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.

Kidney exchange is a transplant modality that has provided new opportunities for living kidney donation in many countries around the world since 1991. It has been extensively studied from an Operational Research (OR) perspective since 2004. This article provides a comprehensive literature survey on OR approaches to fundamental computational problems associated with kidney exchange over the last two decades. We also summarise the key integer linear programming (ILP) models for kidney exchange, showing how to model optimisation problems involving only cycles and chains separately. This allows new combined ILP models, not previously presented, to be obtained by amalgamating cycle and chain models. We present a comprehensive empirical evaluation involving all combined models from this paper in addition to bespoke software packages from the literature involving advanced techniques. This focuses primarily on computation times for 49 methods applied to 4,320 problem instances of varying sizes that reflect the characteristics of real kidney exchange datasets, corresponding to over 200,000 algorithm executions. We have made our implementations of all cycle and chain models described in this paper, together with all instances used for the experiments, and a web application to visualise our experimental results, publicly available.

A day ahead scheduling model of a smart hydrogen-based microgrid taking into account PV production and electrical load demand forecasting errors

Enhancing pallet load stability: A MILP model for the Manufacturer’s Pallet Loading Problem with interlocking constraints

Mixed-integer linear programming models for 3D irregular strip packing problems

This paper presents an Integer Linear Programming (ILP) model to construct a weekly lecture timetable for the Mathematics Study Program at HKBP Nommensen University, Pematangsiantar. The case study comprises 25 courses, three rooms (RK~11, RK~12, and LAB~1), five teaching days (Monday--Friday), and 13 time periods per day. The model enforces hard constraints on room, lecturer, and cohort non-overlap; consecutive periods according to credit load; room-type compatibility between theory and practicum sessions; and an institutional worship-time restriction on Tuesday. Lecturers' availability is represented by a binary acceptance matrix collected at the course level, and rejected time periods are penalized in the objective. The ILP is implemented in Python using the PuLP (Python Linear Programming) library and solved with the CBC (Coin-or Branch and Cut) solver. For the real instance, the solver returns an optimal solution with objective value $Z^*=0$ (no scheduled period falls in a rejected slot) in approximately 94 seconds. The resulting timetable is conflict-free and operationally interpretable, with a weekly room-time utilization of about 31.3\%. To support verification and communication to stakeholders, the paper also provides a heatmap of the acceptance matrix and a graphical timetable by room and day.

ABSTRACT Annually, large amounts of citrus waste are generated across supply chains. This waste yields minimal profit and improper disposal can cause environmental pollution, highlighting the need for improved citrus supply chain design. In recent years, the circular economy has emerged as a preferable alternative to linear models, while green productivity aims to enhance both economic and environmental performance. Accordingly, this study develops a novel bi-objective mixed-integer linear programming (MILP) model for a citrus supply chain. The first objective maximizes total profit, and the second maximizes green productivity. Citrus waste is converted into bioethanol, biogas, bio-oil, and biochar in biorefineries using biochemical and thermochemical technologies. The epsilon-constraint method generates Pareto-optimal solutions, which are ranked using the EDAS method. The model is validated through a real case study in Mazandaran province, Iran, and further assessed via sensitivity analyses. Results show that establishing biorefineries under economic and environmental considerations is feasible, achieving zero citrus waste by converting all waste into valuable bio-products. Additionally, green productivity increases by 36% with only a 1.7% reduction in supply chain profit.

The model considered in this study is a multi-objective linear programming (MOLP) model under uncertainty, in which the coefficients of the objective functions are represented by q-rung orthopair fuzzy numbers (q-ROFNs), while the right-hand side constraint parameters are treated as probabilistic quantities. The random variables are assumed to follow known probability distributions and are characterized by specified means and variances. By employing an appropriate score function and considering several probability distributions, namely Gamma, log-normal, and exponential distributions, the initial probabilistic q-rung orthopair fuzzy (q-ROF) MOLP problem is transformed into an equivalent deterministic MOLP model. The Zimmermann methodology with linear membership degrees (MDs) is then applied to represent the preferences of the decision-maker and obtain a satisfactory compromise solution. A numerical example is provided to demonstrate the applicability and efficiency of the proposed methodology. The study concludes with final observations and suggestions for future research.

