Search Results (919)

Vehicle-to-Grid (V2G) technology has been widely applied in recent years. Under the time-of-use pricing, users independently decide the charging and discharging behavior to maximize economic benefits, charging during low-price periods, discharging during high-electricity periods, and avoiding battery degradation. However, such behavior under inappropriate electricity prices can deviate from the grid’s goal of minimizing peak–valley load difference. Based on the basic electricity data of a community in Beijing and electricity vehicle (EV) random travel behavior obtained through Monte Carlo simulation, this study establishes a user optimal decision model that is influenced by battery degradation and electricity costs considering depth of discharge, charging rate, and charging energy loss. A mixed-integer linear programming algorithm with the objective of minimizing the cost of EV users is constructed to offer the participation power of V2G. By analyzing grid load fluctuations under different electricity pricing strategies, the study derives the formulation and adjustment rules for optimal electricity pricing that achieve ideal load stabilization. Under 30% V2G participation, the relative fluctuation of grid load is reduced from 31.81% to 5.19%. This study addresses the challenge of obtaining optimal electricity prices to guide users to participate in V2G to minimize the peak–valley load fluctuation. Full article

Carbon Capture and Storage (CCS) is a critical technology for reducing anthropogenic CO₂ emissions, but its large-scale deployment is complicated by uncertainties in geological storage performance. These uncertainties pose significant financial and operational risks, as underperforming storage sites can lead to costly infrastructure modifications, inefficient pipeline routing, and economic shortfalls. To address this challenge, we propose a novel optimization workflow that is based on mixed-integer linear programming and explicitly integrates probabilistic modeling of storage uncertainty into CCS infrastructure design. This workflow generates multiple infrastructure scenarios by sampling storage capacity distributions, optimally solving each scenario using a mixed-integer linear programming model, and aggregating results into a heatmap to identify core infrastructure components that have a low likelihood of underperforming. A risk index parameter is introduced to balance trade-offs between cost, CO₂ processing capacity, and risk of underperformance, allowing stakeholders to quantify and mitigate uncertainty in CCS planning. Applying this workflow to a CCS dataset from the US Department of Energy’s Carbon Utilization and Storage Partnership project reveals key insights into infrastructure resilience. Reducing the risk index from $15\%$ to $0\%$ is observed to lead to an $83.7\%$ reduction in CO₂ processing capacity and a $77.1\%$ decrease in project profit, quantifying the trade-off between risk tolerance and project performance. Furthermore, our results highlight critical breakpoints, where small adjustments in the risk index produce disproportionate shifts in infrastructure performance, providing actionable guidance for decision-makers. Unlike prior approaches that aimed to cheaply repair underperforming infrastructure, our workflow constructs robust CCS networks from the ground up, ensuring cost-effective infrastructure under storage uncertainty. These findings demonstrate the practical relevance of incorporating uncertainty-aware optimization into CCS planning, equipping decision-makers with a tool to make informed project planning decisions. Full article

In this paper, an IES optimal cooperative scheduling method based on a master–slave game is proposed considering a carbon emission trading (CET) and carbon capture system (CCS) combined operation with power to gas (P2G). We analysed the behaviour of integrated energy system operators (IESO) and energy suppliers (ES) when the system is operating in different states. This paper first introduces the structure of IES and the mathematical model of the game frame. Secondly, mixed integer linear programming and particle swarm optimization (MILP–PSO) are used. The final simulation results show that in the main scenario, IESO and ES have an income of CNY 181,900 and CNY 279,400, respectively, and the actual carbon emission is 106.75 tons. The overall income is balanced, and the carbon emission is in the middle. The results provide a reference value for operators and users to make decisions. Full article

This paper explores the configuration and deployment of UAV nests for power inspection operations, focusing on potential nest failures. It proposes a two-stage location-allocation method. The problem is divided into two subproblems, each modeled as an integer linear programming (ILP) problem. The first subproblem identifies the minimal set of nodes for nest construction using the commercial solver Gurobi. The second subproblem involves UAV nest type selection and task allocation, solved with an ILS-SA heuristic algorithm. A case study in China shows that our method reduces total costs by 33.9% and decreases the number of UAV nests by 32% compared to the current greedy deployment method used by the power grid company. These results demonstrate the effectiveness and practicality of our approach in improving the reliability and cost-efficiency of UAV-based power inspection systems. Full article

