The purpose of the journal is to present scientific ideas in the area of operational research (OR) that will contribute to theoretical aspect and practical applications of OR. The journal publishes only original scientific papers in that area. The scope of the journal covers the following topics: linear and non-linear programming, integer programing, combinatorial and discrete optimization, multi-objective programming, stohastic models and optimization, scheduling, macroeconomics, economic theory, game theory, statistics and econometrics, marketing and data analysis, information and decision support systems, banking, finance, insurance, environment, energy, health, neural networks and fuzzy systems, control theory, simulation, practical OR and applications. Journal publisher: Croatian Operational Research Society Co-publishers: University of Zagreb, Faculty of Economics & Business J. J. Strossmayer University of Osijek, Faculty of Economics in Osijek University of Split, Faculty of Economics, Business and Tourism J. J. Strossmayer University of Osijek, School of Applied Mathematics and Informatics University of Zagreb, Faculty of Organization and Informatics
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Environmental fiscal policy and greenhouse gas emissions in the EU-27: Evidence from a dynamic panel GMM model
This paper examines the effects of environmental fiscal policy variables on greenhouse gas (GHG) emissions in the EU-27 from 2009 to 2023. The Arellano and Bond difference GMM estimator is used to address potential endogeneity and persistence of GHG emissions. The panel model is estimated using the total GHG emissions as the dependent variable, while energy taxes, transport taxes, and government environmental protection expenditure serve as independent variables. The results indicate significant persistence in GHG emissions. Energy taxes and government environmental protection expenditure have a negative and statistically significant effect on emissions in both the short run and the long run, confirming the effectiveness of these fiscal instruments in reducing emissions. However, transport taxes show a positive and significant relationship with emissions, suggesting that their current structure, which is linked primarily to vehicle ownership rather than fuel consumption, is not effective in reducing emissions. Robustness checks using population as a control variable and CO$_2$ emissions as an alternative dependent variable confirm the stability of these results. The findings suggest that energy taxes and environmental expenditures are effective fiscal instruments for reducing emissions in the EU, while the design of transport taxes requires reconsideration to improve their environmental effectiveness.
Copyright (c) 2026 Croatian Operational Research Review
Mitigating the consequences of disruptions by locating temporary facilities and balancing the redistribution of users
Many service systems are subject to disruptions that can reduce their operational capacity, forcing users to find alternative ways to meet their service needs. One way to mitigate such effects is to locate temporary facilities where users can receive services. Also, users can be served in facilities unaffected by the disruptions. This paper considers the problem of locating temporary facilities after a disruption and redistributing users to minimize the average travel distance. Compared with existing models, the proposed approach allows limited overcapacity and balances it across facilities to ensure a more even redistribution of users. A mathematical formulation of mixed integer programming is proposed and used to determine the locations of temporary facilities and the balanced redistribution plan. The final number of temporary facilities is determined using a TOPSIS method. The proposed approach integrates an exact approach with the TOPSIS method and enables the straightforward addition of new criteria without modifying the mathematical formulation. Testing on small-sized hypothetical examples demonstrates that, without capacity constraints, overcapacity in some facilities can reach 150%, whereas the proposed approach limits it to 45% and balances it so that differences among facilities do not exceed 10%. The results of testing illustrate that the proposed approach effectively solves the multi-objective location and redistribution problem while avoiding computationally intensive methods such as multi-criteria optimization or metaheuristics. The proposed approach provides a flexible and implementable framework that balances system management and user objectives under disruptions.
A discrete-time infinite-server batch arrival queue with application to serverless computing
Serverless computing systems behave like an infinite server queue, dynamically expanding the number of instances to handle incoming batch tasks. In serverless computing, to leverage its scalability, efficiency, and cost-effectiveness, it is essential to apply an infinite server queue with batch task arrival. The model is used to estimate resource usage and to optimize cost-performance trade-offs. This paper analyzes a discrete-time infinite-server batch/single-arrival queue with application to a serverless computing system. We obtain the probability-generating function of the system size, which characterizes a functional equation; we then solve it recursively to find state probabilities at various epochs and some performance measures. Unlike existing discrete-time infinite-server models, this paper explicitly compares the late-arrival system with delayed access and the early-arrival system policies in the context of batch arrivals, and establishes convergence to their continuous-time counterparts. The model's numerical results have been presented in graphs and tables to illustrate the impact of batch-size distributions and system parameters.
