Mathematical Decision Model Research Articles

Intelligent Decision-Making Algorithm for UAV Swarm Confrontation Jamming: An M2AC-Based Approach

Unmanned aerial vehicle (UAV) swarm confrontation jamming offers a cost-effective and long-range countermeasure against hostile swarms. Intelligent decision-making is a key factor in ensuring its effectiveness. In response to the low-timeliness problem caused by linear programming in current algorithms, this paper proposes an intelligent decision-making algorithm for UAV swarm confrontation jamming based on the multi-agent actor–critic (M2AC) model. First, based on Markov games, an intelligent mathematical decision-making model is constructed to transform the confrontation jamming scenario into a symbolized mathematical problem. Second, the indicator function under this learning paradigm is designed by combining the actor–critic algorithm with Markov games. Finally, by employing a reinforcement learning algorithm with multithreaded parallel training–contrastive execution for solving the model, a Markov perfect equilibrium solution is obtained. The experimental results indicate that the algorithm based on M2AC can achieve faster training and decision-making speeds, while effectively obtaining a Markov perfect equilibrium solution. The training time is reduced to less than 50% compared to the baseline algorithm, with decision times maintained below 0.05 s across all simulation conditions. This helps alleviate the low-timeliness problem of UAV swarm confrontation jamming intelligent decision-making algorithms under highly dynamic real-time conditions, leading to more effective and efficient UAV swarm operations in various jamming and electronic warfare scenarios.

Optimization of urban transport vehicle tasks for large, mixed fleet of vehicles and real-world constraints

Planning the operation of urban public transport vehicles is the first stage of operational planning and consists in combining timetable tips, which are input data, into blocks that constitute the daily tasks of vehicles. For a large mixed fleet of vehicles of various types, especially those with battery power that requires recharging, operating from many depots, with numerous requirements and rolling stock constraints, the problem is a major engineering challenge, even for an experienced team of planners. IT solutions based on realistic, mathematical decision-making models and fast optimization algorithms can be of great assistance. For the problem formulated this way, a mathematical decision model with a multi-criteria objective function was built, taking into account technical, economic, and ecological criteria, natural, and binary decision variables. The model takes into account the real requirements and constraints, a mixed fleet of different types vehicles, including electric buses, multiple depots, technical trips (dead heads), and battery charging. The considered problem is an NP-hard combinatorial optimization problem. The use of classical, exact algorithms to solve this problem is not possible for schedules with many thousands of line trips and fleets of hundreds or thousands of vehicles. This research proposes an original, dedicated heuristic, enabling to obtain an acceptable, but still suboptimal solution, in a very short time. The tests of the proposed heuristic algorithm were carried out on real databases of public transport systems of the two selected medium and large Polish cities. In particular, multiple depots, a mixed fleet of different types of vehicles, and real-world constraints were taken into account. The results of computer experiments carried out using the developed heuristic were compared with the results obtained manually by a team of experienced and expert planners. For the developed multi-criteria decision-making model results comparable to and better than those prepared manually by experts were obtained in a very short time using the proposed heuristics. It is the basis for further development works on expanding the model and improving the optimization algorithm.

An analytical decision-making model for integrated green supply chain problems: A computational intelligence solution

This paper presents an integrated mathematical decision-making model to reduce environmental footprints using process integration. By doing so, we address the research question: How can supplier selection, ergonomic factors, and green practices be integrated into mathematical decision-making models based on the vendor-managed inventory policy? We use the Branch and Bound method to provide optimal solutions and a metaheuristic optimization approach in computational intelligence for large-scale problems. This paper employs a multi-criteria decision-making method to compare proposed algorithms results based on six criteria. Our findings reveal that integrating the sourcing process with inventory decisions significantly improves cost performance. Furthermore, our results demonstrate that the proposed model effectively balances environmental and economic objectives using a carbon tax. Moreover, sensitivity analysis results indicate that optimizing water and energy consumption can significantly improve carbon footprints. In addition, the study shows that ergonomic factors, including lighting and temperature, have a substantial impact on performance. The primary contributions of this paper include the incorporation of a multi-sourcing strategy, green practices, ergonomic factors, and supplier selection into vendor-managed inventory decision models.

