Comparison of waste bin placement optimization methods: A case study in Zurich.

• 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.

Spatiotemporal optimization model for minimizing oil spill dispersion and resource allocation.

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 effective integration of cross-domain knowledge remains a significant challenge in the conceptual design stage. While various methods exist to leverage interdisciplinary knowledge, they often face limitations in automatically handling the heterogeneity of knowledge representation (e.g. text, images) and in supporting the automated generation of conceptual solutions. In order to solve the above problems, this study proposes a patent knowledge-driven intelligent conceptual design method. Firstly, starting from the user ‘s needs, the function analysis is carried out to determine the function of the system to be designed; secondly, according to the function of the system to be designed, relevant patents are retrieved, and natural language processing technology is used for intelligent extraction to obtain the source system and its functional information and structural information. Thirdly, the functional information and structural information obtained by the style migration algorithm are migrated as different features, and the migration results are saved for subsequent design. Finally, the computer-aided design scheme is intelligently generated, and the generation scheme is screened according to the Louvain algorithm and the integer linear programming algorithm to obtain the optimal matching path, and the proposed method is verified by the intelligent parking system.

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.

In many application areas, practitioners must make diagnostic decisions under operational constraints. For example, when diagnosing concussion—one of the most common types of traumatic brain injuries—clinicians may assess patients under time constraints imposed by athletic, emergency department, or military settings. Yet, many existing machine learning (ML) techniques fail to account for such operational constraints in the construction of a diagnostic battery. Accordingly, this research proposes a novel approach to generating ML models that enforce operational constraints such as time and interpretability. Motivated by the need to incorporate stochasticity in the time associated with each concussion subtest (i.e., feature), we model this prediction problem as a chance-constrained mixed integer program and propose several reformulations to enhance tractability. We then apply our models to data from the NCAA–DoD CARE Consortium, a large, multi-site study of sports-related concussion among collegiate athletes and military cadets. Compared to diagnostic batteries commonly used in current practice, the concussion diagnosis batteries designed by our methods are both time-efficient (achieving >97% reduction in time needed to administer the battery) and highly accurate (maintaining area under the curve > 0.93). As such, our method can design practically relevant ML models that can be applied broadly across many industries and application areas.

Pseudo-cost based branching is a popular branching strategy used by Mixed Integer Programming (MIP) solvers. This strategy relies on pseudo-cost updates from various parts of the search tree for making accurate branching decisions. Since such updates are not instantly available during a distributed computation, parallel MIP solver implementations that use pseudo-cost branching may not perform well when the underlying cluster is scaled horizontally. To address this issue, we propose integrating a repository of pre-calculated pseudo-costs into a parallel implementation of CPLEX. Although all the facilities needed for such an implementation are currently not available, experiments with hard-to-solve instances indicate that the proposed implementation can help limit the number of nodes explored during the distributed computation.

Edge general position in graphs: Graph products, integer linear programming and some applications

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 novel approach for railway maintenance budgeting using a hybridization of machine learning and integer programming

Expanding volume asymmetry in unary systems via cyclodextrin-based giant molecules

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

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

• Quickest Evacuation Location Problem: a novel optimisation model for concurrent shelter location and evacuation planning • QELP merges Facility Location problems and Quickest Flows on dynamic networks • Multiple objectives minimising evacuation makespan, minimising budget and balancing the utilisation rate of active shelters • A tailored implementation of the robust version of the Augmented epsilon-constraint method is adopted to test the model • An original Matheuristic is designed and implemented and demonstrates high performance on realistic large-scale instances Effective evacuation planning is critical in humanitarian operations to save lives. This paper introduces the Quickest Evacuation Location Problem (QELP), a novel optimisation model that combines the quickest flow problem with discrete facility location to support humanitarian operations. Its scope falls into the field of enhancing evacuation planning and design by identifying, among a finite set of candidates, the set of shelters that would allow the quickest possible evacuation process. To secure flexible and realistic decision support, a multi-objective mixed integer programming model is developed, aiming to minimise the evacuation makespan and the total budget required to install and operate the shelters, while also balancing the utilisation rate of activated shelters. The Robust Augmented ε -constraint method is adopted as a solution scheme, and it is successfully combined with an original Matheuristic approach to boost its performance while approximating the Pareto Set on increasing-size networks. Despite the complexity of time-expanded networks, experiments on realistic instances demonstrate scalable performance and clear trade-offs among the three objectives, confirming the suitability of the QELP in providing decision-makers with valuable support for real-world planning processes in humanitarian operations.

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.

