Search Results (32)

The research develops a multi-stage stochastic Mixed-Integer Linear Programming (MILP) model for managing dispatch schedules in microgrids with significant renewable energy integration. The primary objective is to optimize the integration of renewable energy sources with energy storage systems and grid power, concurrently aiming to reduce operational costs and address uncertainties associated with renewable energy resources. The model effectively captures the variability inherent in renewable sources through the use of scenarios and implements a multi-stage MILP formulation that incorporates storage and load constraints. The methodology employs stochastic optimization techniques to regulate fluctuations in renewable generation by analyzing diverse energy availability scenarios. The optimization process is designed to minimize grid power consumption while maximizing the utilization of renewable energy via storage and load constraints that guarantee a balanced energy supply. The model achieves optimal operational costs by producing results that amount to 46,600 USD while successfully controlling renewable energy variability. The research demonstrates two main achievements by integrating high renewable penetration levels and providing valuable insights into how energy storage systems and grid independence lower costs. Full article

Global ambitions for net-zero emissions and resource circularity are propelling industry from linear “make-use-dispose”models toward closed-loop value creation. Remanufacturing, which aims to restore end-of-life products to a “like-new” condition, plays a central role in this transition. However, its stochastic inputs and complex, multi-stage processes pose significant challenges to traditional production planning methods. This study delivers an integrated overview of remanufacturing scheduling by combining a systematic bibliometric review of 190 publications (2005–2025) with a critical synthesis of modelling approaches and enabling technologies. The bibliometric results reveal five thematic clusters and a 14% annual growth rate, highlighting a shift from deterministic, shop-floor-focused models to uncertainty-aware, sustainability-oriented frameworks. The scheduling problems are formalised to capture features arising from variable core quality, multi-phase precedence, and carbon reduction goals, in both centralised and cloud-based systems. Advances in human–robot disassembly, vision-based inspection, hybrid repair, and digital testing demonstrate feedback-rich environments that increasingly integrate planning and execution. A comparative analysis shows that, while mixed-integer programming and metaheuristics perform well in small static settings, dynamic and large-scale contexts benefit from reinforcement learning and hybrid decomposition models. Finally, future directions for dynamic, collaborative, carbon-conscious, and digital-twin-driven scheduling are outlined and investigated. Full article

Recent European regulations promote distributed energy resources as alternatives to centralized generation. This study compares utility-scale and distributed photovoltaic (PV) systems coupled with Battery Energy-Storage Systems (BESSs) in the Italian electricity market, analyzing different battery sizes. A multistage stochastic mixed-integer linear programming model, using Monte Carlo PV production scenarios, optimizes day-ahead and intra-day market offers while incorporating PV forecast updates. In real time, battery flexibility reduces imbalances. Here we show that, to ensure dispatchability—defined as keeping annual imbalances below 5% of PV output—a 1 MW PV system requires 220 kWh of storage for utility-scale and 50 kWh for distributed systems, increasing the levelized cost of electricity by +13.1% and +1.94%, respectively. Net present value is negative for BESSs performing imbalance netting only. Therefore, a multiple service strategy, including imbalance netting and energy arbitrage, is introduced. Performing arbitrage while keeping dispatchability reaches an economic optimum with a 1.7 MWh BESS for utility-scale systems and 1.1 MWh BESS for distributed systems. These results show lower PV firming costs than previous studies, and highlight that under a multiple-service strategy, better economic outcomes are obtained with larger storage capacities. Full article

This study introduces a novel approach for optimizing residential energy systems by combining linear policy graphs with stochastic dual dynamic programming (SDDP) algorithms. Our method optimizes residential solar power generation and battery storage systems, reducing costs through strategic charging and discharging patterns. Using stylized test data, we evaluate battery storage optimization strategies by comparing various SDDP model configurations against a linear programming (LP) benchmark model. The SDDP optimization framework demonstrates robust performance in battery operation management, efficiently handling diverse pricing scenarios while maintaining computational efficiency. Our analysis reveals that the SDDP model achieves positive financial returns with small-scale battery installations, even in scenarios with limited photovoltaic generation capacity. The results confirm both the economic viability and environmental benefits of residential solar–battery systems through two key strategies: aligning battery charging with renewable energy availability and shifting energy consumption away from peak periods. The SDDP framework proves effective in managing battery operations across dynamic pricing scenarios, achieving performance comparable to LP methods while handling uncertainties in PV generation, consumption, and pricing. Full article