A peer-to-peer trading model to enhance resilience: A blockchain-based smart grids with machine learning analysis towards sustainable development goals

Blockchain technology, with its peer-to-peer trading feature, influences the management of energy consumption by offering the potential to transform transparency, efficiency, and sustainability within the energy sector. Nonetheless, there is a need to develop analytical decision-making models tailored for managing peer-to-peer energy transactions to improve energy resilience. Therefore, the purpose of this paper is to address the research question: How can energy distribution systems be protected via blockchain technology to enhance energy resilience and mitigate vulnerabilities to disruptions? This paper employs a conceptual research model design and a mathematical decision-making model to address the research question by capturing the peer-to-peer trading capability of blockchain technology. The theory of planned behavior provides theoretical explanations for the proposed model. The sample includes longitudinal energy consumption data from 2015 to 2023 in Texas. The findings indicate a significant improvement in energy efficiency along with a considerable decrease in total electricity consumption. Post hoc analysis results reveal that the seasonal autoregressive integrated moving average algorithm is effective as a reliable input for the proposed mathematical model. The significant implications are to implement blockchain-based smart grids in which energy systems become more resilient to disruptions, as the peer-to-peer capability enables users to trade energy. The proposed model suggests that energy will be used more efficiently and effectively. This paper contributes to prior works by introducing a mathematical model that captures the trading behavior of energy consumers. Moreover, this paper proposes the SARIMA algorithm to predict energy demand.

Bayesian System Identification of a River

Hydrological systems like rivers and lakes are a vital part of any community. Mathematical models of such systems underpin management, decision making and control of rivers. There is always uncertainty associated with the models, and in this paper we consider Bayesian system identification of a river. Bayesian system identification delivers an a-posteriori probability distribution of the unknown parameters. This uncertainty description is useful for solving chance-constrained problems encountered in the control and management of rivers. The Bayesian system identification approach is demonstrated by applying it to the upper part of the Murray River in Australia using real water level and flow measurements. The obtained models show good simulation performance capturing the observed water levels well. Moreover, posterior distributions of the parameters are delivered which are useful for control of rivers.

Towards neutrosophic Circumstances goal programming approach for solving multi-objective linear fractional programming problems

Indeterminacy is common in practical decision-making circumstances. So the mathematical models of decision making represent the situations in a better way if the parameters are considered as neutrosophic. This article studies a general framework of multi-objective neutrosophic linear fractional programming problem (MONLFPP) and proposes unique approach. The issue's parameters are thought of as triangular neutrosophic numbers. The problem is converted into an equal crisp multi-objective linear programming problem (MOLPP) with the help of variable transformation technique and a ranking function. Fuzzy goal programming is used to solve the MOLPP that has been obtained. Finally, the usefulness of the proposed technique is established using two mathematical models.

ECONOMIC GROWTH FORECAST MODEL URBAN SUPPLY CHAIN LOGISTICS DISTRIBUTION PATH DECISION USING AN IMPROVED GENETIC ALGORITHM

