Abstract Increasing disruptions such as pandemics, geopolitical tensions, and supply chain interruptions have exposed vulnerabilities in centralized pharmaceutical manufacturing. To improve resilience, decentralized supply chains with strategically placed facilities are crucial. We formulate the multiperiod facility location and demand allocation problem as a Markov decision process and train an attention‐based actor‐critic with a graph‐attention encoder and pointer‐style decoder. On US Medicare Part D demand series over 6‐10‐year horizons, the learned policies attain total costs within 2.6‐5.0% of exact mixed‐integer linear programming (MILP) baselines while delivering orders‐of‐magnitude faster inference (0.2s per batch). Monte Carlo stress tests with facility outages and demand surges show graceful degradation and high service levels, and criticality maps reveal sites whose loss would most increase cost. The results demonstrate that learning‐to‐optimize can support resilient, timely facility planning at a national scale, complementing exact solvers for rapid what‐if analysis and contingency planning.

Accurate detection of small objects in video analytics is limited by low pixel resolution and insufficient visual cues. While software-based enhancements often fail to recover missing details, Pan–Tilt–Zoom (PTZ) cameras can physically increase spatial resolution through optical zoom. However, mechanical latency and configuration complexity hinder their real-time applicability. We propose ZoomPatch, a real-time video analytics framework tailored for small object detection. ZoomPatch actively schedules PTZ adjustments to capture optically enhanced subframes of regions of interest (ROIs) and fuses inference results back to the global reference frame. Specifically, it introduces a dynamic Cycle Length Proposer to adapt analysis cycles based on scene motion, and a Mixed Integer Linear Programming (MILP)-based Configuration Decider to determine the optimal sequence of pan, tilt, and zoom adjustments under time budget constraints. Simulation-based experimental evaluations across diverse workloads demonstrate that ZoomPatch significantly outperforms fixed-perspective, super-resolution (SR), and greedy baselines. Notably, in the detection task using YOLOv10, ZoomPatch improves the F1-score from 0.33 to 0.47 (a 42% increase) compared to the fixed-perspective baseline. Furthermore, ZoomPatch yields performance gains of 30% and 7% over the SR baseline (0.36) and the greedy baseline (0.44).

The synthesis of phase-pure out-of-plane ordered MAX phases (o-MAX) Cr2VAlC2 and Cr2V2AlC3 is notoriously challenging and often hindered by parasitic reactions inherent to conventional elemental powder routes. This work combines thermodynamic calculations with experimental synthesis to validate the proposed solid-state reaction pathways employing Cr2AlC and VC as starting compositions to prepare high-purity o-Cr2VAlC2 and o-Cr2V2AlC3 MAX phases in the Cr–V–Al-C system. The thermodynamic formability of 312 and 413 MAX phases is evaluated by calculating the formation enthalpies and Gibbs free energies for both fully ordered o-MAX phases and their corresponding solid solutions, confirming the high thermodynamic stability of o-MAX compounds in comparison to solid solution forms from both typical elemental powder metallurgy and solid-state reaction synthesis. Combining the linear programming optimization algorithm for reaction thermodynamics and the systematic experimental verifications of phase formation kinetics, high yields of o-Cr2VAlC2 (82.0 wt %) and o-Cr2V2AlC3 (88.7 wt %) MAX phases are obtained with starting compositions as Cr2AlC/VC = 1:1.2 and 1:1.9 at the sintering temperature of 1500 °C. Using the JMAK equation, the apparent activation energies for phase nucleation and growth of o-Cr2VAlC2 and o-Cr2V2AlC3 phases are found to be 313.6 and 98.4 kJ mol–1, respectively. The calculated electronic density of states and bond orders for solid solutions and fully ordered MAX phases confirm that the stabilization of higher-order o-MAX phases in the Cr–V–Al-C system is mainly attributed to the significant reduction of Cr–C and V–C bond orders for those antisite atoms in disordered structures. This work elucidates a new pragmatic strategy to precisely tailor both reaction thermodynamics and kinetics for the synthesis of o-MAX phases in general.

