marine fisheries. These models originate from the theoretical concepts of the natural resource economics namely the open access, limited entry and the intertemporal fishery models. Such management models are deemed necessary because of the need to sustain the depleting resource and degrading environment. Marine fisheries had been managed under open access for a long time before government intervention took effect sometime during the 1960s. Open access and government intervention during the earlier phase of economic development contributed to the immediate pressure on fisheries. Community development programs geared to alleviate poverty among the fishermen apparently contradicted the effort of sustaining fisheries. Even today this fundamental management objective of sustainable development of fishery resource is not fully adhered to. This study suggests that ability to sustain fishery requires government intervention that can direct resource use to steady state or intertemporal optimal levels.     

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 of an inland fishery resource under incomplete information

A new mathematical model for finding the optimal harvesting policy of an inland fishery resource under incomplete information is proposed in this paper. The model is based on a stochastic control formalism in a regime‐switching environment. The incompleteness of information is due to uncertainties involved in the body growth rate of the fishery resource: a key biological parameter. Finding the most cost‐effective harvesting policy of the fishery resource ultimately reduces to solving a terminal and boundary value problem of a Hamilton‐Jacobi‐Bellman equation: a nonlinear and degenerate parabolic partial differential equation. A simple finite difference scheme for solving the equation is then presented, which turns out to be convergent and generates numerical solutions that comply with certain theoretical upper and lower bounds. The model is finally applied to the management of Plecoglossus altivelis, a major inland fishery resource in Japan. The regime switching in this case is due to the temporal dynamics of benthic algae, the main food of the fish. Model parameter values are identified from field measurement results in 2017. Our computational results clearly show the dependence of the optimal harvesting policy on the river environmental and biological conditions. The proposed model would serve as a mathematical tool for fishery resource management under uncertainties.     

Resource leasing and optimal periodic capital investments

In this paper we analyse a fishery resource exploitation model in which a single firm or a cartel has leased the rights to manage the resources independently. Two variables, resource level and the capital level, determine the dynamics of the resource system. The leasing contract includes an incentive for the agent to maintain the resource level high. The main result is that sole-agent resource management and efficiency of the resource use do not necessarily imply that the fishery is stabilized at a unique steady state level. Instead, the optimal resource exploitation may lead to periodic capital investments in fishing vessels and gear which in turn causes cycles in the resource economy. We show analytically that nonzero discount rate and low capital depreciation rate both favor the conditions under which periodic optimal solutions may occur. Simulation results related to a Baltic herring fishery are used to illustrate the results.This research was partly supported by the Austrian Science Foundation under contract number P7783. The support of the Academy of Finland and Yrjö Jahnsson Foundation to V. K. is greatly appreciated. We thank Carl Folke, Mikael Hildén and Steffen Jørgensen and three anonymous referees for helpful comments. V. K. thanks the Beijer Institute of the Royal Swedish Academy of Science for its hospitality.     

PARTIAL VERSUS GENERAL STORAGE POLICY: COMMODITIES AND RESOURCES

This paper examines joint storage considerations when both commodities and resources can be stored, e.g., grain and water for irrigation. Results suggest that when separate agencies control public resource and commodity storage, suboptimal storage rules occur unless (i) each agency is sensitive to the policies of the other, (ii) commodity inventories are adjusted in response to prices, and (iii) resource inventories are adjusted in response to both commodity demand and resource supply conditions. For example, the common case where water storage depends on weather and reservoir conditions alone is not sufficiently general. The results imply that water management agencies that tend to be dominated by engineers and hydrological considerations need to incorporate economic considerations into decision processes.     

