Operations Research Research Articles

Transparency of combinatorial optimisations via machine learning and explainable AI

Abstract In this golden age of artificial intelligence, transparency and responsible decision-making are paramount. While machine learning (ML) and operational research (OR) optimisations are fundamental aspects of AI, the benefits of explainable AI (XAI) for combinatorial optimisations remain underexplored. This study investigates the convergence of XAI and OR, emphasising the importance of transparency in combinatorial optimisations. Using the Knapsack problem as an example, we demonstrate that interpretable ML models can effectively solve combinatorial optimisation challenges and enhance transparency. Additionally, we illustrate the application of post-hoc XAI methods to OR optimisations solved with ML, providing transparent, human-friendly explanations. The key contributions of this work include proposing the application of the SAGE framework for transparent OR, demonstrating the integration of XAI with combinatorial optimisations, and offering practical guidelines for creating transparent explanations. These contributions can aid decision-makers in understanding, communicating, and trusting combinatorial optimisation solutions, paving the way for enhanced transparency in operational research across various sectors.

Operations research in perioperative clinical decision-making.

Operations research in perioperative clinical decision-making.

Comparison of Virtual and In-Person ATS Methods in Epidemiologic, Clinical, and Operations Research Programs.

Background: The Methods in Epidemiologic, Clinical, and Operations Research (MECOR) program of the American Thoracic Society aims to strengthen research capacity in low- and middle-income countries. Objective: To compare the impact of online versus in-person MECOR level 1 and level 2 courses in Türkiye on program and research project completion rates and to understand student preferences for alternative program delivery. Methods: We enrolled all students who participated in MECOR Türkiye level 1 courses from 2020 to 2023. Through an online questionnaire, we collected information on progress of the research project developed at MECOR levels 1 and 2 and the students' progression through the end of the program. Research project progression (from design to data analysis) and three-level MECOR course completion was compared between the delivery methods, and student preference of online versus in-person courses was evaluated. Results: Sixty-five students attended MECOR course level 1 from 2020 to 2023, among whom 61 responded to the questionnaire. For the level 1 course, there was no statistical difference in completion rates of research projects in online versus in-person courses (P = 0.22). The preference for online teaching was higher (40%) among those who attended the online offering than among those who attended the in-person course (9.8%; P = 0.005). Forty students attended a MECOR level 2 course; numerically more students (87.5%) who attended an in-person course were at a data collection/analysis stage of their research project compared with the online students (56.3%; P = 0.10). At level 2, 12 students (37.5%) who attended online and 4 (50%) who attended in person also completed level 3 (P = 0.56). There was no significant difference between the groups who took level 2 in person versus online in preference of course format (78.1% and 87.5% preferred in-person level 2, respectively; P = 0.86). Conclusion: Completion rates of research projects planned during the course and the overall program completion were not significantly affected by the virtual or in-person nature of the level 1 or level 2 MECOR courses, and the students' preferences for virtual courses vary depending on their own experience.

Distributionally robust optimization

Distributionally robust optimization (DRO) studies decision problems under uncertainty where the probability distribution governing the uncertain problem parameters is itself uncertain. A key component of any DRO model is its ambiguity set, that is, a family of probability distributions consistent with any available structural or statistical information. DRO seeks decisions that perform best under the worst distribution in the ambiguity set. This worst case criterion is supported by findings in psychology and neuroscience, which indicate that many decision-makers have a low tolerance for distributional ambiguity. DRO is rooted in statistics, operations research and control theory, and recent research has uncovered its deep connections to regularization techniques and adversarial training in machine learning. This survey presents the key findings of the field in a unified and self-contained manner.

Network- and Demand-Driven Initialization Strategy for Enhanced Heuristic in Uncapacitated Facility Location Problem

As network scale and demand rise, the Uncapacitated Facility Location Problem (UFLP), a classical NP-hard problem widely studied in operations research, becomes increasingly challenging for traditional methods confined to formulation, construction, and benchmarking. This work generalizes the UFLP to network setting in light of demand intensity and network topology. A new initialization technique called Network- and Demand-Weighted Roulette Wheel Initialization (NDWRWI) has been introduced and proved to be a competitive alternative to random (RI) and greedy initializations (GI). Experiments were carried out based on the TRB dataset and compared eight state-of-the-art methods. For instance, in the ultra-large-scale Gold Coast network, the NDWRWI-based Neighborhood Search (NS) achieved a competitive optimal total cost (9,372,502), closely comparable to the best-performing baseline (RI-based: 9,189,353), while delivering superior clustering quality (Silhouette: 0.3859 vs. 0.3833 and 0.3752 for RI- and GI-based NS, respectively) and reducing computational time by nearly an order of magnitude relative to the GI-based baseline. Similarly, NDWRWI-based Variable Neighborhood Search (VNS) improved upon RI-based baseline by reducing the overall cost by approximately 3.67%, increasing clustering quality and achieving a 27% faster runtime. It is found that NDWRWI prioritizes high-demand and centrally located nodes, fostering high-quality initial solutions and robust performance across large-scale and heterogeneous networks.

