A singular stochastic control model for sustainable population management of the fish-eating waterfowl Phalacrocorax carbo

During recent years, the possibility that damage at the time of earthquake could change depending on the deterioration condition of infrastructure has been noted through analytical analyses. Faced with such a possibility, management policy should be optimized by internalizing the external elements of earthquake damage, evaluating the appropriateness of management policy for infrastructure, and optimizing the system. In this study, the deterioration process for infrastructure was modelled using the Markov process model, and a methodology to determine the optimal management policy is proposed by considering the two risks: i) the risk that infrastructure fails because of deterioration independent of external elements such as an earthquake, and ii) the risk that changes due to deterioration fails the infrastructure at the time of earthquake. Using an example of the application the following two points are demonstratively shown: i) the optimal management policy would change in the case in which earthquake risk is not considered, and ii) the optimal management policy would change depending on the earthquake occurrence probability in the case in which earthquake risk is considered.

Feeding damage from a fish-eating bird Phalacrocorax carbo to a fish Plecoglossus altivelis is severe in Japan. A stochastic impulse control model is introduced for finding the cost-effective and ecologically conscious population management policy of the bird. The optimal management policy is of a threshold type; if the population reaches an upper threshold, then taking a countermeasure to immediately reduce the bird to a lower threshold. This optimal policy is found through solving a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). We propose a numerical method for HJBQVIs based on a policy iteration approach. Its accuracy on numerical solutions and the associated free boundaries for the management thresholds of the population, is investigated against an exact solution. The computational results indicate that the proposed numerical scheme can successfully solve the HJBQVI with the first-order computational accuracy. In addition, it is shown that the scheme captures the free boundaries subject to errors smaller than element lengths.

Stochastic optimization serves as a central tool for effective population management. We present an impulse control model and a related singular control model for finding the cost-effective and sustainable population management policies of fish-eating birds, predators of fishery resources. The impulse control model considers the cost proportional to the amount of the killed bird and the fixed cost, while singular counterpart considers only the proportional cost. Their optimal controls are discussed from both qualitative and quantitative viewpoints.

This study identifies the optimal management policy of a given energy storage system (ESS) installed in a grid-connected wind farm in terms of maximizing the monetary benefits and provides guidelines for defining the economic value of the ESS under optimal management policy and selecting the optimal size of the ESS based on economic value. Considering stochastic models for wind power and electricity price, we develop a finite-horizon periodic-review Markov decision process (MDP) model to seek the optimal management policy. We also use a simple optimization model to find the optimal storage capacity and charging/discharging capacity of the ESS. By applying our analytic approach to a real-world grid-connected wind farm located in South Korea, we verify the usefulness of this study. Our numerical study shows that the economic value of the ESS is highly dependent on management policy, wind electricity variability, and electricity price variability. Thus, the optimal size of ESS should be carefully determined based on the locational characteristics and management policy even with limited investments. Furthermore, this study provides a meaningful policy implication regarding how much of a subsidy the government should provide for installing ESS in a wind farm.

We consider a class of singular stochastic control problems arising frequently in applications of stochastic control. We state a set of conditions under which the optimal policy and its value can be derived in terms of the minimal r-excessive functions of the controlled diffusion, and demonstrate that the optimal policy is of the standard local time type. We then state a set of weak smoothness conditions under which the value function is increasing and concave, and demonstrate that given these conditions increased stochastic fluctuations decrease the value and increase the optimal threshold, thus postponing the exercise of the irreversible policy. In line with previous studies of singular stochastic control, we also establish a connection between singular control and optimal stopping, and show that the marginal value of the singular control problem coincides with the value of the associated stopping problem whenever 0 is not a regular boundary for the controlled diffusion.

In Japan, the aging of infrastructure is progressing and the infrastructure management costs are expected to increase. Furthermore, to reduce the damage caused by frequent disasters to infrastructure, policies that ensure the resilience of infrastructure to disasters, as well as infrastructure management policies, must be implemented. In this chapter, we consider a hypothetical situation in which the infrastructure deteriorates over time and the damage caused by a disaster varies according to the state of the infrastructure’s deterioration. In such a case, it is thought that infrastructure management policies during normal times (i.e., not during disasters) also serve as disaster prevention policies, and a method is introduced to optimize management policies by taking both the lifecycle costs and disaster risks of infrastructures into account. Sensitivity analyses are then conducted on the probability of disaster occurrence, the rate of deterioration of infrastructure, and the relationship between the state of deterioration of infrastructure and the damage caused by disasters, to derive optimal management policies for various situations. We specifically assume that the probability of disaster occurrence increases over time, and we propose that optimal management policies during normal times may change meaningfully depending on the probability of disaster occurrence. The results are then discussed in the context of infrastructure finance.KeywordsInfrastructure asset managementDisaster risk reductionInfrastructure financeOptimal control theory

Optimality necessary conditions in singular stochastic control problems with nonsmooth data

This paper investigates the relationship between the stochastic maximum principle and the dynamic programming principle for singular stochastic control problems. The state of the system under consideration is governed by a stochastic differential equation, with nonlinear coefficients, allowing both classical control and singular control. We show that the necessary conditions for optimality, obtained earlier, are in fact sufficient provided some concavity conditions are fulfilled. In a second step, we prove a verification theorem and we show that the solution of the adjoint equation coincides with the derivative of the value function. Finally, using these results, we solve explicitly an example.

