Probability of freedom from foot-and-mouth disease virus serotype Asia 1 in Southeast Asia, China and Mongolia.

ABSTRACT International humanitarian organizations face challenges in inventory management due to unpredictable disasters, evolving emergencies, participant coordination, long planning horizons, and broad geographical coverage. This paper develops an international humanitarian inventory coordination framework, using multi‐stage stochastic programming to make long‐term (monthly or quarterly) procurement, inventory, and transportation decisions. As a counterpart of monetary expense in the objective, a target‐based disutility , that is monotonically non‐increasing and convex, is proposed to measure the suffering caused by insufficient consumption. The model is solved by the generalized Stochastic Dual Dynamic Programming (SDDP), which allows convex recourse functions. The SDDP takes historical demands as input and generates an optimal policy for making future decisions without knowing exact demand information. Unlike deterministic equivalent formulations based on scenario trees, this policy is implementable for out‐of‐sample data. Extensive numerical experiments are conducted with publicly available data from the United Nations Humanitarian Response Depot, the United Nations Office for the Coordination of Humanitarian Affairs (OCHA), and the EM‐DAT international disaster database. The method can generate a policy in under two hours using 216 months (18 years) of data from the 34 most disaster‐vulnerable countries or territories where the OCHA works. The SDDP policy offers up to 21% cost savings over myopic or deterministic policies. Results demonstrate that good out‐of‐sample coordination results can be achieved with a moderate sample size, a reasonable number of iterations, and within the current OCHA organization structure.

Virtual power plants (VPPs) enable the efficient participation of distributed renewable energy resources in electricity markets by aggregating them. However, the profitability of VPPs is challenged by market volatility and regulatory constraints, such as price caps and imbalance penalties. This study examines the joint impact of varying price cap levels and imbalance penalty structures on the bidding strategies and revenues of VPPs. A stochastic optimization model was developed, where a three-stage scenario tree was utilized to capture the uncertainty in electricity prices and renewable generation output. Simulations were performed under various market conditions using real-world price and generation data from the Korean electricity market. The analysis reveals that higher price cap coefficients lead to greater revenue and more segmented bidding strategies, especially under asymmetric penalty structures. Segment-wise analysis of bid price–quantity pairs shows that over-bidding is preferred under upward-only penalty schemes, while under-bidding is preferred under downward-only ones. Notably, revenue improvement tapers off beyond a price cap coefficient of 0.8, which indicates that there exists an optimal threshold for regulatory design. The findings of this study suggest the need for coordination between price caps and imbalance penalties to maintain market efficiency while supporting renewable energy integration. The proposed framework also offers practical insights for market operators and policymakers seeking to balance profitability, adaptability, and stability in VPP-integrated electricity markets.

Foot-and-mouth disease (FMD) significantly impacts global livestock industries, with raw milk transportation posing a recognized pathway for viral dissemination, particularly in endemic regions. This study aimed to evaluate the risk of FMD virus (FMDV) introduction and transmission to dairy farms via raw milk transportation in Ban Thi District, Thailand. A qualitative risk assessment methodology, adhering to WOAH guidelines, was employed. Data were collected through structured farmer surveys (n = 109), expert interviews (n = 12), and reviews of national disease surveillance data and scientific literature. The risk assessment, utilizing a scenario tree approach for domestic dairy cattle, revealed a moderate overall risk of FMDV transmission. This finding is primarily attributed to critical gaps in on-farm biosecurity practices, potential contamination at milk collection centers, and significant challenges in detecting subclinical carrier animals. While the qualitative approach presented inherent limitations and uncertainties, the study successfully highlighted key vulnerabilities. The results underscore the urgent necessity for implementing targeted biosecurity protocols, developing more robust surveillance strategies for FMDV carriers, and establishing standardized risk assessment frameworks to mitigate potential outbreaks and protect the regional dairy industry.