The dual-resource constrained flexible job shop scheduling problem with variable sublots (DRCFJSP-VS) can be decomposed into four subproblems: the sublot splitting subproblem, the sublot sequencing subproblem, the machine assignment subproblem, and the worker assignment subproblem, which are difficult to solve efficiently using conventional methods. The introduction of variable-size batch splitting and the constraints of multiple levels and skills of workers further increase the complexity of the problem, making it difficult to solve efficiently using conventional methods. This paper proposes a mixed-integer linear programming (MILP) model to solve this complex problem and introduces a two-stage multi-objective evolutionary algorithm (TSMOEA). In the first stage of the algorithm, an improved multi-objective discrete difference evolutionary algorithm is used to optimize the dual-resource constrained flexible job shop scheduling problem; in the second stage, an adaptive simulated annealing algorithm is used to search for variable-size batch splitting strategies. To validate the feasibility of the model, the solution results are obtained using the CPLEX solver and compared with the results of TSMOEA. The performance of TSMOEA is compared with NSGA-II, PSO, DGWO, and WOA on improved instances. The results show that TSMOEA outperforms the other algorithms in both IGD and HV metrics, demonstrating its superior solution quality and robustness. Full article

As energy and carbon markets evolve, it has emerged as a prevalent trend for multiple virtual power plants (VPPs) to engage in market trading through coordinated operation. Given that these VPPs belong to diverse stakeholders, a competitive dynamic is shaping up. To strike a balance between the interests of the distribution system operator (DSO) and VPPs, this paper introduces a bi-level energy–carbon coordination model based on the Stackelberg game framework, which consists of an upper-level optimal pricing model for the DSO and a lower-level optimal energy scheduling model for each VPP. Subsequently, the Karush-Kuhn-Tucker (KKT) conditions and the duality theorem of linear programming are applied to transform the bi-level Stackelberg game model into a mixed-integer linear program, allowing for the computation of the model’s global optimal solution using commercial solvers. Finally, a case study is conducted to demonstrate the effectiveness of the proposed model. The simulation results show that the proposed game model effectively optimizes energy and carbon pricing, encourages the active participation of VPPs in electricity and carbon allowance sharing, increases the profitability of DSOs, and reduces the operational costs of VPPs. Full article

In this paper, we address biopharmaceutical manufacturing scheduling problems with heterogeneous parallel mixed flowshops. The mixed flowshop consists of three stages, one batch process and two continuous processes. The objective function is to minimize the total tardiness. We formulated a mixed-integer linear programming model for the problem to obtain optimal solutions to small-size problems. We present a genetic algorithm and particle swarm optimization, which are used to find efficient solutions for large-size problems. We show that the particle swarm optimization outperforms the genetic algorithm in large-size problems. We conduct a sensitivity analysis to obtain managerial insights using the particle swarm optimization algorithm. Full article

The flexible job shop scheduling problem is a typical and complex combinatorial optimization problem. In recent years, the assembly problem in job shop scheduling problems has been widely studied. However, most of the studies ignore the learning effect of workers, which may lead to higher costs than necessary. This paper considers a flexible assembly job scheduling problem with learning effect (FAJSPLE) and proposes a hybrid multi-objective artificial bee colony (HMABC) algorithm to solve the problem. Firstly, a mixed integer linear programming model is developed where the maximum completion time (makespan), total energy consumption and total cost are optimized simultaneously. Secondly, a critical path-based mutation strategy was designed to dynamically adjust the level of workers according to the characteristics of the critical path. Finally, the local search capability is enhanced by combining the simulated annealing algorithm (SA), and four search operators with different neighborhood structures are designed. By comparative analysis on different scales instances, the proposed algorithm reduces 55.8 and 958.99 on average over the comparison algorithms for the GD and IGD metrics, respectively; for the C-metric, the proposed algorithm improves 0.036 on average over the comparison algorithms. Full article