ABSTRACT The Flexible and Interactive Tradeoff Elicitation (FITradeoff) method is a Multi‐Attribute Decision‐Making (MADM) approach designed to capture the preferences of a Decision Maker (DM) while minimising cognitive effort. To reduce the frequency of interactions and optimise the preference elicitation process, this paper introduces an innovative FITradeoff method integrated with Stochastic Multi‐Attribute Acceptability Analysis‐2 (SMAA‐2). The proposed method follows six steps: (1) It identifies the central weight vectors of each potentially optimal alternative obtained through SMAA‐2. (2) It formulates pairwise tradeoffs based on their ratios and selects the most informative ones based on their probability of identifying potentially optimal alternatives. (3) It selects the most informative pairwise tradeoff and its ratio based on the minimum number of potentially optimal alternatives. (4) It engages the DM to express a preference relation. (5) It constructs an updated weight space with the identified pairwise tradeoff constraint and iterates the previous steps until an optimal alternative is identified. (6) A Genetic Algorithm‐based Linear Programming (GA‐based LP) model is developed to evaluate the robustness and efficiency of our approach. To prove the feasibility and validate the effectiveness of the proposed approach, a case study on the selection of Battery Energy Storage Systems (BESS) is conducted. Additionally, a comparative analysis with the traditional FITradeoff method is included; the results demonstrate that the proposed method identifies the optimal solution while reducing the DM's cognitive burden, highlighting its potential to improve decision‐making processes.

ABSTRACT Assembly planning is a critical stage in manufacturing, accounting for up to 40–60% of production time and over 20% of costs. Although most studies on matrix-structure assembly systems focus on minimizing automated guided vehicle (AGV) trajectories, far less attention has been devoted to workstation utilization and task sequencing, both of which are essential for system profitability. This paper addresses the scheduling problem in robotic matrix-structure assembly systems (RMSAS) for multi-model production, where sequencing, task assignment, and workstation efficiency are strongly interdependent. Three approaches are evaluated: a Mixed-Integer Linear Programming (MILP) model, a math-heuristic (M-H) formulation, and a dispatching rule based on longest remaining processing time (LRPT). Results indicate that MILP guarantees optimality but suffers from scalability issues due to the NP-hard nature of the problem, while remaining a valuable benchmark. The M-H formulation achieves near-optimal solutions in a practical amount of time, significantly reducing computational effort. LRPT offers rapid scheduling but results in lower utilization and longer makespan. Overall, the M-H formulation stands out as a practical and efficient approach, advancing RMSAS scheduling beyond AGV path minimization toward enhanced workstation performance.

This paper proposes a customer-focused resilience enhancement planning framework in power distribution systems considering a leader-follower approach under appropriate regulatory mechanisms. The regulator, distribution system operator (DSO), and customers are the key players in this framework, implemented through a three-step process. Firstly, the regulator establishes a penalty-reward model (PRM). Subsequently, the revenue-cap regulation is applied, and finally, customers' participation is incorporated through a leader-follower approach, modeled using a bi-level optimization problem. This approach considers the individual objectives of the DSO (as the leader) and interested customers to invest in self-generation (as followers), reflecting the accuracy, realism, and practicality of this framework since each entity looks for optimizing its own objective. Furthermore, the incentives provided by the DSO for customers' participation are directly modeled into the objectives of both the leader and followers. The proposed stochastic bi-level optimization problem, which takes the form of a mixed-integer linear programming (MILP) model, is solved using a reformulation and decomposition technique based on the column-and-constraint generation. Deploying the IEEE 33-bus test system exposed to a hurricane, the capability of the proposed framework is validated in enhancing the energy supply resilience under the regulatory objectives while achieving economic benefits for all involved entities.

• We proposed a novel NFV model that balances cost, workload, and resource use. • We modeled server reliability to guide VNF placement and reduce congestion. • We linearized the non-convex MINLP using dynamic programming for scalability. • We developed a cutting-plane heuristic to accelerate convergence. • We validated our approach on real topologies, outperforming baseline solutions. This paper introduces a novel optimization framework for Network Functions Virtualization (NFV) that addresses the efficient implementation of end-to-end service requests in physical networks. Our approach characterizes each server node by a reliability function reflecting its computational load, which aids in balancing workloads and mitigating congestion. By optimizing the reliability metric along the route, our approach ensures robust end-to-end service quality. We formulate the NFV deployment problem as a non-convex mixed-integer non-linear programming (MINLP) model aimed at minimizing both deployment and operational costs while maximizing resource utilization, addressing also per-node installation conflicts and inter-VNF incompatibilies. Given the NP-hard nature of the problem, we develop efficient linearization techniques and bounding schemes, using also dynamic programming, to convert the formulation into a tractable mixed-integer linear programming (MILP) model. Additionally, a cutting-plane-based heuristic with a warm-start strategy is proposed to further accelerate convergence. Experimental evaluations on real-world network topologies demonstrate that our framework offers scalable and cost-effective solutions compared to existing approaches.

Spatial optimization of the sustainable aviation fuel supply chains from forest residues via fast pyrolysis/hydrotreatment considering feedstock ash content variability

Convex hull pricing (CHP) is a pivotal approach to enhance market transparency by minimizing uplift costs. This pa per revisits the mathematical foundation of CHP and provides an explicit formulation of the Lagrangian dual formulation for network-constrained unit commitment (NCUC), further defining the CHP. Here, a convex hull model for single-unit commitment (1UC) problems is established with ramping constraints and minimum on/off time, making this explicit formulation implementable and further delivering the optimal Lagrangian dual solution via two linear programming (LP) models. The first LP reformulates the NCUC by replacing mixed-integer constraints with convex hull relaxations, while the second, obtained by fixing the inner variables in the Lagrangian dual problem of the NCUC to their optimal val ues from the first LP, generates the optimal Lagrangian dual solution. Numerical experiments on the IEEE-118 and Polish-2383 sys tems validate the superiority of CHP in reducing uplift costs and of this proposed pricing method in computational efficiency.