The proposed way of estimating the associated macroeconomic index based on a supply chain network is a novel strategy that might give useful insights for firms and organizations trying to enhance their supply chain logistics operations. To aid in this process, the suggested technique utilizes multiple regression analysis and adaptive extreme learning machine models to determine the relative importance of each indicator in the supply chain logistics decision-making process. Firms may be able to save expenses and boost economic value by employing enhanced genetic algorithms and mathematical modeling to develop a logistics distribution model for urban supply chains based on reconstructive genetic algorithms. It is possible that the paper's study of the issues plaguing the current distribution of logistics in metropolitan areas would prove valuable to organizations that are seeking to improve their own supply chain logistics procedures. This paper appears to take a thorough strategy that might assist assure the accuracy of the forecasting method by preprocessing macroeconomic indicators using imputation, classification, and other approaches to generate a time series consistency model. Some novel ways that may shed light on logistics in the supply chain include using a two-dimensional discrete mesh structure built on wireless sensors to depict the national economic development scenario and using a coding matrix to convey the extent of economic growth. A thorough and all-encompassing way that might aid organizations in making better judgments about their supply chain logistics strategies is to employ multiple regression analysis, an adaptive extreme learning machine model, and other approaches to examine the effect degree of each key indicator. Experiments demonstrating excellent and steady prediction accuracy of the algorithm model are encouraging and point to the possible usefulness of the suggested forecasting approach. The paper's contributions, including its analysis of supply chain logistics cost accounting, determination of the basic path optimization, improvement of the genetic algorithm, and design of the mathematical model of supply chain logistics distribution path decision, all look promising in terms of their potential to help businesses cut costs and boost economic value. The positive outcome of the successful design of the mathematical model demonstrates the possible efficacy of the suggested technique.

A hybrid mathematical model for international target market decision: the case of fibreboard industry

ABSTRACT Determining the target market constitutes one of the most important strategic decisions. During the target market selection, many factors need to be considered and evaluated systematically and the most accurate choice is required to be made. In this study, the target country market selection is made for the fibreboard industry, which is one of the main sectors of the forest products industry in Turkey. For this purpose, multi-criteria decision-making (MCDM) methods, which are considered the most appropriate decision-making techniques among alternatives with many criteria, are utilised. AHP, VIKOR and TOPSIS methods are used to identify the most appropriate target market. Furthermore, a hybrid mathematical model including goal programming is proposed. And to handle ambiguity and fuzziness in international market decisions, a fuzzy goal programming model is developed. Economic, risk, supply chain and sectoral strategies are determined as the main criteria. 29 target countries are identified by including the countries ranking first in the exports of Turkey in the sector and the target countries determined by Ministry of Development. Target countries are ranked with MCDM. The rankings of the solution are compared via correlation tests. The first 10 countries are selected for the target market by employing the proposed models.

A novel mathematical multi-criteria decision-making model for optimizing life cycle energy and cost in construction projects planning

ABSTRACT Today, energy management systems are usually assessed as key to sustainable development goals. One of the best criteria for energy management systems in construction projects is Life Cycle Energy Analysis (LCEA). This research is a quantitative-qualitative study based on a Multi-Criteria Decision-Making (MCDM) model. This research involves four stages: library study, statistical survey, descriptive study, and case study. The review of previous studies showed that the LCEA and MCDM alone could not provide a comprehensive energy consumption management assessment model, due to inherent uncertainty and the existence of various analysis parameters; however, when are used in an integrated framework; the LCEA & MCDM hybrid approach serves as the best instruments to assess energy management systems. This research has proposed a newly developed hybrid multi-objective mathematical decision-making model to select appropriate and optimum options for all building shell components to optimize and manage the Cost and Energy of the Building Life Cycle. The life cycle energy analysis of an educational building in a case study showed that optimization using the proposed model saves about 16% of energy during the lifetime of the building. In addition, the investment payback period for this optimization is less than seven months in the first year of operation.

Cost analysis of chronic pain due to musculoskeletal disorders in Chile.