Abstract In the classical firefighter game, a fire breaks out on some vertices of an undirected connected graph at time zero. At each subsequent time step, a fixed number of firefighters can protect one vertex each from catching fire. Afterwards, the fire spreads from each burning vertex to every adjacent vertex that is neither burning nor defended. The game ends when the fire can no longer spread. The goal is to find a defense strategy that maximizes the number of non-burning (saved) vertices. In this work, we first revisit the classical integer linear programming formulation and then present several improvements for it, as well as two new formulations and tighter bounds on the maximum duration of the game. Moreover, we relax the classical assumptions that all vertices have uniform values and costs, i.e., we allow vertices to have different values and costs for being defended. Furthermore, instead of a fixed number of firefighters, we are given a defense budget that we can spend each time step to defend the vertices. We call this the cost-value firefighter game. We present three different integer linear programming formulations for the problem, along with a series of inequalities to strengthen the formulations and tight bounds on the maximum duration of the game.

Urban Transportation Network Design (TND) is a highly complex system engineering. It has always been regarded as a very difficult problem in urban planning and transportation. This study tries to sort out and summarize the existing research system and development process in this field. From the perspective of mathematical modeling, the multi-objective property, nonlinear characteristics, uncertainty and NP-hard computational complexity of the TND problem are explained one by one, and a series of solution difficulties derived from them also appear. Classical optimization methods, such as linear programming, integer programming, bi-level programming models and so on, have advantages in solving structured problems. But their limitations in large-scale dynamic situations are also pointed out. In comparison, new intelligent and simulation optimization methods, such as heuristic algorithms, data-driven modeling strategies and simulation-optimization coupling frameworks, provide more potential ways to solve complex traffic network design problems. The current mainstream research paradigm can be summarized as the progressive process of "theoretical analysis—optimization solution—simulation verification". Different tools work together in this process to deepen the understanding of the problem and improve the solution efficiency. Network planning with dynamic and multiple uncertainties still faces many unsolved difficulties. Big data technology, artificial intelligence methods and the interdisciplinary integration may become the key driving forces for the future breakthrough in the TND field. This review aims to provide basic theoretical reference and framework support for the follow-up related research.

Sustainable irrigation planning under increasing water scarcity requires efficient allocation of limited water resources while simultaneously considering land suitability and agricultural productivity. In this study, we aim to identify optimal cropping patterns for sustainable irrigation management using an optimization-based decision-support framework applied to the Nam Mang 3 Irrigation Project in Lao PDR, based on data from 2022. Focusing on the dry season (November–April), we evaluated six major crops—rice, beans, maize, tomato, cucumber, and watermelon—under six irrigation scenarios to assess the impacts of land suitability and water availability. The analysis incorporated a water availability range from 17.70 to 18.10 mm3 to evaluate system robustness. Linear Programming (LP), the Genetic Algorithm (GA), and the African Vultures Optimization Algorithm (AVOA) were employed to determine optimal crop allocation. The proposed framework explicitly incorporates varied soil types and land-use constraints, providing a more realistic representation than conventional homogeneous assumptions. The results indicate that AVOA outperformed other models in terms of stability. Under the evaluated scenarios, the optimal cultivated area ranged from 3192 to 3200 ha, with total profits fluctuating between 34,125,930 and 34,314,900 US$. These findings demonstrate that integrating soil variability and sensitivity-based optimization significantly enhances irrigation planning, providing a practical, robust decision-support tool for planners to design adaptive and sustainable cropping strategies in water-scarce regions.

Linear fractional programming problems in an interval environment

Lightweight cryptography aims to achieve security with minimal resource footprints and low computational overhead. In particular, efficient implementations of linear layers are recognized as a crucial component. Boyar et al. showed that finding an optimal implementation of linear layers reduces to the Shortest Linear Program (SLP) problem, which is NP-hard. Consequently, various heuristic methods have been developed to search for near-optimal solutions. In this work, low-latency implementations are prioritized, and a heuristic search algorithm named HILL (Heuristic Implementation for Low-Latency Linear layers) is proposed. To further balance cost and delay, the h-XOR metric is integrated into HILL, where 2/3-input XOR gates are dynamically weighted to achieve an optimized trade-off between the circuit area and depth. Compared with the heuristic search proposed by Li et al. (FSE 2019), which yields an AES MixColumns implementation requiring 315 gate equivalents (GEs) at depth 3, our approach achieves 270.4 GEs at the same depth, corresponding to a 14.2% area reduction. To the best of our knowledge, this is one of the most efficient hardware implementations of AES linear layers in terms of both area and depth. Furthermore, implementation costs are minimized for all 4254 Maximum Distance Separable (MDS) matrices proposed by Li et al.