The maritime inventory routing problem (MIRP) integrates vessel routing and inventory management over a planning horizon to optimize logistical operations in marine environments. While existing models predominantly address short-term planning with single vessels, this research advances the field by presenting a tightened mixed-integer linear programming (MILP) model designed for long-term planning with multiple vessels. The proposed model leverages an improved mathematical formulation and state-of-the-art optimization solvers to enhance computational performance. To demonstrate its applicability, the model was evaluated using benchmark instances from the literature and new instances derived from the logistics of Chilean scientific bases in Antarctica, a challenging and underexplored maritime environment. The results show computational time reductions of up to 98% for small to medium-sized instances, achieved through the incorporation of valid inequalities into the model and the use of advanced hardware and solvers. For larger instances, optimal or near-optimal solutions were achieved within one hour for a planning horizon of 60 time units, with optimality gaps below 24.7% for a 120-time-unit horizon. These findings highlight the potential of the model to support decision-making in complex maritime logistics scenarios, extending its application to long-term, multi-vessel operations in remote and environmentally sensitive regions. The proposed framework provides a valuable tool for enhancing the sustainability and efficiency of maritime logistics systems. Full article

The ongoing transformation of district heating systems (DHSs) aims to reduce emissions and increase renewable energy sources. The objective of this work is to integrate solar thermal (ST) and seasonal aquifer thermal energy storage (ATES) in various scenarios applied to a large DHS. Mixed-integer linear programming (MILP) is used to develop a comprehensive model that minimizes operating costs, including heat pumps (HPs), combined heat and power (CHP) units, electric heat boilers (EHBs), heat-only boilers (HOBs), short-term thermal energy storage (TES), and ATES. Different ATES scenarios are compared to a reference without seasonal TES (potential of 15.3 GWh of ST). An ATES system with an injection well temperature of about 55 °C has an overall efficiency of 49.8% (58.6% with additional HPs) and increases the integrable amount of ST by 178% (42.5 GWh). For the scenario with an injection well temperature of 20 °C and HPs, the efficiency is 86.6% and ST is increased by 276% (57.5 GWh). The HOB heat supply is reduced by 8.9% up to 36.6%. However, the integration of an ATES is not always economically or environmentally beneficial. There is a high dependency on the configurations, prices, or emissions allocated to electricity procurement. Further research is of interest to investigate the sensitivity of the correlations and to apply a multi-objective MILP optimization. Full article

Shipbuilding and offshore projects frequently require schedule adjustments due to unforeseen factors such as material supply delays, technical issues, and adverse weather conditions. These adjustments are often managed manually, resulting in significant time consumption and an increased risk of human error. Unlike production scheduling, little attention has been given to design scheduling, particularly in the context of rescheduling. To address this gap, this paper presents an optimization model that automates the rescheduling process for shipbuilding and offshore unit design projects. The model generates updated schedules that accommodate necessary changes while minimizing deviations from the initial schedule. In a real-world case involving 857 tasks, the model generated a schedule in under one second, preserving approximately 80% of the original schedule and achieving a 20% improvement in adherence compared to the original scheduling method. Furthermore, the model demonstrated exceptional scalability by efficiently generating optimized schedules for 108,700 tasks in under three minutes. These results demonstrate the model’s capability to provide rapid, efficient, and scalable rescheduling solutions, enabling quick and iterative refinement processes. Full article