The magnitude of the cost of chronic pain has been a matter of concern in many countries worldwide. The high prevalence, the cost it implies for the health system, productivity, and absenteeism need to be addressed urgently. Studies have begun describing this problem in Chile, but there is still a debt in highlighting its importance and urgency on contributing to chronic pain financial coverage. This study objective is to estimate the expected cost of chronic pain and its related musculoskeletal diseases in the Chilean adult population. We conducted a mathematical decision model exercise, Markov Model, to estimate costs and consequences. Patients were classified into severe, moderate, and mild pain groups, restricted to five diseases: knee osteoarthritis, hip osteoarthritis, lower back pain, shoulder pain, and fibromyalgia. Data analysis considered a set of transition probabilities to estimate the total cost, sick leave payment, and productivity losses. Results show that the total annual cost for chronic pain in Chile is USD 943,413,490, corresponding an 80% to the five diseases studied. The highest costs are related to therapeutic management, followed by productivity losses and sick leave days. Low back pain and fibromyalgia are both the costlier chronic pain-related musculoskeletal diseases. We can conclude that the magnitude of the cost in our country's approach to chronic pain is related to increased productivity losses and sick leave payments. Incorporating actions to ensure access and financial coverage and new care strategies that reorganize care delivery to more integrated and comprehensive care could potentially impact costs in both patients and the health system. Finally, the impact of the COVID-19 pandemic will probably deepen even more this problem.

Inventory control under different forms of uncertainty: Ambiguity and stochastic variability

AbstractInventory decision makers routinely face ambiguity due to the psychological awareness that there is unknown information about salient events that is knowable in principle. Researchers on inventory control behavior in the face of uncertainty have primarily focused on uncertainty due to stochastic variability. However, most decision situations in the naturally occurring world involve both forms of uncertainty—ambiguity and stochastic variability. We report the results of two experiments that partial out the effects of ambiguity and stochastic variability by orthogonal manipulation of these two forms of uncertainty in a newsvendor task. Contrary to established mathematical models of decision making under uncertainty, increased ambiguity results in increased mean absolute percentage error, and a corresponding decrease in profit. We also find a systematic bias toward underordering associated with increased ambiguity, which is over and above the bias associated with increased stochastic variability. We do not see evidence for learning with repeated play, so that the effects of induced ambiguity appear to persist. Finally, based on our findings, we suggest measures that managers can use to ameliorate the effects of ambiguity.

Testing and Enhancing a Pivotal Organizational Structure Decision-Making Model

This paper presents and empirically tests a new point-system-based mathematical decision-making model for determining the most effective organizational structure for any firm type. The model proposes that companies can determine their most effective structure by assessing 11 literature-based characteristics that best describe the firm. Through a survey of 143 executive MBA students, this paper provides results, conclusions, and implications of the first empirical test of a math-based organizational structure decision-making model. The research presented suggests that 11 key variables, or organizational characteristics, should be included in any predictive structure model. Corporate executives need and seek theoretical and practical guidance regarding how to best organize, structure, or re-structure their firm to gain and sustain competitive advantage. The model tested herein provides real-world guidance to managers regarding how to decide which organizational structure is most effective for any given firm.

Identifying future partner agencies: helping Brazos Valley Food Bank in the fight against food insecurity

Brazos Valley Food Bank (BVFB) is a non-profit organization in the Bryan-College Station area of Texas. It distributes food supplies through partner agencies and special programs to eradicate hunger in Brazos Valley. However, a big gap exists between the meals distributed by BVFB and the size of the food-insecure population. This research is motivated by BVFB’s desire to reach more people by recruiting more sustainable partner agencies. We used Geographic Information Systems (GIS) to map food desert areas lacking access to nutritious food. We combined expert knowledge with multi-criteria decision-making (MCDM) to address the challenges and time consumption of manually identifying sustainable partner agencies for local food delivery. We identified evaluation criteria for all agencies based on BVFB managers’ preferences using a qualitative approach, and then applied three quantitative decision-making models: the Weighted Sum Model (WSM), the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and the Multi-criteria Optimization and Compromise Solution (VIKOR) models to obtain ranking results. We compared the quantitative models’ rankings to BVFB managers’ manual choices and discussed the impacts of our research. The key innovation of the research is to develop a mixed method by combining expert knowledge with mathematical decision models and GIS to support spatial decision making in food distribution. Although our results were specific to BVFB, these procedures can be applied to food banks in general. Future studies include finetuning our models to measure and address human biases, wider applications and more data collections.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ОРГАНИЗАЦИОННЫХ СИСТЕМ