For the past few years, pharmaceutical logistics has undergone significant changes, especially in the period referred to as the post-pandemic era, which brought major transformations to healthcare systems around the world. This research provides a novel model to enhance pharmaceutical supply chain services by routing, locating, and allocating urgent and non-urgent patients to home delivery services or automated medicine lockers. Two scenarios are proposed, with one scenario considering two types of vehicles and creating different routes to deliver medicine to automated medicine lockers or patients, and the other not distinguishing between them. The proposed mixed integer linear programming model uses a three-objective for the green open vehicle routing problem to identify the routing total costs, greenhouse gas emissions under varying speed levels due to risk of traffic congestion, and patient satisfaction. The concept of triage is also embedded into the model to prevent assigning the urgent patients to automated medicine lockers as much as possible. The problem is solved using an improved non-dominated sorting genetic algorithm-II and the LP-metric method, verified through real-world applications. Although experimental studies justify applying automated medicine lockers to cut costs significantly, 14.74% for the first scenario and 13.511% for the second, the resulted model also highlights its application to optimizing home healthcare performance. It is achieved by including greenhouse gas emissions and patient satisfaction within the framework and utilizing automated medicine lockers for pharmacy supply chain services improvement.

Urban waste generation is increasing worldwide at a dramatic pace, making it crucial to develop efficient, cost-effective, and environmentally responsible waste management systems for fast-growing urban areas. This paper addresses a bi-objective facility location problem arising from the real-world waste industry, in which different classes of recyclable urban waste must be collected from sources and delivered to treatment or disposal facilities. The decisions are the number and location of the new intermediate transfer facilities to be opened and the optimal waste flow across the network. The goals are the minimization of the total costs and the CO2 emissions. We present a single-period mixed integer linear programming model and then extend it to a multi-period setting, which better reflects the dynamics of waste production with seasonal fluctuations and generalize to further applications. We apply an ϵ -constraint algorithm to solve our models on two real-world case studies, obtaining approximated-but-well-structured Pareto sets of non-dominated solutions with 25% reduction of emissions with respect to the current state. The efficacy of the models is confirmed by further computational experiments on randomly created instances, showing that the models can be employed for analogous applications.

Interactive optimisation (IO) combines the analytical power of optimisation frameworks with human’s contextual expertise. However, prior IO approaches require human users to repeatedly provide the same type of input or directly modify the model to incorporate different information. As a result, IO frameworks elicit a narrow range of human knowledge or require substantial optimisation expertise from users. To address these limitations, an IO framework is proposed that allows human users to respond to multiple types of queries. The framework aims to produce higher-fidelity stochastic multi-objective mixed-integer linear programming models. It employs targeted questions to elicit specific information from users, a Monte Carlo-based framework to transform human responses into input data for a scenario-based optimisation model formulation, and uses a Conditional Value at Risk (CVaR) formulation to balance expected performance with risk tolerances. Computational experiments on a supplier selection problem demonstrate that this framework can narrow the reality gap and converge towards the ground-truth solution. Moreover, it dynamically adapts to user feedback, and when the human expresses insufficient confidence in the solution’s performance, it can recommend solutions with narrower performance confidence intervals.

Patient transportation within departments (i.e., Intra-Hospital) by hospital transporters involves frequent operations, and their outcomes impact multiple stakeholders. Stakeholders include patients, healthcare and medical professionals, and hospital managers. Hospital managers in the transportation department coordinate patient transport tasks. Each hospital has specific requirements and complies with regulations (e.g., Labor and Data Protection). Uncertain situations (i.e., task delays, new tasks, or task cancellations) affect multiple stakeholders and service quality. Thus, route planning for Intra-Hospital Patient Transport is complex, multi-objective, and non-continuous, which ensures fair workload distribution for high-quality service. The objectives are to optimize the number of transporters and the parameters (i.e., travel and idle times and their statistical measures) for efficient route plans with maximal operational flow on each shift. Our work employs multimodal methods (i.e., a combination of metaheuristics and Discrete Event Simulation) with perceptible strategies (i.e., Mixed Integer Programming and scoring strategy) to improve automated route plans. Our methods account for uncertainties and practical characteristics derived from retrospective data. Our empirical study compares the performance of multimodal methods across different data sets extracted from one-month retrospective data provided by the hospital. The empirical results show that Discrete Event Simulation provides 45% - 65% computationally fast solutions. Thus, multimodal optimization methods guided by our perceptible strategies build statistical models for each data set, considering multiple objectives to support hospital managers by automating efficient route plans.