Comparative analysis of modern machine learning models for retail sales forecasting
Accurate demand forecasting is critical for brick-and-mortar retailers to optimize inventory management and minimize costs. This study evaluates statistical baselines, tree-based ensembles (XGBoost and LightGBM), and deep learning architectures (N-BEATS, N-HiTS, and the Temporal Fusion Transformer) on retail sales data characterized by intermittent demand, substantial missingness, and frequent product turnover. Models are compared across four configurations varying by aggregation level and imputation strategy, using evaluation protocols that reflect typical deployment patterns for each model class. Localized tree-based methods achieve superior performance, with XGBoost attaining the lowest RMSE of 4.833. While SAITS-based imputation improved neural network performance in aggregated settings, these models remained inferior to ensemble methods. The results suggest that, under the studied constraints, model selection should prioritize alignment with problem characteristics over architectural sophistication.
Benchmarking Croatian airports: A data-driven approach through DEA window analysis
This study benchmarks the efficiency of seven certified international airports in Croatia using Data Envelopment Analysis (DEA) with a window framework under variable returns to scale, explicitly addressing the challenge of a small number of decision-making units through dynamic window specification. Efficiency scores were calculated across overlapping three-year periods from 2019-2023, allowing performance dynamics to be captured during both crisis and recovery phases. The results reveal substantial heterogeneity across airports. Osijek Airport emerged as the most consistently efficient, outperforming larger hubs such as Zagreb and Split, while Zadar and Rijeka demonstrated notable efficiency improvements over time. In contrast, Dubrovnik Airport recorded persistently low efficiency despite traffic recovery, suggesting structural cost rigidity and seasonal vulnerability. These findings highlight the operational resilience of smaller regional airports and signal performance constraints among major hubs. By integrating traffic trends with efficiency outcomes, the study shows that rising passenger volumes alone do not ensure improved economic performance. The results provide a timely, evidence-based framework for airport managers and policymakers to enhance strategic planning, improve resource allocation, and strengthen the financial sustainability and competitiveness of Croatia’s air transport sector.
Doubly effective one round election model: Improving efficiency and fiscal savings
Electoral processes are usual in most countries around the world. The most dominant electoral system is the standard Two-Round System (TRS). Despite the variety of models for electing public representatives, all result in public expenditure. In democratic societies, we cannot avoid such an expense, but we can minimize it. Minimizing expenses in line with simplicity and justice of the electoral processes is the primary goal of this paper. We propose an entirely new one-round election model that can replace and successfully simulate the existing two-round model. Our proposed solution is unique, and we have named it the Doubly Effective One Round election model (DEOR election model). The literature contains many similar approaches, such as Ranked Choice Voting (RCV)/Instant-Runoff Voting (IRV), Single Transferable Vote (STV), Approval Voting, or Majority Judgment, but this proposed model is entirely new. As the new model is based on a ranking method, it offers additional advantages and possibilities, which are explained and illustrated through several examples in the paper. In addition to its efficiency, the application of this model can bring significant fiscal savings.
Linking dynamic managerial capabilities and organizational agility: The role of technological innovation
In an era of rapid technological change and increasing environmental uncertainty, organizational agility has become a key driver of firm competitiveness, underscoring the importance of understanding how dynamic managerial capabilities enable agile organizational responses. The current study investigates the relationship between dynamic managerial capabilities and organizational agility, with a particular focus on the mediating role of technological innovation. It employs a quantitative approach, analyzing survey data from SMEs in Vietnam using partial least squares structural equation modeling (PLS-SEM). The findings reveal that dynamic managerial capabilities positively affect organizational agility, and that technological innovation serves as a mediator in this relationship. Managers with strong dynamic capabilities enable firms to enhance their agility through continuous technological advancements. This study contributes to the literature on dynamic managerial capabilities and innovation by empirically validating the role of managerial capabilities in fostering organizational agility through technological innovation. In practice, it provides valuable insights for business leaders on leveraging managerial capabilities and adopting technology to navigate uncertain market conditions effectively.