Nigeria's centralized electrical infrastructure has regularly failed to satisfy the country's rising energy consumption, therefore impeding technical advancement and economic growth. Renewable Distributed Generations (RDGs) including solar PV, wind, and small hydro provide a sustainable route toward distributed energy access and enhanced grid dependability when combined. On operational stability, coordination, and growth planning, however, the variability and spatial dispersion of RDGs present difficult problems. Leveraging intelligent, autonomous agents representing smart microgrids, generating units, storage systems, and load centers, this work proposes a Multi-Agent System-based Optimal Expansion Planning (MAS-OEP) framework. These agents link long-term investment planning with real-time operational methods under uncertainty utilizing a two-stage stochastic optimization structure to generate distributed decisions. While scenario trees organize future situations, probabilistic models, Monte Carlo simulations, fuzzy sets, and Markov chains are used to reflect uncertainty in wind output, load demand, and market prices. The hybrid optimization system combines accurate methods such as Mixed- Integer Linear Programming (MILP) and Genetic Algorithms (GA) at the agent level with heuristic techniques at the upper level. Under general direction from a Central Coordination Agent (CCA), coordination is accomplished through peer-to--peer energy trading using the Contract Net Protocol (CNP) and Agent Communication Language (ACL). Furthermore, improved by the Genetic Vertical Sequencing Protocol (GVS) are system scalability, durability, and adaptability to evolving grid environments. While trade-off studies expose ideal balances between energy storage and backup generation, simulation findings demonstrate the efficacy of the concept in minimizing costs, increasing renewable usage, and reducing emissions. Thus, the suggested MAS-OEP architecture offers a scalable, intelligent, and strong method to control distributed energy expansion under uncertainty. It greatly raises operational dependability, environmental sustainability, and economic efficiency of Nigeria's power system. Future studies should investigate how to improve agent decision-making by means of real-time analytics, reinforcement learning, and adaptive regulatory models. Recommendations for full-scale deployment are strong policy support, secure communication infrastructure, and stakeholder capacity building. For Nigeria and other developing nations, this work provides a strong basis for improving smart, robust, and adaptive energy systems, simulation results demonstrate improved renewable utilization, reduced emissions, and enhanced grid stability, validating the robustness of the research framework.

A scenario model to support freedom from African swine fever virus in Western Canada populated with data from Canada West Swine Health Intelligence Network and CanSpotASF.

A rolling horizon heuristic approach for a multi-stage stochastic waste collection problem

Mapping risks: A value chain approach to brucellosis introduction in Zhijiang's Cattle Population, China.

This work develops a practical multi-period optimization approach that incorporates real-world constraints, including discrete decisions and conic risk constraints. Expanding upon earlier single-period models, our framework employs a binary scenario tree derived from monthly returns of randomly selected S&P 500 stocks to represent market evolution across multiple periods. The formulation captures essential portfolio constraints, such as transaction fees, sector diversification, and minimum investment thresholds, resulting in a robust and comprehensive optimization approach. To efficiently solve the resulting mixed-integer second-order cone programming (MISOCP) problem, we employ an outer approximation algorithm with a warmstart strategy, which significantly improves solution runtimes and computational efficiency. Numerical experiments demonstrate the model’s effectiveness, showing an average improvement of 10.71% in iteration count and 15.24% in computational time when using the warmstart approach.

Based on the definition of volatility and conditional value risk (CVaR), this paper introduces the implied volatility into CVaR model, and further analyzes the partial differential equation of stock portfolio optimization in the form of BS model. In the process of multi-stage investment, in order to reasonably control the investment risk of each stage, the CvaR model based on implied volatility is constructed by using the scenario tree method. With the data of 1166 trading days as the data, 4 stock assets as the data set of this study, the optimization model is applied to the calculation and analysis. The numerical simulation shows that the stock price fluctuation of the four multi-cycle stocks ranges from -23.45% to 41.97%, showing a clustering phenomenon. Among them, the volatility of stocks A and C is more obvious than that of stocks B and D, and the probability density tails of stocks are longer in the cycle, and they all show thick tail characteristics, indicating that the introduction of implied volatility of CVaR model makes the risk control of actual equity asset investment more reasonable.