Introduction. Modern rates of development of information systems and web-technologies are increasingly being introduced into the life of all mankind, including organizational systems, which requires the improvement of management and decision-making processes. In modern sources of literature, the consideration of management processes is given on the basis of analysis, but from the side of the synthesis of the mathematical model of management decisions, they are not considered, which allows us to consider the ongoing research as an urgent task. For the head of the organizational system, the solution of the problem of management is the most important task based on the complex interaction of all departments of the managed system. Practical relevance: When a destructive impact occurs in a managed system, a decision-maker should have a management decision model that allows timely management decisions to counter emerging threats. Counteraction is carried out at the expense of the resources available to the decision-maker. The mathematical model of a management decision makes it possible to respond in a timely manner to emerging threats in the system and make appropriate management decisions with a given level of the efficiency indicator of the decision being made. The application of the Kolmogorov differential equations makes it possible to link the finding of a mathematical modeling system with various states of the controlled system. Discussion: The resulting indicator of the effectiveness of the decision makes it possible to link three states of the system when considering the target process, namely, the process of threat formation, the process of threat identification and the process of threat neutralization. By setting the required indicator of the effectiveness of a management decision, it allows the manager to respond in a timely manner to the destructive impact, to use the available resources to ensure the achievement of the management goal.

Stability and Change in Diffusion Model Parameters over Two Years

In recent years, mathematical models of decision making, such as the diffusion model, have been endorsed in individual differences research. These models can disentangle different components of the decision process, like processing speed, speed–accuracy trade-offs, and duration of non-decisional processes. The diffusion model estimates individual parameters of cognitive process components, thus allowing the study of individual differences. These parameters are often assumed to show trait-like properties, that is, within-person stability across tasks and time. However, the assumption of temporal stability has so far been insufficiently investigated. With this work, we explore stability and change in diffusion model parameters by following over 270 participants across a time period of two years. We analysed four different aspects of stability and change: rank-order stability, mean-level change, individual differences in change, and profile stability. Diffusion model parameters showed strong rank-order stability and mean-level changes in processing speed and speed–accuracy trade-offs that could be attributed to practice effects. At the same time, people differed little in these patterns across time. In addition, profiles of individual diffusion model parameters proved to be stable over time. We discuss implications of these findings for the use of the diffusion model in individual differences research.

Optimal Policies for Quantum Markov Decision Processes

Markov decision process (MDP) offers a general framework for modelling sequential decision making where outcomes are random. In particular, it serves as a mathematical framework for reinforcement learning. This paper introduces an extension of MDP, namely quantum MDP (qMDP), that can serve as a mathematical model of decision making about quantum systems. We develop dynamic programming algorithms for policy evaluation and finding optimal policies for qMDPs in the case of finite-horizon. The results obtained in this paper provide some useful mathematical tools for reinforcement learning techniques applied to the quantum world.

Optimal patient protocols in regional acute stroke care

In acute stroke care two proven reperfusion treatments exist: (1) a blood thinner and (2) an interventional procedure. The interventional procedure can only be given in a stroke centre with specialized facilities. Rapid initiation of either is key to improving the functional outcome (often emphasized by the common phrase in acute stroke care “time=brain”). Delays between the moment the ambulance is called and the initiation of one or both reperfusion treatment(s) should therefore be as short as possible. The speed of the process strongly depends on five factors: patient location, regional patient allocation by emergency medical services (EMS), travel times of EMS, treatment locations, and in-hospital delays. Regional patient allocation by EMS and treatment locations are sub-optimally configured in daily practice. Our aim is to construct a mathematical model for the joint decision of treatment locations and allocation of acute stroke patients in a region, such that the time until treatment is minimized. We describe acute stroke care as a multi-flow two-level hierarchical facility location problem and the model is formulated as a mixed integer linear program. The objective of the model is the minimization of the total time until treatment in a region and it incorporates volume-dependent in-hospital delays. The resulting model is used to gain insight in the performance of practically oriented patient allocation protocols, used by EMS. We observe that the protocol of directly driving to the nearest stroke centre with special facilities (i.e., the mothership protocol) performs closest to optimal, with an average total time delay that is 3.9% above optimal. Driving to the nearest regional stroke centre (i.e., the drip-and-ship protocol) is on average 8.6% worse than optimal. However, drip-and-ship performs better than the mothership protocol in rural areas and when a small fraction of the population (at most 30%) requires the second procedure, assuming sufficient patient volumes per stroke centre. In the experiments, the time until treatment using the optimal model is reduced by at most 18.9 minutes per treated patient. In economical terms, assuming 150 interventional procedures per year, the value of medical intervention in acute stroke can be improved upon up to € 1,800,000 per year.