Can student attitudes toward immigration be changed? Evidence from a survey experiment in Croatia
Extreme right-wing parties are increasing in polls around Europe, largely fueled by an anti-migrant rhetoric. Political economy literature points to, on average, net positive effects that migrants bring to the economy, but the balance on the political market is more worrisome. For a small open economy, overly dependent on tourism, whose population reduced by more than 1 million in the last 30 years, the question of successful integration of migrants represents a first order condition of public policy. Thus the research question set in this paper is how to change attitudes on immigration among students in the Croatian society. Our approach is based on an experiment within a survey and it is tested on a sample of 1,450 students from five university cities in Croatia (Osijek, Pula, Rijeka, Split and Zagreb). Results indicate that there is a sizeable and statistically significant effect for the treated groups vis-a-vis their attitudes on the effect that migrants have on the labour market, social security system, overall safety and the economic development of Croatia.
Country-specific financial distress prediction using decision trees: Empirical evidence from Slovakia and Croatia
This paper develops and compares financial distress (FD) prediction models for Slovak and Croatian firms based on a decision tree (DT) approach. The study aims to identify the crucial financial variables that predict firm FD in these two post-transition economies that share historical and institutional similarities but differ in the structure of the economy. A database of Slovak and Croatian enterprises was analysed, focusing on firms being classified as prosperous or non-prosperous based on standardized accounting parameters from financial reports. DTs were employed since they can model complex, nonlinear relationships without diminishing interpretability. The results indicate that high levels of total indebtedness, equity leverage, and debt-to-equity ratios are cross-sectionally associated with an increased likelihood of FD. In the Slovak context, liquidity, particularly the current ratio, showed greater importance than profitability measures, whereas in Croatia profitability ratios, especially return on assets, gained relatively higher relevance compared to liquidity. The findings close a research gap concerning country-specific differences in Central and Eastern European (CEE) FD predictors. The paper provides theoretical contributions by refining knowledge on insolvency drivers in post-transition economies and practical contributions by understanding tailored early warning systems. The study is limited by sample restrictions and the omission of macroeconomic factors. Future research may incorporate wider contextual determinants and alternative machine learning (ML) approaches.
Multimethod survival analysis for identifying predictors and forecasting mortality in a heart patient cohort study
This study presents a multi-method survival analysis of 125 cardiac patients from IIMCT-Pakistan Railway Hospital in Rawalpindi, Pakistan. Parametric accelerated failure-time modeling identified the Weibull distribution as optimal for describing time-to-event data. Semi-parametric analyses, including Cox proportional hazards and Bayesian Cox regression, consistently identified hypertension, ischemic heart disease, and smoking as significant predictors of elevated mortality risk. Higher systolic blood pressure demonstrated a protective effect. Kaplan-Meier analysis revealed steadily declining survival rates up to 300 days with no significant gender differences. The random survival forest model achieved robust predictive accuracy, identifying ischemic heart disease, smoking, and age as the most influential predictors. Our multi-methodological approach demonstrates the value of integrating parametric, semi-parametric, Bayesian, and machine learning techniques for comprehensive risk assessment in cardiac patient cohorts, offering potential for enhanced clinical risk stratification and personalized prognosis.
Reliability and performance evaluation of retrial repairable systems with an unreliable repairer using the GSPN model
Generalized Stochastic Petri Nets (GSPNs) are widely used in reliability analysis to model and optimize the dependability of complex systems, enabling assessments of availability, failure probabilities, and repair processes through stochastic timing. This study investigates a repairable redundant retrial system incorporating warm and cold standbys and an unreliable repairer through a Generalized Stochastic Petri Nets. The repairer experiences both active (during repair) and passive (idle) breakdowns. Component and repairer lifetimes are exponentially distributed. A component that fails undergoes immediate repair if the repairer is available; otherwise, it enters a retrial FCFS orbit. A Continuous Time Markov Chain (CTMC) derived from the GSPN model yields steady state probabilities and availability. System reliability and time to first failure are then determined via Laplace transforms. Numerical examples demonstrate the system reliability performance.