We consider a multi-stage generalization of the interval-based stochastic dominance (ISD) principles introduced by Liu et al. [Interval-based stochastic dominance: Theoretical framework and application to portfolio choices. Ann. Oper. Res., 2021, 307, 329–361]. The ISD criterion was motivated specifically in a financial context to allow for contiguous integer SD orders on different portions of a portfolio return distribution against a benchmark distribution. A continuous spanning of SD conditions between first-, second-, and third-order stochastic dominance was introduced in that context, relying on a reference point. Here, by extending the partial order to random data processes, we apply ISD conditions to a multi-period portfolio selection problem and verify the modeling and computational implications of such an extension. Several theoretical and methodological issues arise in this case that motivate this contribution. The problem is formulated in scenario form as a multistage stochastic recourse program, and we study two possible generalizations of ISD principles in which we either enforce ISD constraints at each stage, independently from the scenario tree process evolution, or we do so conditionally along the scenario tree. We present a comprehensive set of computational results to show that, depending on the benchmark investment policy and the adopted ISD formulation, stochastic dominance conditions of first- or second-order can be enforced dynamically over a range of possible values of the reference point, and their solution carries a specific rationale. The computational constraints induced by the multistage ISD formulation are also emphasized and discussed in detail.

Abstract This study presents an innovative approach to risk‐aware decision‐making in water resource management. We focus on a case study in the Netherlands, where risk awareness is key to water system design and policy‐making. Recognizing the limitations of deterministic methods in the face of weather, energy system, and market uncertainties, we propose a scalable stochastic Model Predictive Control (MPC) framework that integrates probabilistic forecasting, scenario generation, and stochastic optimal control. We utilize Combined Quantile Regression Deep Neural Networks and Non‐parametric Bayesian Networks to generate probabilistic scenarios that capture realistic temporal dependencies. The energy distance metric is applied to optimize scenario selection and generate scenario trees, ensuring computational feasibility without compromising decision quality. A key feature of our approach is the introduction of Exceedance Risk (ER) constraints, inspired by Conditional‐Value‐at‐Risk (CVaR), to enable more nuanced and risk‐aware decision‐making while maintaining computational efficiency. In this work, we enable the Noordzeekanaal–Amsterdam‐Rijnkanaal (NZK‐ARK) system to participate in Demand Response (DR) services by dynamically scheduling pumps to align with low hourly electricity prices on the Day Ahead and Intraday markets. Through historical simulations using real water system and electricity price data, we demonstrate that incorporating uncertainty can significantly reduce operational costs—by up to 44 percentage points compared to a deterministic approach—while maintaining safe water levels. The modular nature of the framework also makes it adaptable to a wide range of applications, including hydropower and battery storage systems.

Yellow crazy ants (YCAs) are an invasive ant with a pantropical distribution, largely due to the international movements of ships and produce. This invasive ant has the capacity to impact a broad range of environmental, domestic and agricultural situations and has the ability to develop into supercolonies and dominate landscapes if uncontrolled. YCAs have been detected in several locations in Australia. During 2018 in New South Wales, YCAs were detected in two locations in the Lismore region. Several awareness techniques were used to gain community support and engagement in the response program. The eradication program relied on the insecticide fipronil (several formulations), and the program subsequently used surveillance data to demonstrate that eradication had been achieved. We used the scenario tree analysis with stochastic models to estimate the likelihood of eradication. We combined the results of the passive and active surveillance systems to predict a 70.4% (62.7-80.7) probability of freedom of detecting one nest, 84.4% (73.9-94.4) probability of freedom for two nests and 98% (93.1-99.9) probability of freedom for five nests. The results from the scenario tree analysis were used to inform program managers regarding the termination of the eradication and surveillance activities.