Izbor protivoklopnih vođenih raketa modelom višekriterijumskog odlučivanja

Introduction: Anti Tank Ground Missiles (ATGMs) are one of the most efficient weapon systems to counter armored and mechanized units. Procurement of these weapons is imperative for armed forces of any country. Adequate evaluation and choice of an efficient ATGM system is a very important factor which affects operational capabilities of armed forces. The purpose of this paper is to present that multi criteria methods can be a useful tool for optimal procurement of ATGMs for armed forces. Methods: The implementation of the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and the MABAC (Multi Attributive Border Approximation Area Comparison) multi criteria methods will be proposed for decision makers to solve the problem of ATGM procurement. In this paper, four models of ATGMs will be proposed as possible solutions. These ATGMs will be presented as alternatives A1, A2, A3 and A4. Results: The implementation of the methods in this paper has led to the conclusion that the alternative A2 has the highest value and therefore the best course of action for decision makers is to chose procurement of this model of ATGMs. Conclusion: The conclusion is that the mathematical models of multi-criteria decision making presented in this paper unequivocally point to the alternative with the best characteristics, thus presenting extremely useful tools for decision makers.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ В СОЦИАЛЬНЫХ И ЭКОНОМИЧЕСКИХ СИСТЕМАХ

In the modern rapidly changing world, there are constant changes in all spheres of human activity, including in the social and economic systems, such as education, law, health care. All areas require study for improving management and decision-making mechanisms in order to increase the efficiency of their functioning and further logic of action improving the process of functioning of processes in social and economic systems. The introduction of the sites of educational organizations into educational institutions of higher education (UHE) has led to the need for the person in charge of the site (LOU) of the organization to have a mathematical model of management decisions to counter emerging threats. In this paper, we will consider the process of forming a mathematical model of an administrative decision, which is obtained on the basis of synthesis from the transition states of the system using the Kolmogorov differential equations, by further transforming them into a system of linear algebraic equations (SLAE) and solving them by the Gauss method. Mathematical modeling is based on synthesis processes using the law of preserving the integrity of the object (ZSCO) and the natural science approach (ESA). The use of the synthesis method allows you to achieve the control goal based on the required performance indicators. The proposed mathematical model helps in solving three processes aimed at monitoring the occurrence of a problem in a controlled system, the process of recognizing the problem and the process of implementing a managerial decision to eliminate the problem. The final obtained mathematical solution for modeling the situation in the social and economic system helps to establish a model of LOU behavior depending on the current situation, which will lead to saving time resources and the possibility of its redistribution for solving other problems. The resulting mathematical model can be further complicated by adding new variables and conditions for the implementation of the control process.

Game Reproduction of the Queuing System as an Economic Laboratory Experiment

This article presents the results of an economic laboratory experiment based on a queuing system. The “classical” problem of the theory of mass service, known as the Erlang problem, with the aim of studying the behavioral theory of games reproduced in this article. It is based on the theory of queuing, which allows the company to avoid inefficient organization of customer service. Considerable attention is paid to the provisions of the behavioral theory of games as a method of making management decisions and their practical application. A mathematical model of decision making studied by queuing theory was compiled. There are Conclusions about the behavior in real economic situations. The experiment presented in the form of a game can be used as an original method of teaching economics.