Dynamic and multi-resource flexible job shop scheduling in pharmaceutical manufacturing: A MILP-based decision support tool

• A Python model for semi-islanded green ammonia production was developed. • The LCOA ranges from 669.30 to 867.94 €/tNH 3 . • Power generation represents the largest share of total system costs. • The LCOA decreases by up to 15.15 % over the next two decades. • Dynamic operation achieves up to a 6 % reduction compared with continuous operation. The study presents a technical and economic assessment of green ammonia production in several counties in Ireland. The system is based on renewable energy sources, namely photovoltaic and offshore wind. Three locations were chosen based on their renewable potential and the availability of export ports to EU (European Union) markets. A high-temporal-resolution model for green ammonia production has been developed for the first time in Ireland. The WSA (Wind Solar Ammonia) model was developed specifically for this research. It uses MILP (Mixed Integer Linear Programming) and optimisation techniques to simulate scenarios at the lowest possible cost. The Python-based model incorporates all relevant energy subsystems and use functions from specialised libraries. The WSA model includes large-scale hydrogen production with proton exchange membrane electrolysers, air separation to produce nitrogen, Haber-Bosch ammonia synthesis, desalination unit. Storages buffers were implemented for green hydrogen, green ammonia, purified sea water, and nitrogen. Both continuous and dynamic operation were simulated, continuous operation reflects industrial reliability, stable equipment performance, and maximised lifetime, while dynamic operation captures renewable intermittency, curtailment reduction, and system flexibility. Cork is identified as the least-cost location, with the dynamic operation system achieving the lowest LCOA (Levelised Cost Of Ammonia) at 791.07 €/t in 2030 and 731.45 €/t in 2040, outperforming the continuous operation system, which records 834.27 €/t in 2030 and 741.62 €/t in 2040. The system achieve a carbon saving up to 94.63 % compared to the ammonia fossil fuel-based comparator.

Design and optimization of an exergy-cascaded hydrogen hub with multi-level heat recovery and high-temperature thermal support: Thermodynamic and exergy assessment, mixed-integer linear programming (MILP)-based co-design, and predictive dynamic operation

A new robust bi-level optimization framework for biomass supply chain network and its accelerated Benders decomposition

ABSTRACT This research develops an integrated mixed‐integer linear programming (MILP) model for closed‐loop supply chain network design that optimises competing economic and environmental objectives including profit maximisation, supplier quality improvement and CO 2 emission reduction. The primary aim of this study is to identify which solution techniques perform best when dealing with different sizes of problems. The multi‐objective particle swarm optimisation (MOPSO) method demonstrated superior performance over NSGA‐II by achieving 35%–45% faster convergence rates and delivering 20%–30% better solution quality. The epsilon‐constraint approach with CPLEX showed better performance for solving smaller problems. The analysis revealed that return rates, together with material recovery expenses, function as essential elements which determine the profitability of the disassembly process. The research proves that multi‐objective optimisation methods work efficiently with real supply chain sizes. These findings support the development of decision support systems for sustainable operations management.

Wafer fabrication consists of hundreds of interrelated processing steps, where planning decisions directly affect equipment utilisation and work-in-process (WIP). Among these steps, photolithography is regarded as a bottleneck due to expensive equipment, re-entrant flows, and machine dedication across layers. Despite its importance, most photolithography planning studies do not explicitly model WIP flows, which are critical under machine dedication. This study addresses this gap by formulating a photolithography planning problem that models WIP flows under machine dedication. The problem is formulated as a mixed-integer linear programming (MILP) model, and its NP-hardness is established via a proof by restriction from the Partition problem. To solve large-scale instances, we develop an MILP-Guided Large Neighbourhood Search (MG-LNS) framework. The approach constructs an initial solution using a rolling-horizon scheme with heuristic rules and decomposed MILP models, and then improves it via structured destroy strategies and MILP-based repair operators. Computational experiments on nine generated benchmark data types show that MG-LNS achieves machine utilisation and target achievement rates exceeding 98%, while maintaining average overproduction and underproduction rates of 0.63% and 2.42%, respectively. Ablation and sensitivity analyses confirm the effectiveness of the proposed framework and demonstrate the impact of objective-weight selection on the contribution of individual objective terms.