REBUILDING THE EASTERN BALTIC COD STOCK UNDER ENVIRONMENTAL CHANGE (PART II): TAKING INTO ACCOUNT THE COSTS OF A MARINE PROTECTED AREA

Abstract This study adds a cost analysis of the Eastern Baltic cod fishery to the existing model presented in Röckmann et al. [2007a] . As cost data on this international fishery do not exist, data from Denmark are extrapolated to the whole international fishery. Additionally, unit and total variable costs are simulated, and the sensitivity to a set of different cost–stock and cost–output elasticities is tested. The study supports preliminary conclusions that a temporary marine reserve policy, which focuses on protecting the Eastern Baltic cod spawning stock in the International Council for the Exploration of the Sea (ICES) subdivision 25, is a valuable fisheries management tool to (i) rebuild the overexploited Eastern Baltic cod stock and (ii) increase operating profits. The negative effects of climate change can be postponed for at least 20 years—depending on the assumed rate of future climate change. Including costs in the economic analysis does not change the ranking of management policies as proposed in the previous study where costs were neglected.     

Dynamic modelling of labour assignment flexibility in the French fresh food industry

Owing to the perishability of fresh produce, the food industry has to react quickly by implementing different policies on labour management. We conduct two intensive surveys which showed that human resource management (HRM) issues in the fresh food industry mainly consist in finding appropriate labour capacity that meets the specific fluctuations in sales. The HRM decisions were taken so that flexible working time more efficiently matched the workload and staffing numbers. These empirical findings are very informative in that they point to how managers make HRM decisions when choosing the kind of employees they have to hire according to the type of additional workload imposed. In addition, they relate to the employment contract (temporary or permanent staff, subcontractor), the time required for employees to be efficient and their quality of work. Following this qualitative research, we mathematically formalize the combinatory possibilities of HRM assignments and the decision problems to be addressed. Finally, we propose a simulation tool for analysing the dynamical consequences of the HRM policies by comparing different policies on labour management.     

OPTIMAL-SUSTAINABLE MANAGEMENT OF MULTI-SPECIES FISHERIES: LESSONS FROM A PREDATOR-PREY MODEL

ABSTRACT. In this paper we consider the meaning of sustainable resource management in multi-dimensional resources. Based on the principle of intergenerational fairness, we define fisheries management as sustainable if it does not lead to a decline in the net present value of the fishery. If sustainability, or intergenerational fairness, were held as an obligation by fishery managers, then the traditional present-value maximization objective would be constrained. Using numerical solutions to a simple predator-prey model, we explore how the optimal-sustainable management of this fishery would differ from management that seeks to maximize the present value of the benefits. General lessons regarding the meaning of sustainable fishery management are discussed.     

Back to the future: A retrospective assessment of model‐based scenarios for the management of the shrimp fishery in French Guiana facing global change

While the number of models dedicated to predicting the consequences of alternative resource management strategies has increased, instances in which authors look back at past predictions to learn from discrepancies between these and observed developments are scarce. In the past decades, the French Guiana shrimp fishery has experienced shrimp market globalization and decreasing levels of shrimp recruitment due to environmental changes. In 2006, a bio‐economic model of this fishery was developed to simulate its possible responses to economic and environmental scenarios up to 2016. Here, we compare here these predictions to the observed trajectories. While the number of active vessels corresponds to that which was predicted, the estimated shrimp stock does not. Important driving factors had not been anticipated, including a general strike, natural disasters, and the end of the global financial crisis. These results show the importance of participative approaches involving stakeholders in the co‐construction and shared representation of scenarios. Recommendations for resource managers

• Effective fisheries resources management and a fortiori, the capacity of the fisheries to adapt to global change, requires understanding of both ecological and economics dynamics.
• The temporal trajectory of the trawling shrimp fisheries has been well monitored, and the decline of both stock and fleet is understood regarding ecological and economic changes: Changes in the environmental conditions of shrimp recruitment, and oil price increase and selling price decrease.
• However, our bio‐economic modeling work showed that, even with a good understanding of the dynamics explaining past trajectories, unpredictable events (strike, natural disasters…) have acted as other key driving factors altering the capacity of the model to represent possible futures.
• These results led us to recommend a better integration of the expertise of social and political scientists in developing models of bio‐economic systems to increase the quality of scenario predictions, and to argue for more participative approaches involving the stakeholders.

