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
Croatian Operational Research Society (CRORS)
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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.
Copyright (c) 2026 Croatian Operational Research Review
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.
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.
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).
An application of an environmentally extended input-output model to the assessment of CO2 emissions of Croatian economic sectors
The adverse effects of pollution and the impacts of different productive sectors on the degradation of the environment have become important issues in economic development analysis. This study aims to estimate the overall carbon footprint of different economic sectors of the Croatian economy. Total CO2 emissions are decomposed by direct and indirect emissions of productive sectors and final demand by applying the environmentally extended input-output analysis (EEIO). EEIO approach enables the decomposition of the total CO2 emissions of specific sectors into emissions related to the production of final goods and services and the production of intermediate inputs delivered to other economic sectors. The highest level of direct emissions has been generated by sectors producing energy products and transportation. As the output of those sectors is required as intermediate inputs used by the other sectors, the EEIO model redistributes emissions to other sectors, delivering final products to domestic users and abroad. Besides transport and electricity, Croatia's highest level of total direct and indirect emissions is found in the construction sector, production of non-metallic mineral products and food industry.
Evaluating upskilling tools for digital, green, and entrepreneurial competences: A multicriteria approach to advancing Europe's green and digital transition
Advancing green and digital transition is a key topic on Europe’s agenda, aligned with the UN’s SDG goals. In this context, this study investigates existing support tools and programs for upskilling digital, green, and entrepreneurial (DGE) competences with the goal to select and reuse the best ones available within the project partner group (11 partners from 9 European countries). The data collection process started with the identification and thorough elaboration of 90 upskilling tools/programs, each differing in their contributions to DGE competences, and in other varying features. The collected database contains more than 30 qualitative and quantitative features per upskilling tool/program. An expert focus group then defined the tool selection criteria and their grading, highlighting the importance of learning outcomes recognition and the development of multiple DGE competence areas, in particular. After the grading process, alternative assessments were analysed using the PROMETHEE II method, resulting in a ranking of the 15 most useful DGE tools/programs. In addition to validating the framework set up for the MCDM that takes into account the complexities of (international) training needs of diverse target groups, the study demonstrated significant application potential. Namely, these tools, both the initial list of 90 and the selected 15, all having confirmed their effectiveness and success in previous projects addressing SDG 4 and SDG 9, are now promoted to (new) relevant stakeholders and prioritised in capacity-building actions in international settings. As such, the collective exercise based on strong scientific foundations had clear practical value.
A memetic NSGA-III for green flexible production with real-time energy costs and emissions
The use of renewable energies strengthens decarbonization strategies. To integrate volatile renewable sources, energy systems require grid expansion, storage capabilities, or flexible consumption. This study focuses on industries that adapt production to real-time energy markets, offering flexible consumption to the grid. Flexible production considers not only traditional goals like minimizing production time, but also minimizing energy costs and emissions, thereby enhancing the sustainability of businesses. However, existing research focuses on single goals, neglects the combination of makespan, energy costs, and emissions, or assumes constant or periodic tariffs instead of a dynamic energy market. We present a novel memetic NSGA-III to minimize makespan, energy cost, and emissions, integrating real energy market data, and allowing manufacturers to adapt energy consumption to current grid conditions. Evaluating it with benchmark instances from literature and real energy market data, we explore the trade-offs between objectives, showcasing potential savings in energy costs and emissions on estimated Pareto fronts.
On the closed-form solution of the monopolist long-run profit maximization problem with linear demand and Cobb-Douglas technology
This paper provides an economic and mathematical analysis of the long-run profit maximization problem of a monopolist with linear demand and a two-input Cobb-Douglas technology to derive the conditions that guarantee the solution to this problem. In addition, the conditions under which the closed-form solution can be derived and the conditions under which the monopolist's profit is positive are discussed. Whenever the problem has a unique solution, the closed-form defines the profit function well for the given demand function. The closed-form solution to the problem depends on the returns to scale. The problem has a unique solution for decreasing returns to scale, for which in general no closed-form can be found. On the other hand, the closed-form of the unique solution can easily be found for constant returns to scale. However, three sub-cases are identified for the case of increasing returns to scale. The analysis is supported by economic interpretations and numerical illustrations.
Going concern prediction – A horse race between traditional and regularization machine learning models
Regularization machine learning (ML) methods have been increasingly applied in accounting research, offering new possibilities in predictive modeling. Their forte lies in the effective regularization methods for resolving the biggest concern of generalization, which is the risk of overfitting the training data. While these sophisticated methods are known to outperform traditional regression approaches in large and balanced datasets, this may not be the case when facing imbalanced and small datasets. Moreover, model validation is also challenging in such settings because traditional performance measures, such as prediction accuracy, may be misleading. We address this problem by comparing two traditional and five regularization-based methods in predicting going concern uncertainty (GCU) on the sample of listed companies in Croatia. We take caution when evaluating the models due to class-imbalanced problems and include different classification performance measures, as well as calibration of the models to account for their uncertainty. As expected, no model performs best across all evaluation criteria, but regularization methods are better calibrated. Given our results, we suggest that model selection should consider the results of the model calibration, a combination of different performance metrics, and the economic impact of the statistical performance of the model, if feasible.