Comparative assessment of flexible manufacturing systems using the EDAS and Shannon entropy method
As global competition intensifies, most manufacturing companies strive to improve their production methods to gain a competitive edge. One such advancement is the adoption of Flexible Manufacturing Systems (FMS), which enable the efficient production of various products in specified quantities with minimal lead times. These systems offer adaptability and efficiency, allowing manufacturers to leverage modern technologies to improve operational performance. However, evaluating or selecting an appropriate FMS involves considering numerous conflicting criteria. To address this complexity, Multi-criteria Decision Making (MCDM) methods are employed. This study conducts a comparative evaluation of eight FMS alternatives using the Evaluation based on the Distance from the Average Solution (EDAS) method, integrated with Shannon Entropy for objective weight determination. Key performance indicators, including production cost, system flexibility, energy efficiency, and operational reliability, are used in the assessment. The Shannon Entropy method ensures unbiased, data-driven weight assignment, while the EDAS method provides a robust framework for ranking alternatives based on their deviation from an average solution. To test the robustness of the ranking, we compared the ranking with other MCDM methods and also conducted a sensitivity analysis using equal weighting criteria. We found that the first and last rankings remained unchanged when we changed the criteria, although there were slight changes in the rankings of some alternatives. The findings highlight the effectiveness of integrating EDAS with Shannon Entropy in selecting the best flexible manufacturing systems, offering valuable insights for manufacturers and decision-makers.
Data inversion in MCDM problems: nonlinear 1/a and linear ReS inversion
A comprehensive analysis of the procedures for consistent normalization/inversion of benefit and cost attributes for multi-criteria decision making (MCDM) and multivariate classification problems is performed. This study demonstrates that the commonly used 1/a transformation for cost attribute inversion introduces structural inconsistencies in normalized data. Nonlinear data inversion does not have a reasonable interpretation of values and leads to a violation of mutual distances in the original data. The measurement scales of various attributes are not consistent and there is a shift in the domains of normalized values. Elimination of these problems is achieved by using the linear inversion Reverse Sorting algorithm (ReS). The ReS algorithm offers more consistent, linear, and interpretable results for handling cost attributes in MCDM. The ReS algorithm is a linear transformation and preserves the original information about the object: dispositions of attribute values, preserves the relative positions of the domains of different attributes and can be applied to both the original and normalized data sets. The ReS algorithm eliminates all the shortcomings of nonlinear inversion and is recommended for inversion of values when coordinating the optimization goals of a multi-criteria problem, as well as in the weighing methods based on information contained in the decision matrix.
Optimization of the traveling salesman problem through a genetic algorithm guided by self-organizing maps
Optimization is a fundamental process for achieving objectives, exemplified by the Traveling Salesman Problem (TSP), which minimizes resource consumption. This study focuses on optimizing travel routes to reduce fuel costs and maximize tourist visits through efficient time management. We employ a genetic algorithm (GA), a powerful optimization technique, to determine routes. A key challenge in GAs is premature convergence, which can prevent optimal solutions. To address this, we introduce a novel approach integrating Self-Organizing Maps with GAs, specifically through a new selection operator designed to enhance GA performance. An application was developed using real-world coordinates of Pakistani cities. Simulation results demonstrate that our proposed method significantly outperforms existing selection operators in terms of final best distance, average best distance, standard deviation, and computational time. Field validation further confirmed an 18.3% distance reduction and 4.53 million in annual savings in a logistics case study.
Study of novel normalization technique on weighting and ranking methodology in multi criteria decision making: Several cases in financial performance
The evaluation of corporate financial performance typically entails the use of multiple financial ratios characterized by heterogeneous properties, including the potential presence of negative values. Within this context, Multi-Criteria Decision-Making (MCDM) approaches have been extensively employed due to their capacity to systematically integrate diverse evaluation criteria into a coherent and objective ranking framework. However, most conventional normalization techniques in MCDM are not specifically designed to accommodate negative data, thereby potentially resulting in distorted weights and inconsistent ranking outcomes. This study proposes a novel normalization approach, termed the Root Distance Ratio (RDR), which is derived from the Weitendorf principle and formulated through a non-linear root transformation. The effectiveness of the RDR method is evaluated by integrating it into four MCDM techniques PSI, ARAS, MABAC, and EDAS across three corporate financial data scenarios, namely datasets with entirely positive values, negative values within benefit criteria, and negative values within cost criteria. The results demonstrate that, across the evaluated cases, the RDR method produces normalized values within the [0,1] interval, generates more proportionally distributed weights, and yields more consistent ranking outcomes compared to conventional normalization techniques. These findings indicate that RDR enhances both the stability and interpretability of financial data-driven multi-criteria decision-making processes, particularly in the presence of negative values.