Global data center electricity demand is projected to double to 945 TWh by 2030, yet no optimization framework jointly sizes renewable generation, battery storage, hydrogen export infrastructure, and flexible computing loads within a single industrial hub. This paper develops a two-layer techno-economic workflow for an integrated renewable–hydrogen–data center hub in Yanbu Industrial City, Saudi Arabia. HOMER Pro provides baseline capacity sizing and dispatch across four scenarios; a Pyomo-based mixed-integer linear program, calibrated to within 2% of the baseline, then extends the system to include a 60 MW data center (30 MW critical, 30 MW flexible), multi-sink hydrogen allocation (domestic, ammonia, methanol), and low-grade waste heat recovery. Battery storage emerges as the dominant cost–carbon lever: its removal raises the levelized cost of electricity (LCOE) from 0.052 to 0.181 USD/kWh (+250%) and increases CO2 emissions from 1.83 to 2763 kt/yr, a factor of 1510. The Integrated Hub reduces annualized costs by 8.2% (36.9 M USD/yr) and emissions by 28% relative to a separate-build counterfactual, driven by shared PV–battery infrastructure and hydrogen export revenues of 58.5 M USD/yr. Export demand raises the electrolyzer capacity factor from 8.65% to 24.3%, cutting the levelized cost of hydrogen from 10.5 to 6.8 USD/kg. Waste heat recovery reduces the levelized cost of heat by 17%, and co-location lowers the levelized cost of compute by 23% (from 0.055 to 0.042 USD/GPU/hr). These results provide quantitative design principles for industrial hub planners considering data center co-location in high-solar regions with hydrogen export ambitions.

This study addresses a multi-objective Facility Location Problem (FLP) to optimize supply chain and logistics network design in Vietnam. The proposed framework is formulated as a Fuzzy Mixed-Integer Linear Programming (FMILP) model and solved using a combination of exact and meta-heuristic algorithms, along with scenario-based analysis to address uncertainty. The model is empirically validated using real-world operational data from a logistics enterprise in Hai Phong, incorporating demand information, candidate warehouse locations, and system constraints. The results indicate that the proposed model significantly reduces logistics costs (a 23.6% reduction in operating costs and a 17.8% reduction in total travel distance), shortens delivery time, and improves service performance (a 7% increase in demand fulfillment rate). These findings confirm the effectiveness of the FMILP-based FLP model and highlight its potential for supporting sustainable and data-driven logistics development in Vietnam.

This paper examines an intermodal transport problem characterised by key operational features, including scheduled maritime and rail transport services at seaport and rail terminals, flexible road transport, and temporary storage options at depots near these terminals to reduce high holding costs prior to scheduled departures. To address this challenge, we introduce an operational freight routing problem within a time-sensitive road-rail-maritime-depot intermodal transport network. We develop a novel mixed-integer linear programming (MILP) model to solve this problem and demonstrate its application through a case study on intermodal route planning for a customer order from Denizli, Türkiye, to Duisburg, Germany. The model generates Pareto-optimal solutions that balance time and cost objectives by selecting optimal schedules for liner vessels and trains while integrating road transport and warehousing alternatives. A comprehensive sensitivity analysis is also conducted to assess the robustness of the MILP model solutions with respect to variations in the cost and time parameters of the case problem. The proposed model improves efficiency and effectiveness in evaluating operational intermodal routing plans and offers a structured operational framework for enhancing intermodal transport operations.

ABSTRACT In the present study, a novel optimization framework is developed by integrating non-linear membership and non-membership functions within an Intuitionistic Fuzzy Optimization-based Multi-Objective Fuzzy Linear Programming (IFO MOFLP) model for irrigation planning. The framework is applied to the Kakrapar Right Bank Main Canal (KRBMC) command area of the Ukai -Kakrapar Water Resources Project, Gujarat, India. Unlike conventional fuzzy optimization, the IFO approach incorporates the degree of acceptance, rejection, and hesitation, improving decision quality under uncertainty. The model considers three objectives: (i) maximization of net irrigation benefits, (ii) maximization of employment generation, and (iii) minimization of cultivation cost, subject to constraints. This study demonstrates, for the first time, the applicability of non-linear membership and non-membership functions in a real-world water resources system. For a selected scaling factor of 0.33, the corresponding acceptance, rejection, and hesitation values were 0.503, 0.282, and 0.215. Under these conditions, the model achieved a net irrigation benefit of Rs. 3585.05 million, employment generation of 10,189.21 thousand man-days, and a cultivation cost of Rs. 2260.13 million, with an irrigation intensity of 76.92%. The results indicate that the non-linear IFO MOFLP framework provides balanced crop allocation and effectively handles conflicting objectives under uncertainty.