Calculation of ecological land-footprint - based on the input-output model and focusing on the imported commodities
The ecological footprint has been a crucial ecological indicator for more than two decades, and the methodology for calculating it has developed significantly over the years. However, some issues and shortcomings still need to be addressed and specified further. This paper focuses on the embedded land requirements of imported commodities in input-output modelling approaches. We propose a refined model to overcome the shortcomings of two former models. Our model quantifies the embedded ecological land-footprint of imported commodities and their allocation between direct final consumption and production. In addition, we allocate the latter again among final consumption and exports using the framework of linear algebra and matrix arithmetic. We also propose ways of extending the model to overcome the general but misleading assumption in the literature that imported commodities have an equal per unit ecological footprint to domestic products, an approach that is based on the idea that trading partners have the same technological background.
Non-cooperative inventory games for defective items and quantity discounts using strategic complementarity
In this paper, the mathematical analysis for obtaining the equilibrium of the inventory games under strategic complementarities, the existence of defective items, and quantity discounts have been analyzed. The inventory system consists of many buyers who order a single type of product from one supplier. They compete with each other as a player in a non-cooperative game with strategic complementary. They maximize a supermodular payoff function and take into account some fraction of defective items from a lot of the arrival products. The concept of supermodular games is used to obtain the equilibria of these problems. A new existence theorem of Nash equilibrium in a specific condition has been proved. The optimum analysis has been justified for two conditions, that is the condition without discount and another without it. The numerical computations are provided using Python programming. At the end, the numerical result shows that elements of the Nash equilibrium set can be altered when discounts are considered. A quantity discount policy can be used by the supplier to prevent players from choosing the least Nash equilibrium.
TOPSIS-based framework for evaluating employee cybersecurity risk
This paper presents the development and initial validation of a TOPSIS-based framework for evaluating employee cybersecurity risk (TFEECR). The framework offers a structured and objective approach to assessing multiple dimensions of employee behavior and attitudes toward cybersecurity. It integrates the Technique for Order of Preference by Similarity to the Ideal Solution (TOPSIS) with Saaty’s criteria weighting, enabling a comprehensive evaluation across five criteria: knowledge, compliance, risky behaviors, attitudes, and training. The framework is validated using simulated data, and it showed robustness in differentiating between high- and low-risk employees. Such results are useful for organizations that want to implement targeted interventions. A sensitivity analysis highlights the framework's adaptability to various settings. This conceptual framework lays the groundwork for future empirical validation and practical application in enhancing organizational cybersecurity.
New results on system of variational inequalities and fixed point theorem
In (Croat. Oper. Res. Rev, 13(1), 131-135, (2022).) A. Benhadid showed by a counterex- ample that a number of publications in the research on the variational inequalities system contains inaccurate results about applying the Lipschitz continuity concept in relation to both the first and sec- ond variables during the proof of the main theorem on the part of authors. In this paper, We suggest to applying fixed point theorem to correct the main results of some publications.
Optimizing maritime routes: A multi-method analysis from Shanghai to Vladivostok
This research analyzes the marine route plan from Shanghai to Vladivostok utilizing Dijkstra’s algorithm, Markov chain analysis, game theory, and congestion analysis. Dijkstra determines the route through Busan and Hungnam as the shortest, with a total distance of 2114 kilometers and minimal travel time. The Markov chain analysis supported the designated path by demonstrating greater transition probabilities compared to other routes, so establishing it as the most probable option. Experts in game theory, particularly on the Nash equilibrium, demonstrated that cooperation significantly reduced operating expenses. Further congestion research corroborated that the Shanghai-Busan-Hungnam-Vladivostok route offers a cost advantage, and even with the inclusion of congestion, the route remains less expensive. The study collectively advocates for the consideration of distance, likelihood, collaboration, and congestion while selecting the optimal maritime route, hence enhancing efficiency in maritime logistics.
ANFIS computing and cost optimization of an M/M/c/M queue with feedback and balking customers under a hybrid hiatus policy
The present investigation studies a hybrid hiatus policy for a finite-space Markovian queue, incorporating realistic features such as Bernoulli feedback, multiple servers, and balking customers. A hybrid hiatus policy combines both a working hiatus and a complete hiatus. As soon as the system becomes empty, the servers switch to a working hiatus. During a working hiatus, the servers operate at a reduced service rate. Upon completion of the working hiatus and in the absence of waiting customers, the servers enter a complete hiatus. Once the complete hiatus period concludes, the servers resume normal operations and begin serving waiting customers. In the context of Bernoulli feedback, the dissatisfied customer can re-enter the system to receive another service. By utilizing the Markov recursive approach, we examined the steady-state probabilities of the system and queue sizes and other queueing indices, viz. Average queue length, average waiting time, throughput, etc. Using the Quasi-Newton method, a cost function is developed to determine the optimal values of the system’s decision variables. Furthermore, a soft computing approach based on an adaptive neuro-fuzzy inference system (ANFIS) is employed to validate the accuracy of the obtained results.
Copyright (c) 2024 Croatian Operational Research Review
Exact methods for the longest induced cycle problem
The longest induced (or chordless) cycle problem is a graph problem classified as NP-complete and involves the task of determining the largest possible subset of vertices within a graph in such a way that the induced subgraph forms a cycle. Within this paper, we present three integer linear programs specifically formulated to yield optimal solutions for this problem. The branch-and-cut algorithm has been used for two models that cannot be directly solved by any MILP solver. To demonstrate the computational efficiency of these methods, we utilize them on a range of real-world graphs as well as random graphs. Additionally, we conduct a comparative analysis against approaches previously proposed in the literature.