This paper proposes a mixed-integer linear programming (MILP) model for the optimal power flow (OPF) problem in distribution grids with step-voltage regulators (SVRs). The OPF problem aims to minimize the total cost of the distribution grid, including the cost of purchasing effective and reactive power from the transmission grid, the cost of generating effective power, and the reactive power of distributed power sources. The constraints considered include the power flow equations, the node voltage constraints, the branch transmission power limits, the power factor limits at the connection point, and the SVR constraint. The MILP model of the OPF problem in the distribution grid was developed from the mixed-integer nonlinear programming (MINLP) model by linearizing the power flow equations and building an accurate linear SVR model. The proposed MILP model is evaluated on an IEEE33-node grid with different load scenarios using the GAMS programming language and the CPLEX commercial solver. The calculation results show that the MILP model is computationally efficient, and the optimal pressure distribution of SVR reduces the operating costs of the distribution grid.

Municipal solid waste planning in a rebuilding city is not only a question of cost or technology choice. It also depends on access, operational feasibility, environmental exposure, and the policy conditions under which the system can be rebuilt. This study develops a policy-driven mixed-integer linear programming (MILP) model for designing a low-carbon municipal solid waste (MSW) network that includes transfer stations, mechanical-biological treatment (MBT) facilities, waste-to-energy (WtE) plants, and landfills. The model evaluates four planning concerns together: total cost, carbon emissions, implementation feasibility risk, and site environmental risk. In addition to the four-goal baseline formulation, the study explicitly examines three carbon-policy regimes: carbon-tax internalization, carbon tax combined with processing subsidy, and cap-and-trade. The model is tested in Idlib Governorate in northwest Syria, where formal municipal data are scarce. For this reason, the case-study dataset combines field-based information, input from eleven experts, geographic information system (GIS)-based risk assessment, fuzzy Full Consistency Method (Fuzzy-FUCOM) weighting, and weighted goal programming. The baseline solution opens three transfer stations, two MBT facilities, one WtE plant, and two landfills, generating about 141,128 MWh of electricity per year at an annual cost of USD 216.8million. The sensitivity results show that waste supply has the largest effect on cost, while the MBT-to-WtE fraction has the strongest effect on emissions and energy recovery. The policy scenarios show a mainly financial effect under the tested settings: carbon tax increases the monetized cost of emissions, processing subsidy reduces part of the treatment cost, and cap-and-trade creates either permit costs or trading revenue depending on the cap. Overall, the framework provides a practical planning structure for MSW network design where data, infrastructure, and governance capacity are limited.

Effective hospital capacity management is critical for enhancing patient care quality, operational efficiency, and healthcare system resilience, notably during demand spikes like those seen in the COVID-19 pandemic. However, devising optimal capacity strategies is complicated by fluctuating demand, conflicting objectives, and multifaceted practical constraints. This study presents a data-driven framework to optimize capacity management decisions within hospital systems during surge events. Two key decisions are optimized over a tactical planning horizon: allocating dedicated capacity to surge patients and transferring incoming patients between emergency departments (EDs) of hospitals to better distribute demand. The optimization models are formulated as robust mixed-integer linear programs, enabling efficient computation of optimal decisions that are robust against demand uncertainty. The models incorporate practical constraints and costs, including setup times and costs for adding surge capacity, restrictions on ED patient transfers, and relative costs of different decisions that reflect impacts on care quality and operational efficiency. The methodology is evaluated retrospectively in a hospital system during the height of the COVID-19 pandemic to demonstrate the potential impact of the recommended decisions. The results show that optimally allocating beds and transferring just 32 patients over a 63 day period around the peak, about one transfer every two days, could have reduced the need for surge capacity in the hospital system by nearly 90%. Overall, this work introduces a practical tool to transform capacity management decision-making, enabling proactive planning and the use of data-driven recommendations to improve outcomes.

Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to "classic" decision trees with constant values in their leaves, model trees can use linear combinations of predictor variables in their leaf nodes to form predictions, which can help achieve higher accuracy and smaller trees. Typical algorithms for learning model trees from training data work in a greedy fashion, growing the tree in a top-down manner by recursively splitting the data into smaller and smaller subsets. This yields a fast algorithm, but the selected splits are only locally optimal, potentially rendering the tree overly complex and less accurate than a tree whose structure is globally optimal for the training data. In this paper, we empirically investigate the effect of constructing globally optimal model trees for classification and regression. The trees we consider feature linear support vector machines at the leaf nodes and are learned using mixed-integer linear programming (MILP) formulations. We use benchmark datasets to compare them to model trees obtained using greedy and dynamic programming-based algorithms, evaluating both tree size and predictive accuracy. We also compare to classic optimal and greedily grown decision trees, random forests, and support vector machines. Our results show that MILP-based optimal model trees can achieve competitive accuracy with very small trees. We also investigate the effect on the accuracy of replacing axis-parallel splits with multivariate ones, foregoing interpretability while potentially obtaining greater accuracy.