This study investigates the challenge of ensuring timely information delivery in wireless powered sensor networks (WPSNs), where multiple sensors forward status-update packets to a base station (BS). Time is partitioned to multiple time blocks, with each time block dedicated to either data packet transmission or energy transfer. Our objective is to minimize the long-term average weighted sum of the Age of Information (WAoI) for physical processes monitored by sensors. We formulate this optimization problem as a multi-stage stochastic optimization program. To tackle this intricate problem, we propose a novel approach that leverages Lyapunov optimization to transform the complex original problem into a sequence of per-time-bock deterministic problems. These deterministic problems are then solved using model-free deep reinforcement learning (DRL). Simulation results demonstrate that our proposed algorithm achieves significantly lower WAoI compared to the DQN, AoI-based greedy, and energy-based greedy algorithms. Furthermore, our method effectively mitigates the issue of excessive instantaneous AoI experienced by individual sensors compared to the DQN. Full article

Hybrid pumped hydro storage plants, by integrating pump stations between cascade hydropower stations, have overcome the challenges associated with site selection and construction of pure pumped hydro storage systems, thereby becoming the optimal large-scale energy storage solution for enhancing the absorption of renewable energy. However, the multi-energy conversion between pump stations, hydropower, wind power, and photovoltaic plants poses challenges to both their planning schemes and operational performance. This study proposes a multistage stochastic coordinated planning model for cascade hydropower-wind-solar-thermal-pumped hydro storage (CHWS-PHS) systems. First, a Hybrid Pumped Hydro Storage Adaptive Initial Reservoir Capacity (HPHS-AIRC) strategy is developed to enhance the system’s regulation capability by optimizing initial reservoir levels that are synchronized with renewable generation patterns. Then, Non-anticipativity Constraints (NACs) are incorporated into this model to ensure the dynamic adaptation of investment decisions under multi-timescale uncertainties, including inter-annual natural water inflow (NWI) variations and hourly fluctuations in wind and solar power. Simulation results on the IEEE 118-bus system show that the proposed MSSP model reduces total costs by 6% compared with the traditional two-stage approach (TSSP). Moreover, the HPHS-AIRC strategy improves pumped hydro utilization by 33.8%, particularly benefiting scenarios with drought conditions or operational constraints. Full article

The electricity landscape is constantly evolving, with intermittent and distributed electricity supply causing increased variability and uncertainty. The growth in electric vehicles, and electrification on the demand side, further intensifies this issue. Managing the increasing volatility and uncertainty is of critical importance to secure and minimize costs for the energy supply. Smart neighborhoods offer a promising solution to locally manage the supply and demand of energy, which can ultimately lead to cost savings while addressing intermittency features. This study assesses the impact of different electric vehicle charging strategies on smart grid energy costs, specifically accounting for battery degradation due to cycle depths, state of charge, and uncertainties in charging demand and electricity prices. Employing a comprehensive evaluation framework, the research assesses the impacts of different charging strategies on operational costs and battery degradation. Multi-stage stochastic programming is applied to account for uncertainties in electricity prices and electric vehicle charging demand. The findings demonstrate that smart charging can significantly reduce expected energy costs, achieving a 10% cost decrease and reducing battery degradation by up to 30%. We observe that the additional cost reductions from allowing Vehicle-to-Grid supply compared to smart charging are small. Using the additional flexibility aggravates degradation, which reduces the total cost benefits. This means that most benefits are obtainable just by optimized the timing of the charging itself. Full article