This study compared acute and chronic adaptations to cluster set (CS) and traditional set (TS) structures during a 6-week linear periodised resistance training programme in the back squat. Thirty-six resistance-trained females and males were randomly assigned to the CS or the TS group. Acute responses were assessed using objective (blood lactate, mean propulsive velocity, velocity loss [VL], countermovement jump [CMJ] height and modified reactive strength index) and subjective measures (rating of perceived exertion [RPE], delayed onset muscle soreness and the short recovery and stress scale). Chronic adaptations included one-repetition maximum (1RM), relative isometric peak force, muscle endurance, CMJ height, velocity at 70% 1RM (v70) and load-velocity (L-V) profiling. CS displayed higher barbell velocities and lower acute fatigue, reflected by VL (g=-0.56 to -2.16), lactate (g=-0.51 to -1.86) and RPE (g=-0.91). TS did not demonstrate lower fatigue in any acute measure. Both protocols elicited comparable improvements in 1RM (CS: g=0.28; TS: g=0.23), muscle endurance (CS: g=0.48; TS: g=0.50) and v70 (CS: g=1.18; TS: g=1.32), with no significant improvements in CMJ height or isometric peak force. Post-intervention L-V profiling revealed distinct adaptations, with CS demonstrating a shallower slope, indicating higher velocities at heavier loads. Sex differences were minimal; females displayed lower lactate and RPE, while longitudinal adaptations were similar. In conclusion, both protocols improved muscle strength and endurance. Collectively, CS provided superior fatigue management, better preservation of barbell velocity and unique L-V profile adaptations.

This study investigates a Vehicle Routing Problem with Drones (VRPD) for multi-type rescue tasks in post-disaster response. Specifically, we consider a truck-and-drone collaborative system that can simultaneously deliver essential relief supplies and assess network conditions with drones in disaster scenarios. To enhance the rescue efficiency, drones can collaborate with different trucks and perform multi-type tasks (delivery and surveillance), making the proposed problem challenging to solve. We first provide a Mixed Integer Linear Programming (MILP) model for the proposed problem. The objective is to minimise the priority cost, which is calculated as the weighted delay cost of serving all rescue tasks and is different from most existing studies on VRPD for parcel deliveries. Then, we develop an Adaptive Simulated Annealing (ASA) algorithm. Since the priority cost depends on the intertwined influence of truck-and-drone routes, the ASA algorithm is integrated with a dynamic programming method to calculate the priority cost. The ASA algorithm can always get the (near) optimal solution on instances with fewer than 30 nodes, and solves larger instances efficiently. Numerical experiments demonstrate that enabling drones to perform multi-type tasks and allowing flexible truck-and-drone collaboration reduces the priority cost by an average of 15.7% across all tested instances, compared with the single-type task and dedicated truck-and-drone collaboration. Sensitivity analysis shows that introducing more drones can reduce the number of trucks involved in the disaster response while achieving similar performance. Moreover, this study reveals a trade-off between minimising priority cost and other objectives, such as minimising travel cost or makespan.

ABSTRACT Surface mines supply more than 96% of the raw minerals used across industrial sectors, making its transportation systems a critical component of operational efficiency and environmental performance. This study develops an integrated stochastic discrete–continuous simulation-based optimization framework for transportation decision-making in surface mining operations. The framework couples a mixed-integer linear programming (MILP) optimization model with a discrete–continuous simulation model to evaluate system performance under operational uncertainty. The proposed approach simultaneously considers economic and environmental objectives by minimizing transportation costs while reducing greenhouse gas (GHG) emissions. The framework is applied to an operating surface copper mine to determine the optimal size of the transportation fleet. Results demonstrate that the integrated simulation–optimization approach improves transporter waiting time at loading points by 33%, leading to a 3.5% increase in production. In addition, the framework enables significant environmental benefits, achieving a 72% reduction in carbon dioxide emissions. Sensitivity analysis is conducted to evaluate the influence of key operational parameters on system performance and to examine trade-offs between cost efficiency and emission reduction.