Optimizing Resource Allocation with the Hungarian Method

This study explores the assignment problem, a critical optimization challenge in operations research, which focuses on the optimal allocation of tasks to agents to minimize costs or maximize efficiency. As businesses face increasingly complex operational demands, effective resource management becomes essential. The study begins with an overview of the characteristics and significance of the assignment problem, followed by a detailed mathematical formulation that includes decision variables, objective functions, and constraints. The Hungarian Method is presented as a systematic approach to solving the assignment problem. It is illustrated through practical examples demonstrating its applicability in real-world scenarios such as workforce allocation and logistics. The results confirm the method's effectiveness in achieving optimal assignments while minimizing costs. This study underscores the importance of mathematical modeling in operations research and its potential to enhance decision-making processes across various industries, ensuring efficient resource utilization and improved operational performance.

Optimized Assignments for Real-World Problems: Insights from E-Hailing and Healthcare

The assignment problem in operations research is a method to assign a set of agents for a set of tasks to minimize cost or maximize profit. The method proves to be beneficial in various industries and has been used extensively, including in the development of e-hailing mobile applications. In this research, a real-life example application of an assignment problem using the Hungarian method was used to solve the assignment of e-hailing drivers to customers and patients to beds in the healthcare industry. The Hungarian method calculation was also checked with Excel Solver to find the objective function, subject to well-defined constraints. The result of this study shows the optimized matchmaking of the shortest distance between the e-hailing driver and the customer. Another example, minimizing the cost of total expense in assigning patients to specific beds in a hospital. This study also highlighted findings by other researchers using the assignment problem method could be used as a foundation to develop a new heuristics-based method, especially in healthcare management.

CYBERPHYSICAL SYSTEMS FOR ENVIRONMENTAL MONITORING: CONCEPTUAL FOUNDATIONS FOR CRITICAL INFRASTRUCTURE PROTECTION UNDER WARTIME CONDITIONS

This paper theoretically substantiates the concept of building distributed environmental monitoring systems for water resources, taking into account modern corporate cybersecurity challenges in the context of the Russian-Ukrainian war and related threats to critical infrastructure. The evolution of cyber threat vectors for IoT infrastructure for environmental purposes under hybrid warfare conditions is analyzed, and a theoretical model of multi-level protection based on the synergy of distributed ledger technologies, adaptive machine learning algorithms, and post-quantum cryptographic protocols is proposed. A conceptual system architecture is developed that takes into account the specifics of functioning under martial law and potential state-level cyberattacks, including international-level backup in NATO countries, national-level distributed data centers, and regional-level enhanced autonomy. Special attention is paid to system survivability under conditions of physical infrastructure destruction and graceful degradation of functionality while maintaining critical monitoring operations even with the loss of up to 70% of components. A mathematical model of a cyber-physical system based on operations research theory is proposed, which allows optimizing the distribution of security resources under conditions of multi-criteria uncertainty, taking into account the military risk multiplier and system adaptability functions. Metrics for evaluating the effectiveness of war-adapted architecture compared to traditional approaches are developed, including indicators of cyber threat resilience, energy efficiency, post-attack recovery speed, and operational autonomy. The system provides resistance to electromagnetic pulses up to 50 kV/m and supports federated learning for IoT in the concept of "guerrilla" machine learning under unstable communications. The practical significance of the research lies in the possibility of using the proposed solutions to modernize existing water management industry systems in Ukraine, taking into account the military context and prospects for post-war critical infrastructure recovery, as well as adaptation for other critical infrastructure sectors, including energy, transport, and telecommunications.

APLICAÇÃO DA TEORIA DAS FILAS EM UMA EMPRESA DE FAST FOOD LOCALIZADA EM BELÉM DO PARÁ

Queues are very common and are part of people's daily lives. However, not all organizations are concerned about their generation in their systems. When they are not studied and planned, they become a major problem for companies, since they can be responsible for customer dissatisfaction and, consequently, generate losses. With that in mind, this article aims to describe, characterize and analyze the behavior of the queue system of a multinational company located in Belém - Pará, using concepts from Operational Research. To this end, the Queue Theory method was applied to evaluate the frequency of arrival, per minute, of people in a queue for two attendants, and the service time. After the study, it was noted that the queue was extremely congested with the number of attendants available at the time, with a high occupancy rate (94%) and generating queues with a relatively long waiting time. Subsequently, scenario simulations were carried out for better evaluation and decision-making. From this, it was inferred that it is necessary to increase the number of attendants in a unit so that waiting times decrease and the system operates more smoothly, so that the customer has a good experience and is satisfied with the service.