This paper investigates a Multi-Stage Stochastic Districting Problem (MSSDP). The goal is to devise a districting plan (i.e., clusters of Territorial Units—TUs) accounting for uncertain parameters changing over a discrete multi-period planning horizon. The problem is cast as a multi-stage stochastic programming problem. It is assumed that uncertainty can be captured by a finite set of scenarios, which induces a scenario tree. Each node in the tree corresponds to the realization of all the stochastic parameters from the root node—the state of nature—up to that node. A mathematical programming model is proposed that embeds redistricting recourse decisions and other recourse actions to ensure that the districts are balanced regarding their activity. The model is tested on instances generated using literature data containing real geographical data. The results demonstrate the relevance of hedging against uncertainty in multi-period districting. Since the model is challenging to tackle using a general-purpose solver, a heuristic algorithm is proposed based on a restricted model. The computational results obtained give evidence that the approximate algorithm can produce high-quality feasible solutions within acceptable computation times.

Background: Despite the significant contribution of small ruminants to the improvement of societal livelihood, several factors hamper their production and productivity, chief among which are various production and reproductive diseases. Brucellosis is one of such diseases that causes huge economic loss and imposes trade restrictions. Methods: A quantitative risk assessment was conducted from July 2023 to January 2024 to evaluate the risk of introduction of brucellosis into Germany via the importation of sheep and goat from Ethiopia. The QRA methods was applied by breaking it into different components, namely, hazard identification and characterization; developing a scenario tree; gathering scientific evidence about the probability of occurrence of these events from published sources; generating mathematical equations taking into account the reliability and variability of the evidences; and, finally, calculating the overall risk of the hazard introduction by running Monte Carlo simulation at 10,000 iterations using @ RISK software, Palisade Co. Result: The overall probability of introducing brucellosis through the annual importation of sheep and goats from Ethiopia is 1.276 × 10-7 (fifth percentile = 3.07 × 10-7; 95th percentile = 3.08 × 10-7). The results of the sensitivity analysis using the tornado graph showed that the estimate's precision can be improved by 49%, 44%, and 35%, respectively, if the factors that contributed most to the uncertainty were changed by one standard deviation. Discussion and Conclusion: If the animals (sheep and goat) pass through all mitigations as outlined in the study, the risk of brucellosis introduction into Germany through the importation of small ruminants from Ethiopia is generally low. The uncertainty around the risk estimate could be reduced if more animal-level prevalence data could be obtained and by employing more sensitive diagnostic tests such as ELISA to detect subclinically infected animals. It is recommended that animal health regulators of the two nations work closely to enhance disease diagnosis and surveillance capabilities.

Optimization-Based Maneuvering Target Tracking Using Multiple Model Horizon Scenario Tree With Model Interaction

Problem definition: Multistage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that can be dynamically adjusted as uncertainty is realized. Often, for example, because of contractual constraints, such flexible policies are not desirable, and the decision maker may need to commit to a set of actions for a certain number of periods. Two-stage stochastic programming might be better suited to such settings, where first-stage decisions do not adapt to the uncertainty realized. In this paper, we propose a novel alternative approach, named as adaptive two-stage stochastic programming, where each component of the decision policy requiring limited flexibility has its own revision point, a period prior to which the decisions are determined at the beginning of the planning until this revision point, and after which they are revised for adjusting to the uncertainty realized thus far until the end of the planning. We then analyze this approach over the capacity expansion planning problem, that may require limited flexibility over expansion decisions. Methodology/results: We provide a generic mixed-integer programming formulation for the adaptive two-stage stochastic programming problem with finite support, in particular, for scenario trees, and show that this problem is NP-hard in general. Next, we focus on the capacity expansion planning problem and derive bounds on the value of adaptive two-stage programming in comparison with the two-stage and multistage approaches in terms of revision points. We propose several heuristic solution algorithms based on this bound analysis. These algorithms either provide approximation guarantees or computational advantages in solving the resulting adaptive two-stage stochastic problem. Managerial implications: We provide insights on the choice of the revision times based on our analytical analysis. We further present an extensive computational study on a generation capacity expansion planning problem with different generation resources including renewable energy. We demonstrate the value of adopting adaptive two-stage approach against the existing policies under limited flexibility and highlight the efficiency of the proposed heuristics along with practical implications on the studied problem. Funding: This work was supported by the National Science Foundation [Grant 1633196] and the Office of Naval Research [Grant N00014-18-1-2075]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2023.0157 .