     

An infinite horizon mathematical programming model of a multicohort single species fishery

Fishery policy evaluation should take account of the initial state of the fishery and the population dynamics of the fish stock. Although multicohort bioeconomic fishery policy evaluation models have been developed, the results from these models depend on the choice of planning period and the desired state of the stock at the end of this period. In this paper it is noted that these limitations can be overcome by evaluating fishery policy over an infinite time horizon, and a mixed integer programming (MIP) model is developed for carrying out this form of analysis in a multicohort single species fishery. This new MIP model allows policies to be evaluated over an infinite horizon by incorporating results from a steady state fishery model into a multiperiod framework. The use of this MIP model in determining policies for reaching and maintaining a steady state is illustrated.     

INTEGRATING MARINE PROTECTED AREAS INTO MODELS FOR FISHERY ASSESSMENT AND MANAGEMENT

ABSTRACT. Marine protected areas (MPAs) have been proposed as an insurance policy against fishery management failures and as an integral part of an optimal management system for some fisheries. However, an incorrectly designed MPA can increase the risk of depletion of some species, and can reduce the value of the system of fisheries it impacts. MPAs may alter structural processes that relate fishery outcomes to management variables and thereby compromise the models that are used to guide decisions. New models and data gathering programs are needed to use MPAs effectively. This paper discusses the motivations and methods for incorporating explicitly spatial dynamics of both fish and fishermen into fishery models so that they can be used to assess spatial policies such as MPAs. Some important characteristics and capabilities which these models should have are outlined, and a topical review of some relevant modeling methodologies is provided.     

The bullwhip effect in supply chain networks

This paper analyzes the propagation and amplification of order fluctuations (i.e., the bullwhip effect) in supply chain networks operated with linear and time-invariant inventory management policies. The supply chain network is allowed to include multiple customers (e.g., markets), any network structure, with or without sharing information. The paper characterizes the stream of orders placed by any supplier for any stationary customer demand processes, and gives exact formulas for the variance of the orders placed and the amplification of order fluctuations. The paper also derives robust analytical conditions, based only on inventory management policies, to predict the presence of the bullwhip effect for any network structure, any inventory replenishment policies, and arbitrary customer demand processes. Numerical examples show that the analytical results accurately quantify the bullwhip effect; managerial insights are drawn from the analysis. The methodology presented in this paper generalizes those in previous studies for serial supply chains.     

THE OPTIMAL MANAGEMENT OF TRANSBOUNDARY FISHERIES: GAME THEORETIC CONSIDERATIONS

One of the most ubiquitous of the fishery management problems to have arisen as a result of E.F.J. is that of managing transboundary resources. Economic analysis of this problem rests upon models blending the standard dynamic economic analysis of fisheries with game theory. The analysis reveals that noncooperation is likely to have severe economic consequences and that cooperative arrangements must deal with possible conflicting goals of management, as well as the division of economic returns from the fishery. While the existing economic analysis of transboundary fishery management is far from complete, it can be shown that the analysis is capable of providing important insights into existing real world cases of transboundary resource management.     

Computation of viability kernels: a case study of by-catch fisheries

Traditional means of studying environmental economics and management problems consist of optimal control and dynamic game models that are solved for optimal or equilibrium strategies. Notwithstanding the possibility of multiple equilibria, the models’ users—managers or planners—will usually be provided with a single optimal or equilibrium strategy no matter how reliable, or unreliable, the underlying models and their parameters are. In this paper we follow an alternative approach to policy making that is based on viability theory. It establishes “satisficing” (in the sense of Simon), or viable, policies that keep the dynamic system in a constraint set and are, generically, multiple and amenable to each manager’s own prioritisation. Moreover, they can depend on fewer parameters than the optimal or equilibrium strategies and hence be more robust. For the determination of these (viable) policies, computation of “viability kernels” is crucial. We introduce a MATLAB application, under the name of VIKAASA, which allows us to compute approximations to viability kernels. We discuss two algorithms implemented in VIKAASA. One approximates the viability kernel by the locus of state space positions for which solutions to an auxiliary cost-minimising optimal control problem can be found. The lack of any solution implies the infinite value function and indicates an evolution which leaves the constraint set in finite time, therefore defining the point from which the evolution originates as belonging to the kernel’s complement. The other algorithm accepts a point as viable if the system’s dynamics can be stabilised from this point. We comment on the pros and cons of each algorithm. We apply viability theory and the VIKAASA software to a problem of by-catch fisheries exploited by one or two fleets and provide rules concerning the proportion of fish biomass and the fishing effort that a sustainable fishery’s exploitation should follow.     