Challenges in sustaining the elimination of visceral leishmaniasis in India.

The South East Asian initiative for elimination of kala-azar from the Indian subcontinent that began in 2005 is coming to fruition, with India in the last mile of elimination. This aptly timed commentary based on the publication of Pandey et al. (2025) entitled 'Kala-azar elimination in India: reflections on success and sustainability' highlights the complementarity of political commitment that ensured socioeconomic development, along with evidence-based operational research, that needs to be sustained for zero transmission to become a reality.

Bayesian DEA framework for market power and efficiency analysis in banking operations

Abstract The accurate measurement of marginal costs and market power is a persistent challenge in production economics and operations research, particularly within the banking sector. This study addresses this problem by proposing a Bayesian likelihood-based approach to estimate the Lerner index under multiple inputs and outputs, extending the nonparametric Data Envelopment Analysis methods of Fukuyama and Tan (J Oper Res Soc 73:445–453, 2022a) with statistical inference. Using data from 36 Chinese banks (2011–2018), the results reveal that market power in loans is generally higher and more stable compared to securities, with significant variations across different bank ownership types. For instance, city banks demonstrate the highest market power in loans, while state-owned banks exhibit the lowest. Efficiency analysis indicates volatility across all bank types, with no clear efficiency patterns. These findings have critical policy implications, emphasizing the need for targeted strategies to enhance market power and efficiency sustainably. For example, rural, city, and joint-stock banks should focus on staff development in non-traditional banking, while state-owned banks could benefit from operational cost reductions. The proposed methodology also provides a robust framework for future studies on market power and efficiency in diverse industries.

Report from the 42nd National Scientifc Conference named after him. Professor Władysław Bukietyński Methods and Applications of Operations Research MZBO

Report from the 42nd National Scientifc Conference named after him. Professor Władysław Bukietyński Methods and Applications of Operations Research MZBO

Exposing gender bias in the mathematics and operational research professions

Exposing gender bias in the mathematics and operational research professions

A Comparative Analysis of Inventory Models: Evaluating the Economic Order Quantity (EOQ) Model with Constant Demand versus Variable Demand Rates

Inventory control management remains a cornerstone of operational efficiency in modern supply chain systems. This study explores the Economic Order Quantity (EOQ) model, a foundational inventory control technique, by comparing its application under two distinct demand scenarios: constant and variable demand rates. This research highlights how demand variability influences optimal order quantities, total inventory costs, and decision-making processes through a detailed theoretical framework, mathematical analysis, and practical implications. From recent literature in operations research and supply chain management, the article provides insights into the adaptability of the EOQ model across diverse demand conditions, offering a comprehensive guide for practitioners and researchers alike.

Newborn and Child Health Services in Urban India: Challenges and the Way Forward

Abstract This article systematically reviewed urban health services for newborns and children using data from various published research work, databases, government portals and relevant websites. The available evidence suggests that the delivery of optimal child healthcare services in urban India remains challenging due to fragmented and weak public healthcare systems, limited capacity of administration for optimal planning, and heterogeneous accessibility for quality health care, compounded by growing pockets of poverty and inappropriate health-seeking behavior. Although newborn and child health continued to be a focus, there is a need for bringing specificity in the work and on areas such as brain development in early years, early childhood development, health of 6–17 years of age, tackling the rising challenge of obesity in children and adolescents. The school-based and community-supported interventions need to be expanded in these areas. The ongoing primary healthcare reforms should be optimally harmonized for improving urban health. Contextual operational research, partnering with professional bodies, building capacities, and monitoring mechanisms are required to achieve the desired outcomes.

Algorithmic Challenges in Ensuring Fairness at the Time of Decision

Greater Price Stability Without Sacrificing Optimal Revenue Guarantees In today’s digital marketplaces, sellers often rely on dynamic pricing—changing prices frequently—to optimize revenue. However, frequent price changes can undermine customer trust. In a new study published in Operations Research, researchers from the U.S. Naval Academy, MIT Sloan, and the University of Illinois at Chicago demonstrate that it is possible to restrict price changes to only decrease over time—through strategic markdowns—while still achieving strong performance guarantees. Their research shows that optimizing pricing trajectories, even under monotonicity constraints, does not compromise optimal regret guarantees for maximizing revenue. This finding challenges the prevailing assumption that taming price experimentation may hinder success. The work opens new avenues for how online platforms can rethink pricing strategies to foster consumer loyalty without sacrificing profitability.