An iterative MILP-based model for optimal V2G scheduling considering battery degradation and thermal dynamics

Hydrogen as a seasonal storage technology to enable Net-Zero Victoria, Australia

Formulating mathematical models from real-world decision problems is a core task in Operations Research, yet it typically requires considerable human expertise and effort, limiting practical application. Recent advances in large language models (LLMs) have sparked interest in automating this process from natural language descriptions. However, challenges including limited modelling expertise, dependence on large-scale training data, and hallucination affect the reliable application of LLMs in optimisation modelling. To address these challenges, we propose SMILO, an expert-knowledge-driven framework that integrates optimisation modelling expertise with LLMs to generate mixed-integer linear programming models. SMILO uses a three-stage architecture built on reusable modelling graphs and associated resources: identifying relevant modelling components, extracting instance-specific information using LLMs, and constructing models through expert-defined templates. This modular architecture separates information extraction from formula generation, enhancing modelling accuracy, transparency, and reproducibility. We demonstrate the implementation of our problem-type-specific modelling framework using workforce scheduling problems spanning manufacturing, logistics, and service operations as illustrative cases. Experiments show that SMILO consistently generates correct models in 93.33% of test instances across five trials, outperforming the baselines by at least 40%. This work offers a generalisable paradigm for integrating LLMs with expert knowledge across diverse decision-making contexts, advancing automation in optimisation modelling.

As global shipping expands, Automated Container Terminals (ACTs) are vital for port competitiveness. However, modern three-stage yard layouts often suffer from spatio-temporal conflicts between dual yard cranes during relay operations, while uncoordinated container placement causes localized overloads and safety hazards. To address these issues, this study proposes a multi-objective mixed-integer linear programming (MILP) model integrating three-stage operations with spatio-temporal mutual exclusion constraints. The model minimizes makespan, external truck waiting time, and inventory disparities across landside bays. To solve this NP-hard problem, an Improved Octopus Optimization Algorithm (IOOA) is developed, featuring discrete space mapping, Euclidean-based state determination, integer flight steps, and local fine-tuning. Numerical experiments demonstrate that this approach significantly reduces the total makespan and truck waiting times while ensuring a highly uniform container distribution across bays. Ultimately, this study mitigates safety risks associated with space overloads and isolated stack collapses, providing a robust decision-making framework to enhance the efficiency and safety of next-generation ACTs.

Mapping cells to spatial locations is crucial for understanding biological processes, disease mechanisms, and therapeutic strategies. However, dropout events in both spatial transcriptomics and scRNA-seq data, along with intercellular interactions and spatial dependencies among spots, challenge the accuracy of spatial mapping. This study proposes a novel method termed Spatial Mapping of single cells via Correlation and Importance between cells and spots (SM-CI). We introduce dropout handling strategies specifically designed for both spatial transcriptomics and scRNA-seq data. Imputation index sets and dropout imputation functions tailored to each data type are developed: the first effectively utilizes spatial location and gene expression information, while the second leverages data from neighboring cell types. Furthermore, we establish criteria for assessing the importance of spots (or cells) in relation to others and construct a linear programming model that integrates these criteria with correlation measures to enhance spatial mapping accuracy. Benchmarking on simulated datasets shows that SM-CI consistently outperforms existing methods across four metrics, while applications to real datasets demonstrate its effectiveness in reconstructing spatial distributions of diverse cell types across tissues. Additionally, ablation experiments validate the effectiveness of the dropout handling strategies and importance assessment criteria.

Subject to the risk of disruptions in high-speed rail (HSR) logistics networks caused by natural disasters or equipment failures, this study proposes an emergency scheduling optimization framework based on truck transshipment. By establishing a Mixed-Integer Linear Programming (MILP) model that integrates vehicle deployment point selection, route planning, and timeliness constraints, it achieves, for the first time, multi-level collaborative decision-making covering "vehicle deployment point selection - truck scheduling - goods transshipment" following an HSR logistics disruption. An Adaptive Large Neighborhood Search (ALNS) algorithm is designed, incorporating a dynamic strategy combining destroy operators (random/worst/Shaw/depot consolidation removal) and repair operators (greedy/regret-2/regret-3 insertion) to generate high-quality scheduling schemes. Using both the Zhengzhou-Qingdao Express Rail Line disruption case and multi-scale random instances, the model's effectiveness is validated: ALNS achieves solution quality comparable to CPLEX with a maximum gap of only 0.037% while substantially reducing computation time, and significantly outperforms GA in both solution quality and efficiency.