ABSTRACT Integrating forest biomass into bioenergy systems poses logistical challenges due to seasonal variations in quality and the dispersed nature of supply. We develop a mixed-integer linear programming model that jointly optimizes procurement timing, multimodal transport (truck−rail−barge), chipping and drying locations, and inventory levels at supply nodes, terminals, and the biorefinery. The model embeds process-state transitions, seasonal moisture profiles, and infrastructure limits. In a large-scale Quebec case study (500 − 3000 dry metric tonne (DMT)/day), integrating rail reduces total system costs by 2.8 − 4.8% and yields mill-gate costs around CAD 119 − 121 per DMT. Terminals near the biorefinery decouple procurement from conversion and support buffer-based strategies through high-moisture periods. The optimization model is computationally tractable and provides a reusable template for planning forest biomass logistics that accounts for seasonal quality, preprocessing, and mode-choice interactions.

This study addresses the limitation of conventional fertilization monitoring methods that fail to capture dynamic nutrient trends for low-carbon precision management by proposing a data-driven approach for fertilization behavior recognition and low-carbon decision optimization based on multi-source agricultural time-series data. Traditional approaches lack temporal continuity and are unable to support real-time behavioral identification or carbon emission-constrained decision-making. The long short-term memory (LSTM) model is selected for its ability to process long-sequence heterogeneous sensor data and accurately recognize sparse fertilization events under environmental noise, while MILP is used to formulate a globally optimal fertilization plan that minimizes carbon emissions subject to crop nitrogen demand and environmental safety constraints. By deploying soil, meteorological, and crop growth sensors to establish an edge-cloud collaborative architecture, this method enables real-time collection and feature extraction of multi-source heterogeneous farmland data. A behavior recognition model combining a bidirectional LSTM network with an attention mechanism is developed to accurately annotate fertilization events and their temporal and spatial parameters. Carbon equivalent is calculated based on nitrogen dynamic balance and lifecycle carbon emission factors. Using carbon emission minimization as the objective function and crop nitrogen requirement and environmental safety as constraints, a mixed integer linear programming (MILP) model is constructed to generate a low-cost, high-yield fertilization plan. Results show that the system's prediction error is 8.5% on day 30, and carbon emission intensity is reduced to 0.365 kgCO₂-eq/kg fertilizer, supporting the feasibility of this AI-driven decision framework in terms of behavior recognition accuracy and carbon emission control effectiveness under the tested plot conditions.

The increasing frequency and severity of disasters highlight the need for responsive humanitarian logistics systems. In post-disaster settings, damaged infrastructure can delay conventional vehicle access, while drones can support timely relief delivery to locations with limited ground accessibility. This study introduces a two-echelon location-routing problem with multiple drones and split deliveries (2E-LRP-MD-SD) for coordinated ground vehicle and drone operations in post-disaster relief distribution. The problem jointly considers distribution centre selection, heterogeneous ground-vehicle deployment, multiple drones per vehicle, synchronised truck-drone routing, and split demand fulfillment. A mixed-integer linear programming formulation is developed to minimise delivery completion time while capturing accessibility asymmetry, capacity restrictions, drone endurance, and temporal synchronisation. To solve larger instances, a three-phase matheuristic, Prescriptive Analytics with Clustering and Optimisation (PACO), is proposed and benchmarked against a Variable Neighbourhood Search (VNS) metaheuristic. A modified subgradient-based lower-bound procedure supports solution-quality assessment. Computational experiments show that 2E-LRP-MD-SD reduces delivery completion time by 15%–42% relative to the ground-vehicle-only system, and that PACO consistently outperforms VNS. The sensitivity analyses show that split deliveries improve efficiency, while drone speed, fleet size, payload–endurance trade-offs, and demand intensity affect delivery completion time. The results inform configuration of truck-drone relief systems under capacity, accessibility, and demand-surge constraints.

Wind affects both energy consumption and routing decisions in UAV delivery, making launch site selection and route planning strongly interdependent. This paper investigates their joint optimization under wind effects. Under a quasi-steady two-dimensional uniform wind-field assumption, wind speed, wind direction, payload status, battery capacity, and time windows are incorporated into the problem. A mixed-integer linear programing model is developed to minimize total system energy consumption by jointly determining launch site selection, task assignment, and flight routes. To solve the problem efficiently, an adaptive large neighborhood search (ALNS) algorithm is proposed. For 9-node and 20-node instances, ALNS obtains the same results as Gurobi. For the 50-node instance, it finds a feasible solution in about 105 s. Results further show that wind conditions influence energy consumption, delivery time, route structure, and launch site choice. These findings support the joint optimization of launch site selection and routing in UAV delivery.