Design of the vertical trajectory for arrival and departure routes at Prague airport

Numerous operational methods and related research focus on the efficient use of controlled airspace and thus on the management of its capacity. During the optimisation processes, various legislative limitations or technological constraints might appear. As the aviation industry continues to evolve, it occasionally happens that one of these pillars lags behind the other. This research focuses on a relatively underexplored aspect of using vertical profiles of air traffic service routes within the TMA Praha to optimise traffic flow in terms of flight efficiency and environmental impact.Virtual points, defining the aircraft’s vertical position limits along the given route, were computed to establish a vertical profile on already published standard departure or arrival routes. These points define the aircraft’s vertical position limits along the given route. Along with the proposal of a vertical profile, newly designed arrival and departure routes were implemented into the air traffic control simulation tool Escape Light and validated simultaneously within X-Plane simulator. Simulation studies conducted in these environments demonstrated significant fuel savings, averaging 13.2 %, with even greater savings observed in the Boeing 737-800, exceeding 25 %. These results confirm that applying vertical profiles positively impacts fuel consumption and contributes to more environmentally friendly operations.

Treated wastewater reuse practices, under a holistic approach at the city scale

This study examines the sustainable incorporation of treated wastewater into urban water management frameworks, tackling the severe issues of water scarcity in cities that are intensified by rapid urban growth and climate change. The research aligns with Sustainable Development Goal 6 (SDG 6), promoting a comprehensive strategy to guarantee universal access to clean water and sanitation. Through a cohesive management framework, the study presents Priority Objectives (PO) such as improving governance structures, creating green infrastructure, and promoting digitalization in urban environments. These objectives are backed by practical Optimization Objectives (OO) that transform strategic plans into actionable solutions aimed at strengthening urban water resilience. The analysis reveals that the integration of treated wastewater can greatly diminish the need for freshwater, enhance urban resilience and diversify water supply systems. The study underscores the essential role of sophisticated treatment technologies, including membrane bioreactors, reverse osmosis, and advanced oxidation processes, while also highlighting the necessity for adaptive policies that can support and encourage the widespread implementation of these systems. The study also emphasize on the necessity of Operations Research and Management Science (OR/MS) methodologies, like multi-objective optimization, system dynamics modeling and structured decision analysis, to enhance strategic decision-making. These quantitative approaches could enable robust scenario planning, effective resource allocation, and comprehensive performance assessment in urban wastewater reuse systems. Moreover, the core requirements for a suggested pilot action aimed at achieving over 90% efficiency in treated wastewater reuse, is presented. This pilot illustrates the significant potential for improving water resource management, showing how such solutions can be crucial in enhancing urban water security and sustainability.

Recent theoretical and practical contributions to the OR environment and CEJOR from the perspective of SSI-SOR

The article summarizes the research topics published in this special issue. The papers in this issue are based on the selected and peer-reviewed papers from the 17th International Symposium on Operations Research in Slovenia – SOR’23, which took place in Bled, Slovenia (https://arhiv.fov.um.si/sor23/), September 20–22, 2023. In addition, we examined the 27 research papers in the last two SSI-SOR CEJOR special issues, 16 in the Cent Eur J Oper Res 31, issue 3, 2023, and 11 in this CEJOR special issue, and grouped them into clusters using keywords according to the methodology published by Kastrin et al. (2021) Methodologies and applications for resilient global development from the aspect of SDI-SOR. The clusters show the main and niche topics presented and, on the one hand, illustrate the European and international state of the art in the field of OR over the last five years and, on the other hand, can serve as a stimulus for further work on upcoming strategic OR topics.

Solving Traveling Salesman Problem Through Genetic Algorithm with Clustering

The Traveling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem, commonly studied in computer science and operations research. Due to its complexity and broad applicability, various algorithms have been designed and developed from the viewpoint of intelligent search. In this paper, we propose a two-stage method based on the clustering concept integrated with an intelligent search technique. In the first stage, a set of clustering techniques - fuzzy c-means (FCM), k-means (KM), and k-mediods (KMD) - are employed independently to generate feasible routes for the TSP. These routes are then optimized in the second stage using an improved Genetic Algorithm (IGA). Actually, we enhance the traditional Genetic Algorithm (GA) through an advanced selection strategy, a new position-based heuristic crossover, and a supervised mutation mechanism (FIB). This IGA is implemented to the feasible routes generated in the clustering stage to search the optimized route. The overall solution approach results in three distinct pathways: FCM+IGA, KM+IGA, and KMD+IGA. Simulation results with 47 benchmark TSP datasets demonstrate that the proposed FCM+IGA performs better than both KM+IGA and KMD+IGA. Moreover, FCM+IGA outperforms other clustering-based algorithms and several state-of-the-art methods in terms of solution quality.