Fully leveraging the regulatory role of cascade hydropower in river basins and realizing complementary joint power generation between cascade hydropower and photovoltaic (PV) systems is a crucial approach to promoting the consumption of clean energy. Given the uncertainty of PV outputs, this paper introduces a short-term scheduling model for cascade hydropower–PV systems. The model aims to maximize electricity consumption by considering individual units, hydropower plant constraints, unit constraints, and grid constraints. By allocating loads among hydropower plants and periods, it optimizes hydropower’s dual roles, supporting grid power supplies and coordinating with PVs, thus boosting the overall system consumption. In terms of model solution, linearization methods and modeling techniques such as piecewise linear approximation, the introduction of 0–1 integer variables, and the discretization of generation headwater are employed to handle the nonlinear constraints in the original model, transforming it into a mixed-integer linear programming problem. Finally, taking a complementary system constructed by 15 units of 4 hydropower stations and 2 photovoltaic groups in a cascade in a river basin in Southwest China as an example, the results show that through the complementary coordination of cascade hydropower and photovoltaic power, under the same grid constraints, the expected value of the power consumption of the complementary system in the model of this paper increased by 863.2 MW·h, among which the power consumption of photovoltaic group 1 increased by 1035.7 MW·h, and the power consumption of photovoltaic group 2 decreased by 172.5 MW·h. Full article

The increasing penetration of distributed renewable energy sources introduces challenges in maintaining balance within power systems. Civic energy initiatives offer a promising solution by decentralizing balancing responsibilities to local areas, with energy clusters serving as an example of such communities. This article proposes a novel mixed-integer linear programming (MILP) model for optimizing the energy mix within a cluster, addressing both planned balancing (day-ahead) and unplanned real-time adjustments. The proposed approach focuses on mid-term decision-making, including the integration of additional wind energy sources into the cluster and the procurement of new demand-side response (DSR) contracts, that allow for short-term planned and unplanned balancing. While increased wind energy enhances the system’s renewable capacity, it also raises operational stiffness, whereas DSR contracts provide the flexibility necessary for effective system balancing. The model incorporates risk aversion by employing Conditional Value at Risk (CVaR) as a risk measure, enabling a nuanced evaluation of trade-offs between cost and risk. The interactive framework allows decision-makers to tailor solutions by adjusting confidence levels and assigning weights to cost and risk metrics. A representative numerical example, based on a typical energy cluster in Poland, illustrates the model’s applicability. This case study demonstrates that the model responds intuitively to varying decision-maker preferences and can be efficiently solved for practical problem sizes. Full article

This study compares time-based and quantity-based consolidation strategies within the Vehicle Routing Problem (VRP) framework to optimize supplier profitability and logistical efficiency. The time-based model consolidates deliveries at fixed intervals, offering predictable routes, reduced customer wait times, and cost efficiency in stable markets. Conversely, the quantity-based model dynamically adjusts delivery volumes to meet fluctuating demand, providing flexibility in dynamic environments but potentially increasing long-term costs due to logistical complexity. Using a mixed-integer linear programming (MILP) model, sensitivity analyses, and scenario-based experiments, the study demonstrates that the time-based model excels in stable conditions, while the quantity-based model performs better in highly variable demand scenarios. These findings provide actionable insights for selecting consolidation strategies that optimize delivery operations and enhance supply chain performance based on market dynamics. Full article

With the continuous adjustment of energy structure and the improvement of environmental protection requirements, combined heat and power microgrids (CHP-MG) have received widespread attention as an efficient and economical way of utilizing energy. The complexity of energy supply relationships and energy coupling within the microgrid system necessitates optimizing the power output of each equipment unit. In this paper, an optimization strategy for a multi-energy microgrid system is proposed based on the efficient energy supply of cogeneration microgrids: decoupling the thermoelectric connection by using the energy storage equipment on the supply side, utilizing the flexibility of the electrical loads and the diversity of the system’s heating methods, and reducing the electrical loads and changing the selection of the heating methods on the demand side. The optimization model in the paper is mainly based on mixed-integer linear programming and demand-side management theory, which simulates the system operation under different scenarios so as to find the optimal equipment output and load management strategies. Simulation results show that the optimized CHP-MG system can ensure a reliable power supply while effectively reducing operating costs, improving energy utilization and promoting sustainable operation of the energy system. The optimized microgrid system offers significant advantages in terms of economic efficiency and energy management when compared to conventional CHP systems. These findings provide actionable insights for policymakers, system operators, and researchers aimed at driving the development of efficient and sustainable energy management solutions. Full article