Optimizing an imperfect production system with varying production cost under selling price and advertising-driven demand
This study develops a production inventory model that accounts for imperfect production processes, acknowledging that a certain percentage of items produced are defective, reason being labor inefficiencies and machinery malfunctions. These defective items are identified and are segregated during the quality check and inspection phase and sold at a discounted price. The model incorporates economies of scale, whereby production costs decreases as productivity increases, and represents production costs as a diminishing function of productivity. Furthermore, the demand rate is modeled as dependent on advertising frequency and selling price, impacting significantly the product demand. The primary objective of this research is to determine the optimal advertising frequency, selling price, and the production cycle that maximize overall system profit. A numerical illustration is provided to validate the model, and a sensitivity analysis is conducted to assess the stability of the system. The findings reveal that increased demand reduces production time and raises pricing potential that leads to boosting of profits. Higher production rates improve efficiency and lower unit costs, while a higher defect rate and rising holding costs adversely impact profitability, which illustrates the importance of quality control and efficient inventory management. These insights highlight the model's practicality and innovation, offering valuable guidance for optimizing operations, managing costs, and achieving sustainable growth.
Determinants of real estate prices in Croatian counties: spatial panel data analysis
This paper examines the determinants of real estate prices across Croatian counties, taking into account not only economic and demographic factors, but also tourism-related variables. The main focus is on spatial spillover effects, which are based on the assumption that real estate prices in one county are influenced by the developments in neighboring counties. The study covers the period from 2011 to 2019 and confirms that real estate prices are influenced by both local and regional factors. The key determinants include the number of tourist accommodation units, population size, and GDP per capita. An important result is the existence of a statistically significant spatial dependence across all specifications. This indicates that changes in real estate prices extend beyond county boundaries, underscoring the interconnectedness of the real estate market. These results underline the need for using spatial econometric models, which provide a more comprehensive understanding of regional price dynamics by capturing spillover effects between counties.
Copyright (c) 2025 Croatian Operational Research Review
On the identification of a distribution for the arrivals to a queueing system: an application from bank data
Queues are an integral part of life. The literature available concentrates on Poisson arrival and exponential service time. The present paper focuses on statistical inference on the parameters of queueing models. The work is data driven. The dataset considered is the queueing system in banks which is publicly available. The number of servers has been estimated for a steady state system. The data has been tested for normality. The goodness of fit test has been done for the arrival pattern, and it is found that the discrete analog of smallest extreme value distribution is a good fit to the data which is an alternative to the widely used Poisson distribution.
Multidecision criteria models for Logistics Performance Index in the EU countries
Key factors influencing multicriteria logistics performance in the European Union (EU) include the weighting of evaluation criteria, infrastructure efficiency, logistics quality, and environmental impact. The Logistics Performance Index (LPI), which evaluates logistics systems across six dimensions, highlights how the importance assigned to these criteria significantly impacts national rankings. This study aims to enhance the understanding of logistics performance dynamics within Europe, supporting informed decision-making and continuous improvement in the region's logistics sector. To determine country rankings, the study applies the CRiteria Importance Through Intercriteria Correlation (CRITIC) method for weighting criteria, alongside the Measurement of Alternatives and Ranking according to COmpromise Solution (MARCOS), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), and Simple Additive Weighting (SAW) methods. The analysis utilizes LPI indicators from the 2023 World Bank dataset. The results indicate that Finland maintains its leading position in the LPI ranking. However, a significant number of countries experience shifts in their rankings depending on the weight assigned to each criterion, underscoring the sensitivity of logistics performance evaluation to methodological choices.
Management ownership and earnings management: application of matching techniques
This paper investigates the effect of managerial ownership on earnings management for the sample of European listed companies. To estimate the treatment effect of a manager who is also a controlling shareholder on earnings management, entropy balancing (EB), propensity score matching (PSM) and Mahalanobis distance matching (MDM) techniques are employed to identify a control sample. The EB method of reweighting control sample observations is compared to PSM and MDM techniques, as well as to standard ordinary least squares (OLS) regression, while controlling for the effects of company size, profitability, solvency, sales growth, and ownership concentration. The results demonstrate a significant positive relationship between management ownership and earnings management only when using the entropy balancing approach, and an insignificant relationship when applying PSM, MDM and OLS methods.
Customer impatience in the GI/M (k)/1/N queue with working vacation: Economic and performance analysis
This study investigates a GI/M (k)/1/N queueing system with Bernoulli feedback and multiple working vacation policy. The model incorporates customer impatience and accounts for the retention of reneged customers. By employing the supplementary variable technique and recursive methods, we derive the steady-state distributions of the customer count at both pre-arrival and arbitrary epochs. Various system performance measures are analyzed. In addition, an economic evaluation is carried out. Numerical illustrations using R software are provided to confirm the analytical findings and highlight the influence of queueing parameters on performance indicators and system costs.