The under-performance of supply chains presents a significant hindrance to disease control in developing countries. Stock-outs of essential medicines lead to treatment interruption which can force changes in patient drug regimens, drive drug resistance and increase mortality. This study is one of few to quantitatively evaluate the effectiveness of supply chain policies in reducing shortages and costs. This study develops a systems dynamics simulation model of the downstream supply chain for amikacin, a second-line tuberculosis drug using 10 years of South African data. We evaluate current supply chain performance in terms of reliability, responsiveness and agility, following the widely-used Supply Chain Operation Reference framework. We simulate 141 scenarios that represent different combinations of supplier characteristics, inventory management strategies and demand forecasting methods to identify the Pareto optimal set of management policies that jointly minimize the number of shortages and total cost. Despite long supplier lead times and unpredictable demand, the amikacin supply chain is 98% reliable and agile enough to accommodate a 20% increase in demand without a shortage. However, this is accomplished by overstocking amikacin by 167%, which incurs high holding costs. The responsiveness of suppliers is low: only 57% of orders are delivered to the central provincial drug depot within one month. We identify three Pareto optimal safety stock management policies. Short supplier lead time can produce Pareto optimal outcomes even in the absence of other optimal policies. This study produces concrete, actionable guidelines to cost-effectively reduce stock-outs by implementing optimal supply chain policies. Preferentially selecting drug suppliers with short lead times accommodates unexpected changes in demand. Optimal supply chain management should be an essential component of national policy to reduce the mortality rate.

A system requiring a waste management license from an enforcement agency has been introduced in many countries. A license system is usually coupled with fines, a manifest, and a disposal tax. However, these policy devices have not been integrated into an optimal policy. In this paper we derive an optimal waste management policy by using those policy devices. Waste management policies are met with three difficult problems: asymmetric information, the heterogeneity of waste management firms, and non-compliance by waste management firms and waste disposers. The optimal policy in this paper overcomes all three problems.

<p>During recent years, the possibility that damage at the time of earthquake could change depending on the deterioration condition of infrastructure has been noted through analytical calculations. Faced with such a possibility, management policy should be optimized by internalizing the external elements of earthquake damage, evaluating the appropriateness of management policy for infrastructure, and optimizing the system. In this study, the deterioration process for infrastructure was modelled using the Markov process model, and a methodology to determine the optimal management policy is proposed by considering the two risks: i) the risk that infrastructure fails because of deterioration independent of external factors such as an earthquake, and ii) the risk of infrastructure failure at the time of earthquake, which changes due to deterioration of the infrastructure. In an example of the application, it is demonstratively shown that the optimal management policy would change in the case where earthquake risk is not considered.</p>

This paper studies the existence of a control problem where the state is governed by a stochastic differential equation allowing both classical control and singular control. By transforming it into a new problem that involves only classical control, it is shown that there exists an optimal control where the classical control variable is in Markovian form and the increment of the singular control variable on any time interval is adapted to the state process on the same time interval.

Studies the control problem where the state is governed by an Ito stochastic differential equation allowing both classical control and singular control. The problem is reformulated as a martingale problem on an appropriate canonical space after the relaxed form of the classical control is introduced. Under some mild continuity hypotheses on the data, it is shown by purely probabilistic arguments that an optimal control for the problem exists. The value function is shown to be Borel measurable. The dynamic programming principle for the problem is established. When assuming Lipschitz continuity on the data, it is shown that the value function is continuous and is the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. >

We address the problem of designing optimal buffer management policies in shared memory switches when packets already accepted in the switch can be dropped (pushed-out). Our goal is to maximize the overall throughput, or equivalently to minimize the overall loss probability in the system. For a system with two output ports, we prove that the optimal policy is of push-out with threshold type (POT). The same result holds if the optimality criterion is the weighted sum of the port loss probabilities. For this system, we also give an approximate method for the calculation of the optimal threshold, which we conjecture to be asymptotically correct. For the N-ported system, the optimal policy is not known in general, but we show that for a symmetric system (equal traffic on all ports) it consists of always accepting arrivals when the buffer is not full, and dropping one from the longest queue to accommodate the new arrival when the buffer is full. Numerical results are provided which reveal an interesting and somewhat unexpected phenomenon. While the overall improvement in loss probability of the optimal POT policy over the optimal coordinate-convex policy is not very significant, the loss probability of an individual output port remains approximately constant as the load on the other port varies and the optimal POT policy is applied, a property not shared by the optimal coordinate-convex policy.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This study assessed the disaster risk reduction and management policies and programs implemented in the Fifth District of Camarines Sur municipalities based on the Sendai framework criteria for local government resilience to disasters. It sought to identify the key vulnerabilities and risk factors and assess the current disaster risk reduction and management policies and programs implemented. The quantitative study utilized descriptive correlational design to gather the necessary data with documentary analysis and questionnaire as the main data gathering instruments. The questionnaire is composed of an adapted and self-made questionnaire which was distributed to 60 respondents. The data were analyzed with the use of the assessment checklist, weighted mean, and Friedman’s analysis of Variance. The municipalities of Baao, Balatan, Bato, Buhi, Bula, and Nabua are highly vulnerable to heavy rain, typhoons, and flooding, however, they are fully compliant with the criterion for disaster risk reduction and management policies and programs which implies good practices along with governance, risk identification, financial capacity, urban development, natural ecosystem, institutional capacity, societal capacity, infrastructure resilience, disaster response, and recovery. On the other hand, the municipality of Balatan complied with the criterion for disaster risk reduction and management policies and programs. The disaster risk reduction and management policies and programs implemented in the municipalities of Fifth District of Camarines Sur are significantly influenced by several barriers such as top-down planning and poor understanding of disaster risk. There is a significant difference between the current disaster risk reduction and management policies and programs implemented in the Fifth District of Camarines Sur indicating notable disparities across municipalities.