As wind penetration rates continue to increase, the main challenge faced by operators is how to schedule flexible resources, such as traditional generation and storage, in the future to ensure the safe and stable operation of power grids under multiple uncertainties. In this paper, a security-constrained multi-stage robust dynamic economic dispatch model with storage (SMRDEDS) is proposed to address multiple uncertainties of wind power outputs and N-1 contingencies. Compared to the traditional two-stage robust dynamic economic dispatch model, the proposed multi-stage dispatch model yields sequential operation decisions with uncertainties revealed gradually over time. What is more, a combined two-stage Benders’ decomposition and relaxed approximation–robust dual dynamic programming (RA-RDDP) is proposed to handle the computational issue of multi-stage problems due to large-scale post-contingency constraints and the convergence issue of the stochastic dual dynamic programming (SDDP) algorithm. First, a two-stage Benders’ decomposition algorithm is applied to relax the SMRDEDS model into a master problem and sub-problem. The master problem determines the generator output and storage charge and discharge, and the sub-problem determines the total generation and storage reserve capacity to cover all the generator N-1 contingencies. Second, a relaxed approximation–RDDP algorithm is proposed to solve the multi-stage framework problem. Compared to the traditional SDDP algorithm and RDDP algorithm, the proposed RA-RDDP algorithm uses the inner relaxed approximation and outer approximation methods to approximate the upper and lower bounds of the future cost-to-go function, which overcomes the convergence issue of the traditional SDDP algorithm and solution efficiency of the RDDP algorithm. We tested the proposed algorithm on the IEEE-3 bus, IEEE-118 bus, and the German power system. The simulation results verify the effectiveness of the proposed model and proposed algorithm. Full article

Rice is one of the primary staple foods in Nepal, and there has been a notable increase in the production of this crop over the past ten years. Nonetheless, there appears to be a growing tendency to import rice. The plain region (Terai) of Nepal produces more than two-thirds of the country’s total rice output, with the highest productivity found in Madhesh Province. However, because of the limited knowledge regarding the technical aspects of rice production, commercial rice growers are facing challenges in using resources to produce output as effectively as possible. There is a pressing need to maximize production based on a limited number of inputs. Thus, this study aimed to examine the technical efficiency of rice farmers and the factors affecting technical inefficiency in the Parsa district of Nepal. This study area is the major domain of the Prime Minister Agriculture Modernization Project (PMAMP), which supports farmers with necessary agricultural inputs, infrastructure development, and innovative practices. Data were collected from 215 rice farmers using multistage purposive sampling and were subjected to a Cobb–Douglas stochastic frontier production function. The results showed that rice producers had a technical efficiency of 0.862. Age and off-farm activities were found to significantly influence the technical efficiency of rice farmers. The technical efficiency of rice producers could be enhanced using a project approach, such as the PMAMP. It is important for the government to implement innovations and technologies in farms with the participation of older farmers because their ability to adapt to novel techniques and technologies is better than that of young farmers. Youth generally prefer off-farm employment opportunities, so domestic investment in agriculture should be promoted to make this sector more appealing. Further, policies and programs focusing on pooling small rice fields and subsidizing the price of tractors will help improve the yield of rice. Full article

Most optimisation research focuses on relatively simple cases: one decision maker, one objective, and possibly a set of constraints. However, real-world optimisation problems often come with complications: they might be multi-objective, multi-agent, multi-stage or multi-level, and they might have uncertainty, partial knowledge or nonlinear objectives. Each has led to research areas with dedicated solution methods. However, when new hybrid problems are encountered, there is typically no solver available. We define a broad class of discrete optimisation problem called an influence program, and describe a lightweight algorithm based on multi-agent multi-objective reinforcement learning with sampling. We show that it can be used to solve problems from a wide range of literatures: constraint programming, Bayesian networks, stochastic programming, influence diagrams (standard, limited memory and multi-objective), and game theory (multi-level programming, Bayesian games and level-k reasoning). We expect it to be useful for the rapid prototyping of solution methods for new hybrid problems. Full article

In recent years, the adoption of renewable energy sources has significantly increased due to their numerous advantages, which include environmental sustainability and economic viability. However, the management of electric microgrids presents complex challenges, particularly in the orchestration of energy production and consumption under the uncertainty of fluctuating meteorological conditions. This study aims to enhance decision-making processes within energy management systems specifically designed for microgrids that are interconnected with primary grids, addressing the stochastic and dynamic nature of energy generation and consumption patterns among microgrid users. The research incorporates stochastic models for energy pricing in transactions with the main grid and probabilistic representations of energy generation and demand. This comprehensive methodology allows for an accurate depiction of the volatile dynamics prevalent in the energy markets, which are critical in influencing microgrid operational performance. The application of the Stochastic Dual Dynamic Programming (SDDP) algorithm within a multi-stage adaptive framework for microgrids is evaluated for its effectiveness compared to deterministic approaches. The SDDP algorithm is utilized to develop robust strategies for managing the energy requirements of 1, 2, and 12 prosumers over a 24 h planning horizon. A comparative analysis against the precise solutions obtained from dynamic programming via Monte Carlo simulations indicates a strong congruence between the strategies proposed by the SDDP algorithm and the optimal solutions. The results provide significant insights into the optimization of energy management systems in microgrid settings, emphasizing improvements in operational performance and cost reduction. Full article