Inverse cost and revenue efficiency in network processes with uncontrollable inputs
Inverse data envelopment analysis (IDEA) estimates the inputs/outputs of each decision-making unit (DMU) based on the perturbations in the outputs/inputs while maintaining relative efficiency. When the cost of inputs or the price of outputs is available, it is possible to calculate cost, revenue, and profit efficiencies. This study develops an inverse network DEA that includes uncontrollable measures. For this purpose, models are presented for calculating relative, cost, and revenue efficiencies. Then, an algorithm is proposed to estimate the inputs of the first stage, considering unchanged technical and cost efficiencies. Also, an algorithm is presented to estimate the outputs of the second stage, considering unchanged output-oriented technical efficiency and revenue efficiency. Then, the introduced algorithms are applied to a numerical example and a dataset related to salmon farming, obtaining logical results. Finally, the proposed method is compared with one of the existing methods, and their differences are discussed.
Assessing the pure technical efficiency of public primary schools in the City of Zagreb
This paper is the first to assess the pure technical efficiency (PTE) of 111 public primary schools in the City of Zagreb during the 2022/2023 school year, using an input-oriented Data Envelopment Analysis (DEA) – BCC model. PTE was measured using two input variables (expenditures and number of teachers) and three output variables (average grades, number of pupils who passed the class, and secondary school enrolment points). The analysis revealed substantial variation in efficiency scores, with 20% of schools identified as fully efficient. The average efficiency score was 0.90, suggesting that, on average, schools could reduce inputs by 10% while maintaining current output levels. A follow-up super-efficiency DEA model was applied to rank efficient schools and identify best practice examples that could serve as models for others. Based on super-efficiency scores, schools were grouped into five performance categories – best practice, efficient, near-efficient, emerging, and low efficiency. Additional findings suggest that larger schools tend to be more efficient and that benchmarking within peer-size groups can help uncover high-performing schools that might otherwise remain under the radar. The results underscore the importance of context-sensitive efficiency evaluation in education and highlight the need for improved data on school characteristics to support more comprehensive, actionable assessments.
Aspects of blocking on time-varying tandem queueing network
Most real-world service systems are susceptible to queue capacity constraints, leading to a blockage of entities. Several blocking mechanisms can be implemented when capacity constraints influence the flow of entities through the system. This study investigates the comparative performance of blocking-after-service (BAS) and blocking-before-service (BBS) mechanisms by modelling a hospital emergency department with a finite capacity queue. The model is based on a two-station tandem network with finite capacity on the intermediate queue, and we developed transient performance measures for the system in both mechanisms. Using a numerical approach, we highlight how these mechanisms influence the time-varying number of patients and the virtual workload in the system. Our results demonstrate that the BAS mechanism slightly outperforms the BBS mechanism in reducing unwanted congestion.
Numerical methods for checking the stability of gyroscopic systems
Gyroscopic mechanical systems are modeled by the second-order differential equation \begin{equation*}\displaystyle M \ddot x(t) + G\dot x(t) + K x(t) = 0, \end{equation*} where \(M\in\mathbb{R}^{n\times n}\) is a symmetric and positive definite matrix, $G \in\mathbb{R}^{n\times n}$ is a skew-symmetric ($G^T=-G$) matrix, and $K\in\mathbb{R}^{n\times n}$ is a symmetric matrix, representing the mass, gyroscopic, and stiffness matrices, respectively. The stability of such systems, which is the primary topic of this paper, is determined by the properties of the associated quadratic eigenvalue problem (QEP)\begin{equation*} {\mathcal G}(\lambda)x=(\lambda^2M+\lambda G+K)x=0, \quad x\in\mathbb{C}^{n},\ x\not=0. \end{equation*} In this paper, we provide an overview of various linearizations of the QEP and propose numerical methods for checking the stability of gyroscopic systems based on solving the linearized problem. We present examples that demonstrate how the use of numerical methods provides a significantly larger stability region, which cannot be detected using the considered non-spectral criteria, or verify stability in cases where non-spectral criteria are not applicable, highlighting the advantages of numerical methods.