MULTISPECIES EXPLOITATION WITH EVOLUTIONARY SWITCHING OF HARVESTING STRATEGIES

In this paper, we propose a bioeconomic model which describes a fishery in which each of two noninteracting species is harvested by a given group of fishers during a defined time period. Then the Fishing Regulatory Authority allows each fisher to reconsider the harvesting decision at fixed (discrete) periods of time. The model derives from an Italian fisheries management experience in the Northern Adriatic Sea, where this kind of “self‐adjusting” fishing policy has been proposed to regulate harvesting of two shellfish species. The proposed dynamic model assumes the form of a hybrid system, as the natural growth functions of the two species (in continuous time) are coupled with a discrete time adaptive system that regulates how agents switch from one harvesting strategy to the other period by period according to an evolutionary mechanism based on profit comparison. In order to obtain some insights into the basic mechanisms of the system, some relevant benchmark cases are analyzed before tackling (mainly numerically) the complete hybrid model. Our results suggest that, for proper sets of parameters, this kind of myopic and adaptive self‐regulation may ensure a virtuous trade‐off between profit maximization and resource conservation, driven by cost externalities and market pressure.     

MANAGEMENT OF A RENEWABLE RESOURCE WITH A FINITE DEMAND ELASTICITY

Optimal management policies are derived for a renewable resource when the demand for output has finite elasticity. The analysis modifies traditional views of this problem by allowing for the possibility that static optimizing policies, which maximize myopic net revenues, may be superior to “Golden Rule” policies which account for longer-run stock effects.     

REBUILDING THE EASTERN BALTIC COD STOCK UNDER ENVIRONMENTAL CHANGE–A PRELIMINARY APPROACH USING STOCK,ENVIRONMENTAL, AND MANAGEMENT CONSTRAINTS

ABSTRACT. . The population dynamics of the Eastern Baltic cod (Gadus morhua callarias L.), unlike many other stocks, shows a strong dependency on environmental conditions. To test the implications of different management policies on the stock and the fishery in a system of global environmental change, we apply a spatially disaggregated, discrete time, age‐structured model of the Eastern Baltic cod stock in 50 year simulation analyses. The simulation provides an analysis of stock, yield, and revenue development under various management policies and environmental scenarios. The policy analysis, focusing on different regulations of fishing mortality, is embedded into three environmental scenarios, assuming low, medium, or high climate and environmental change. The environmental assumptions are based on simulation results from a coupled atmosphere‐ocean regional climate model, which project salinity in the Baltic Sea to decrease by 7–47% in the period 2071–2100 relative to the reference period 1961 1990. Our simulation results show that a significant reduction in fishing mortality is necessary for achieving high long‐term economic yields. Moreover, under the environmental scenarios presented, a stock collapse cannot be prevented. It can, however, be postponed by the establishment of a marine reserve in ICES subdivision 25.     

基于收益管理和仿真的第三方仓储资源分配

针对不确定市场需求条件下第三方仓储资源的能力规划与分配问题,构建随机数学规划模型,理论分析证明了最优资源分配量的存在性,并指出最优资源分配量是单位资源成本的递减函数、单位资源收益和单位损失成本的递增函数。鉴于解析求解的复杂性,基于收益管理思想,结合离散事件仿真技术和响应曲面法,提出一种新的分析求解框架:收益管理用于细分顾客、构建资源分配策略,仿真模型刻画系统随机特性并评估系统绩效指标,响应曲面法则优化分配策略并探寻绩效改进方向。案例研究和仿真实验结果显示,根据顾客类别分配仓储能力的策略优于传统的先到先服务策略,收益管理、响应曲面法与仿真的综合集成,能够提高系统收益,从而使本文所提方法体系得到了有效验证。