Ensuring equitable access to healthcare services is paramount for the enhancement of societal welfare and the optimisation of public health outcomes. Within the context of West Java Indonesia, accelerated population growth coupled with geographic disparities has resulted in heightened pressure on the existing healthcare infrastructure, thereby rendering numerous communities inadequately served. Although CHCs are already widespread in Indonesia, their distribution remains uneven, especially in growing urban areas. Consequently, there is growing recognition of the need to strategically expand community healthcare centres (CHCs) to improve access across underserved areas. These CHCs are instrumental in providing vital services, encompassing preventive care, maternal and child health, immunisation, dental services, and outpatient care. This study presents an integrated approach combining population forecasting, spatial demand estimation, and optimisation modelling to support long-term planning of CHCs in Kota Bandung. Kota Bandung was selected as the study area due to its high population density, significant spatial disparities in healthcare access, and strategic importance in regional health planning. Using an ARIMA model, the researchers forecasted population growth through 2045. The year aligns with Indonesia's national long-term vision, Visi Indonesia 2045. They then estimated daily CHC demand using spatial grid and population density data, applying a standard utilisation rate. Three mixed-integer linear programming (MILP) models were developed to optimize facility locations by maximizing coverage, minimizing travel time, or balancing both. This method allows planners to explore various scenarios based on local needs and constraints. The forecasting model reveals a consistent escalation in the demand for primary healthcare services within the Bandung region, with distinct growth hotspots identified in presently underserved locales. Optimisation scenarios produced by the MILP models indicate that the strategic positioning of new CHCs can substantially augment service coverage while simultaneously mitigating disparities in healthcare access. Scenario-based simulations were conducted to explore how different planning objectives-such as maximizing coverage or minimizing travel time-impact CHC placement outcomes. The results suggest that the most equitable arrangement of CHCs would enhance accessibility for marginalized populations by more closely aligning resources with geospatial demand. This integrated modelling framework presents a pragmatic paradigm for long-term health infrastructure planning in contexts characterized by resource limitations. By synthesizing demand forecasting with location-optimisation methodologies, regional health authorities are empowered to make data-informed decisions to enhance access and equity in primary healthcare services. These findings bolster broader initiatives aimed at achieving Universal Health Coverage in Indonesia.

This article addresses a two-stage flow-shop scheduling problem (FSSP) considering uncertain job processing and release time. To minimize the worst-case expected makespan, a distributionally robust optimization (DRO) approach is designed. By introducing effective bounds and valid inequalities, the problem is transformed into a mixed integer linear program (MlLP), which is solvable via off-the-shelf commercial solvers. To verify the performance of the model, the DRO model is compared with the stochastic linear program (SLP) and its deterministic counterpart under various parameter settings, where the DRO model exhibits greater robustness and computational efficiency in handling almost all the scenarios. Besides, the DRO model demonstrates a prominent advantage when the uncertain interval of the mean is larger, the release time is less scattered and more jobs are scheduled. It is discovered that the proposed DRO model is capable of providing robust schedules in a highly volatile environment, thereby enhancing the resilience and robustness of manufacturing operations.

PipeNetGen: A methodology for generating synthetic water distribution network models.

Designing carbon pricing and subsidies in federated electricity markets is complicated by fragmented governance and regional disparities. This study develops the Policy–Response–Optimization System (PROS), a modular framework that couples policy levers, behavioral investment thresholds, and system-level optimization. Investor behavior is represented through the Willingness Index (WI) and Marginal Abatement Benefit per Policy (MABP), calibrated with survey data and historical adoption records, and embedded within a Mixed-Integer Linear Programming (MILP) model. Applied to Australia’s National Electricity Market, PROS assesses 117 carbon–subsidy scenarios. Results identify a robust Synergistic Zone around carbon prices of 50–60 AUD/tCO₂ and subsidies of 15–25 AUD/MWh , yielding higher investor activation and fiscal efficiency. Monte Carlo simulations confirm stability with ≥ 80% scenario retention under stochastic policy shocks. Regional heterogeneity is pronounced: Queensland shows weak responsiveness due to coal lock-in, whereas Tasmania and South Australia respond strongly under moderate incentives. Validation against 2024–25 AEMO outcomes confirms behavioral realism, while CCS deployment remains constrained by commercialization barriers. This paper contributes by: (i) embedding a survey and data-calibrated behavioral layer (WI, MABP) into MILP; (ii) mapping a two-dimensional policy space to identify a robust Synergistic Zone; and (iii) validating behavioral realism against observed investments under evolving Safeguard and CIS policies.

Day-ahead optimization model for renewable energy communities considering load shifting, electric vehicles and vehicle-to-grid technology

Mixed-integer linear programming and constraint programming formulations for solving the three-stage no-wait surgery scheduling problem