A hybrid approach to approximate the Pareto front of the MOST problem
This study introduces a hybrid NSGA-II algorithm with Multi-VNS for approximating the Pareto front of the multi-objective spanning tree (MOST) problem, building on recent approaches that have adapted NSGA-II combined with local search heuristics. By exploiting the property that a spanning tree is acyclic and that the addition of an edge generates a unique cycle, our mutation operator adds edges to a given spanning tree $T$ of a connected graph $G$, thereby reducing the size of the MOST problem. By applying the exact mutation operator with low probability, this reduced problem is solved, producing a set of mutant solutions. The NSGA-II selection operator then approximates the Pareto front, which is further refined by a Multi-VNS metaheuristic to balance diversification and intensification. Comparative experiments with both exact and approximate methods demonstrate promising results.
Risk-based decision-making: extended F-Entropy method with correction factor based 2D-FAHP method
In complex decision-making processes using multi-criteria decision-making methods, experts' beliefs and judgments, as well as their knowledge, are influential in the comparisons between criteria and alternatives, which may lead to overlapping importance rankings of criteria. In this study, to increase the degree of representativeness of uncertainties in overlapping criteria evaluations, a correction term is integrated into the fuzzy entropy method, so that the risk cost levels of the main criteria of equal importance differ according to the number of sub-criteria. The integrated correction term into the fuzzy entropy calculation is proposed as a relative importance weight multiplier in the two-dimensional fuzzy AHP process steps. Although the \(\alpha\)-alpha truncation method is proposed for the Fuzzy AHP method, the decision matrix is converted into crisp values in the process stages and directly reduced to the Classical AHP method. Within this article, using the judgment matrix with interval values is proposed instead of exact judgment values as to not distort the fuzzy structure of the result values. In the article, the two-dimensional fuzzy Entropy weights obtained by using the alpha-cutting method can be used as a relative importance weight multiplier in the fuzzy AHP process proposed in two dimensions to obtain clear importance rankings of the criteria. Thanks to the method approach proposed, OCTAVE Allegro logic is combined to create a relative risk matrix according to the risk environment conditions for the criteria alongside the ranking level.
Solution to the single parametric linear programming problems via simplex-based algorithms: handling the uncertainties in costs, left or right-hand sides
Parametric programming is one of the notable approaches to expressing the uncertainties encountered in real life. Many studies express the parameters of the objective function and right-hand side parametrically, but only a few include the parametric coefficient matrix of the constraints. This paper examines the feasibility and optimality conditions of the simplex table and proposes a simplex-based algorithm (dual-simplex, generalized-simplex, or primal-simplex). In the solution process, each case is considered independently through the mathematical analysis of simplex multipliers. Distinct numerical examples illustrate each case to demonstrate the algorithm's implementation.
A profit maximization model for sustainable inventory under preservation technology and linear time-dependent holding cost
This paper presents sustainable inventory model with constant deterioration rate when holding cost is time dependent. Demand rate is price and stock dependent. Preservation technology and carbon emission are considered for more sustainable approach. Shortages are allowed and are fully backlogged. In addition, a mathematical model is constructed to maximize the total profit function and the concavity is shown using three-dimensional graph. A numerical experimentation is carried to compute the total profit and the order quantity. To validate the proposed model, the sensitivity analysis is conducted for the total profit function as well as the order quantity. Results and observations are also discussed along with managerial insights.
Measuring trade facilitation for the emerging seven countries (E7) using multi-criteria decision-making methods
Countries provide opportunities for traders not only in imports but also in export performance by simplification and harmonization of documents in order to facilitate certain policy areas that have a tremendous impact on trade volumes. The OECD has established various indicators at different levels and compared countries to measure the trade facilitation between countries. This study aims to compare the procedures applied by the emerging seven countries (E7- Brazil, China, India, Indonesia, Mexico, Russia, and Türkiye) using trade facilitation indicators (TFIs) and multi-criteria decision-making methods. We employ MEREC, WENSLO, ENTROPY, LOPCOW, CVM, CRITIC, ANGLE, and GINI methods to determine the weights of 11 TFIs identified by the OECD. The most suitable weighting method is established through multi-dimensional analysis. E7 countries are then evaluated using the MABAC and ARTASI methods, with a sensitivity analysis comparing results against 38 OECD member countries. In terms of performance across all TFIs, Russia ranks first (MABAC-0.253, ARTASI-1.821), Mexico second (MABAC-0.186, ARTASI-1.802), and Türkiye third (MABAC-0.117, ARTASI-1.731).