Current automatic parking systems often separate path planning and trajectory tracking, increasing complexity and failing to meet the parking needs of autonomous cars. Consequently, this study presents an approach based on Multi-stage Nonlinear Model Predictive Control (MSNMPC) for integrated autonomous parking path planning and trajectory tracking optimization. The method represents the evolution of uncertainty parameters over time through a scenario tree, and the MSNMPC controller with a predictive horizon P defines P + 1 phases, each with specific cost and constraint functions that depend only on the vehicle state and control inputs of that phase to satisfy the constraints of all phases of the parking process. In addition, the method integrates path planning and tracking control into one optimization problem, which is solved online to achieve integrated parking control. Simulation confirms that, in comparison to MPC with RRT* hierarchical control, the integrated parking scheme of MSNMPC has less lateral error and offers superior flexibility and tracking performance. To verify the generality of the scheme, it was validated in the diagonal parking scenario and the vertical parking scenario, respectively. The results show that, compared to the control experiments, the parking elapsed time has been reduced by 10.76% and 9.02%, respectively, enhancing parking efficiency. In addition, the parking error has decreased by 30.77% and 38.46%, respectively, thus improving parking accuracy. Moreover, the minimum safe distance in the control scheme for addressing uncertainty factors is 0.7 m greater than that of the control experiments, meeting the driving requirements for driverless vehicles in parking scenarios.

We consider a risk-averse stochastic capacity planning problem under uncertain demand in each period. Using a scenario tree representation of the uncertainty, we formulate a multistage stochastic integer program to adjust the capacity expansion plan dynamically as more information on the uncertainty is revealed. Specifically, in each stage, a decision maker optimizes capacity acquisition and resource allocation to minimize certain risk measures of maintenance and operational cost. We compare it with a two-stage approach that determines the capacity acquisition for all the periods up front. Using expected conditional risk measures, we derive a tight lower bound and an upper bound for the gaps between the optimal objective values of risk-averse multistage models and their two-stage counterparts. Based on these derived bounds, we present general guidelines on when to solve risk-averse two-stage or multistage models. Furthermore, we propose approximation algorithms to solve the two models more efficiently, which are asymptotically optimal under an expanding market assumption. We conduct numerical studies using randomly generated and real-world instances with diverse sizes, to demonstrate the tightness of the analytical bounds and efficacy of the approximation algorithms. We find that the gaps between risk-averse multistage and two-stage models increase as the variability of the uncertain parameters increases and decrease as the decision maker becomes more risk averse. Moreover, a stagewise-dependent scenario tree attains much higher gaps than a stagewise-independent counterpart, whereas the latter produces tighter analytical bounds. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work of Dr. X. Yu was partially supported by the U.S. National Science Foundation Division of Information and Intelligent Systems [Grant 2331782]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0396 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0396 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Abstract This article proposes a multi‐objective and multi‐stage low‐carbon planning approach for park integrated energy systems (PIES) considering the impacts of random outages from the superior electrical grid. This approach incorporates optimal multi‐stage construction sequencing and stepped carbon emission trading to leverage the economic and low‐carbon benefits of long‐term planning. First, the islanding modes of PIES are described using four random variables: island type, duration, start time, and typical day of occurrence, from which islanding scenarios are generated based on scenario tree. Next, a multi‐objective planning model that considers both economics and reliability is constructed, with the objectives of minimizing the total lifecycle planning cost and the expected economic loss during islanding. The improved Normalized Normal Constraint (NNC) method is proposed to solve the multi‐objective planning problem. Then, the fuzzy membership function is used to determine the optimal compromise solution, resulting in a planning scheme that balances economic efficiency and supply reliability. Finally, simulations indicate that, at the cost of a slight increase in planning expenses, the proposed model significantly reduces the loss costs under islanding modes compared with single‐objective economic‐focused planning. Additionally, the improved NNC method can achieve a more uniform Pareto frontier compared with the conventional NNC method.