This paper addresses the optimal stochastic allocation of distributed energy resources in distribution networks. Typically, uncertain problems are analyzed in multistage formulations, including case generation routines, resulting in computationally exhaustive programs. In this article, two probabilistic approaches are proposed–range probability optimization (RPO) and value probability optimization (VPO)–resulting in a single-stage, convex, stochastic optimal power flow problem. RPO maximizes probabilities within a range of uncertainty, whilst VPO optimizes the values of random variables and maximizes their probabilities. Random variables were modeled with hourly measurements fitted to the logistic distribution. These formulations were tested on two systems and compared against the deterministic case built from expected values. The results indicate that assuming deterministic conditions ends in highly underestimated losses. RPO showed that by including ±10% uncertainty, losses can be increased up to 40% with up to −72% photovoltaic capacity, depending on the system, whereas VPO resulted in up to 85% increases in power losses despite PV installations, with 20% greater probabilities on average. By implementing any of the proposed approaches, it was possible to obtain more probable upper envelopes in the objective, avoiding case generation stages and heuristic methods. Full article

Unpredictable natural disasters brought by extreme climate change compound difficulties and cause a variety of systemic risks. It is thus critical to provide possibilistic scheduling schemes that simultaneously involve emergency evacuation and relief allocation. But the existing literature seldom takes emergency evacuation and relief supplies as a joint consideration, nor do they explore the impact of an unpredictable flood disaster on the scheduling scheme. A multi-stage stochastic programming model with updating information is constructed in this study, which considers the uncertainty of supply and demand, road network, and multiple types of emergency reliefs and vehicles. In addition, a fuzzy algorithm based on the objective weighting of two-dimensional Euclidean distance is introduced, through moderating an effect analysis of the fuzzy number. Computational results show that humanitarian equity for allocating medical supplies in the fourth period under the medium and heavy flood is about 100%, which has the same as the value of daily and medical supplies within the first and third period in the heavy scenarios. Based on verifying the applicability and rationality of the model and method, the result also presents that the severity of the flood and the fairness of resources is not a simple cause-and-effect relationship, and the consideration of survivor is not the only factor for humanitarian rescue with multi-period. Specifically, paying more attention to a trade-off analysis between the survival probability, the timeliness, and the fairness of humanitarian service is essential. The work provides a reasonable scheme for updating information and responding to sudden natural disasters flexibly and efficiently. Full article

In this study, a mixed integer, linear, multi-stage, stochastic programming model is developed for multi-product aggregate production planning (APP). An approximation is used with a model that employs discrete distributions with three and four values and their respective probabilities of occurrence for the random variables, which are demand and production capacity, each one for every product family. The model was solved using the deterministic equivalent of the multi-stage problem using the optimization software LINGO 19.0. The main objective of this research is to determine a feasible solution to a real APP in a reasonable computational time by comparing different methods. Since the deterministic equivalent was difficult to solve, a proposal model with bounds in some decision variables was developed using some properties of the original model; both models were solved for different periods. We demonstrated that the proposed model had the same solution as the original model but required fewer iterations and CPU time, which implies an advantage in real APP. Finally, a sensitivity analysis was performed at varying service levels finding that if the service levels increase, the cost increases as well. Full article

Selecting the optimal locations and timing for prescribed burning is challenging when considering uncertainties in weather, fire behavior, and future fire suppression. In this study, we present a sample average approximation (SAA) based multistage stochastic mixed integer program with recourse to optimize prescribed burning decisions. The recourse component of the SAA model considers post-fuel-treatment suppression decisions to manage fire spreads in multiple future planning periods. Our research aims at studying how an SAA model may benefit from using random fire samples to find good locations for prescribed burning during the first planning period. Two hypothetical test cases are designed to compare the impact of fire sample sizes on solution quality, and to illustrate how to identify high-quality period-one prescribed burning solutions. Results suggest that running SAA models using larger fire sample sizes can lead to better period-one solutions, but this benefit will diminish after the sample size reaches to certain thresholds. We found multiple period-one prescribed burning decisions that may result in similar effects in mitigating future wildfire risks. Full article