Energy management systems operating under dynamic electricity pricing require fast and cost-optimal control strategies for flexible loads. Mixed-integer linear programming (MILP) can compute theoretically optimal control trajectories but is computationally expensive and typically relies on accurate load forecasts, limiting its practical real-time applicability. This paper proposes a supervised imitation learning (IL) framework that learns optimal setpoint trajectories for a conventional proportional (P) controller directly from electricity price signals and temporal features, thereby eliminating the need for explicit load forecasting. The learned model predicts setpoint trajectories in an open-loop manner, while a lower-level P controller ensures stable closed-loop operation within a two-stage control architecture. The approach is validated in an industrial case study involving load shifting of a refrigeration system under dynamic electricity pricing and benchmarked against MILP optimization, reinforcement learning (RL), heuristic strategies, and various machine learning models. The MILP solution achieves a cost reduction of 21.07% and represents a theoretical upper bound under perfect information. The proposed Transformer model closely approximates this optimum, achieving 19.33% cost reduction while enabling real-time inference. Overall, the results demonstrate that the proposed supervised IL approach can achieve near-optimal control performance with substantially reduced computational effort for real-time energy management applications.

This study develops a multi-period Mixed Integer Linear Programming model for Closed-Loop Supply Chain (CLSC) network design in the electronics sector. The model explicitly integrates two dynamic drivers of consumer behavior—discounts and environmental awareness—into the return rate formulation. The model defines the flow of production, remanufacturing, shipping, returned product quantity, waste volume, and consumer return rate across multiple planning periods, with the goal of minimizing total costs. The numerical case study is based on synthetic data constructed based on parameter ranges in previous CLSC studies to reflect realistic operational conditions. The numerical results show manufacturing costs as the largest component (68.36%), followed by transportation (8.23%) and distribution handling (6.69%). Sensitivity analysis indicates (i) higher discounts and greater awareness significantly increase the return rate, increase remanufacturing volume, and reduce waste; and (ii) increasing Fd results in significant cost savings, with the highest outcome minimizing combined production and remanufacturing costs. These findings support a targeted strategy of discounts and environmental awareness, aligning remanufacturing capacity with returns, and achieving profitability. For policymakers, this model offers a decisionsupport tool to assess discounts and awareness programs, encouraging sustainable and profitable CLSC operations that align with circular economy principles.

The article addresses the development and improvement of the control system for the epichlorohydrin production unit. The epichlorohydrin production process is analyzed in detail from the perspective of automation of technological processes and evaluated as a control object. The key parameters affecting the technological process are identified, the functional structure of the unit is developed, and the main tasks of the control system are explained. To ensure optimal control of the technological process, mathematical models were constructed, and process identification was performed based on regression analysis. Based on these models, an optimization problem was formulated, and the Simplex method of linear programming was applied to solve it. Optimization results allowed for determining more efficient parameters for the technological regime. To maintain the required technological conditions, an automatic regulation system for the unit was designed. The dynamic characteristics of the control object were studied, a dynamic model was developed, and a single-loop automatic regulation system was synthesized for temperature control. The quality indicators of the regulation system were analyzed, ensuring its stable operation. The article also describes the technical, software, and data support of the control system in detail. During the selection of technical equipment, high-reliability measurement and regulation devices from Fisher-Rosemount, widely used in modern automation, were employed. The study demonstrates the potential for increasing the efficiency of epichlorohydrin production control and improving product quality. Keywords: Epixlorohydrin production, automation of technological processes, control system, automatic regulation system, mathematical modeling, regression analysis, optimization problem, simplex method, chemical reactor control automation, optimization, microprocessor-based systems.

This study examines distribution optimization and its impact on manpower planning in the tilapia fillet processing industry in East Java, Indonesia. The research aims to evaluate how optimized distribution configurations influence workforce requirements across supply chain nodes. A quantitative analytical approach was applied using operational distribution data, with distribution optimization conducted through linear programming and the relationship between distribution volume and workforce demand analyzed using Spearman correlation. The results indicate that optimized distribution structures significantly reduce transportation costs and improve workforce allocation efficiency. The findings highlight that distribution optimization can support more adaptive manpower planning and enhance operational efficiency in fisheries supply chains.

Abstract Model checking undiscounted reachability and expected-reward properties on Markov decision processes (MDPs) are key for the verification of systems that act under uncertainty. Popular algorithms are policy iteration and variants of value iteration; in tool competitions, most participants rely on the latter. These algorithms generally need worst-case exponential time. However, the problem can equally be formulated as a linear programme, solvable in polynomial time. In this paper, we give a detailed overview of today’s state-of-the-art algorithms for MDP model checking with a focus on performance and correctness. We highlight their fundamental differences, and describe various optimizations and implementation variants. We experimentally compare floating-point and exact-arithmetic implementations of all algorithms on three benchmark sets using two probabilistic model checkers. Our results show that (optimistic) value iteration is a sensible default, but other algorithms are preferable in specific settings. This paper thereby provides a guide for MDP verification practitioners—tool builders and users alike.