Elaboration of a Concept for a Simulation-Based Modelling and Decision Support System Employing Virtual Reality Technology for Adaptive Planning in Industrial Enterprises

Elaboration of a Concept for a Simulation-Based Modelling and Decision Support System Employing Virtual Reality Technology for Adaptive Planning in Industrial Enterprises | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Elaboration of a Concept for a Simulation-Based Modelling and Decision Support System Employing Virtual Reality Technology for Adaptive Planning in Industrial Enterprises Ramil Nezhmetdinov This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9606058/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In a dynamically changing market environment, industrial enterprises are faced with the need to quickly adapt production systems to achieve key performance indicators. Traditional decision support systems (DSS) often lack sufficient flexibility and visual clarity to analyze multiple alternative configurations of an enterprise. This article presents a conceptual approach for developing a simulation-based modeling DSS with visualization of results in a virtual reality environment designed for enterprise planning. Based on a critical analysis of modern methods (discrete-event simulation (DES), systems based on differential-algebraic equations (DAE), quasi-continuous simulators), their limitations have been identified in the context of modeling and optimizing complex, combinatorially variable design alternatives for enterprise entities. As a solution, an architecture is proposed that integrates the concept of virtual test benches and experimental digital twins. Particular attention is paid to the use of multi-criteria "black box" optimization methods in combination with surrogate modeling in search for Pareto-optimal configurations. This paper describes the requirements for a user interface based on interactive radial diagrams, enabling decision makers to effectively navigate the solution space. The proposed approach aims to cover the gap between complex engineering calculations and strategic planning needs, serving as a tool for justified decision-making regarding enterprise configuration under uncertain conditions. decision support system (DSS) digital twin simulation modeling production flexibility discrete-event simulation virtual test bench multi-criteria optimization production planning Figures Figure 1 Figure 2 Figure 3 Figure 4 1. INTRODUCTION Modern industrial enterprises operate under high rates of external environmental dynamics, which requires production systems to be flexible [1]. Production flexibility is considered as a system's ability to change the range of manufactured products comprising both mastered and innovative, the volume of output and the delivery time of products to consumers [2]. Achieving target key performance indicators (output volume, production cycle duration, production costs and inventory) under these conditions is impossible without the effective decision support system [3]. The analysis of modern DSS for design and operational planning presented in [4, 5] indicates a shift towards hybrid methods that combine simulation modeling, optimization algorithms and advanced visualization tools. Heylala et al. [4] emphasize the need to create user-friendly interfaces and integrate heterogeneous modeling methods. Trigueiro de Souza Júnior et al. [5] suggest the predominance of metaheuristic algorithms (43.1% are for the evolutionary algorithms) in solving stochastic optimization problems of planning (36.4% of the problems considered) and logistics (16.7%). The concept of digital twins is rapidly advancing in parallel with the development of optimization methods. According to Kritzinger's classification [6], a digital twin is characterized by a fully automated bidirectional data flow between a physical object and its virtual model (Figure 1). However, for strategic planning purposes, according to the author, the behavioral adequacy of the model is as critically important as the automation of data flows, it implies the use of a detailed three-dimensional simulation [7, 8]. Despite the progress in certain areas, there is a gap between deterministic engineering calculations (e.g., in Matlab/Modelica-type environments), abstract discrete-event simulation (DES) and detailed technological processes 3D visualization [9, 10]. Existing three-dimensional simulation DSS have significant limitations: 1. Lack of functionality for automatic modeling a combinatorial set of enterprise entities design alternatives. 2. Insufficient support for automated procedures of optimal solutions searchthat handle complex combinations of the alternatives. 3. The user interface is designed for the analytical engineer rather than the strategic decision maker (SDM). The purpose of this article is to elaborate a conceptual architecture for a three-dimensional simulation DSS that eliminates these limitations and is intended to support decision making in the adaptive planning of industrial enterprises. 2. EXISTING APPROACHES ANALYSIS AND PROBLEM STATEMENT The analysis made by the authors allows to classify existing approaches to developing DSS for industrial enterprises by the level of abstraction and scope of application. The results are summarized in Table 1 . Table 1 Comparative Analysis of Modeling Approaches in DSS for Enterprise Modeling Approach/System type Abstraction level Sphere of usage 3D-visualization Variant optimization Focus on decision makers DAU systems (Matlab, Modelica) High Design of units and control systems Low/conditional Limited No (engineers) Discrete-event simulation (DES) (AnyLogic, Plant Simulation, Delmia) Medium (processes, queues) Flow analysis, logistics, macro-planning Medium/simplified Average (requires integration) Partially (preparation and production planning) Quasi-continuous 3D simulators (Process Simulate, 3D Experience) Low (kinematics, operations) Simulation of equipment behavior and human factors for site inspection High Low (manual selection) No (technologists) Proposed approach Hybrid Adaptive enterprise planning High (detailed) High (automatic) Yes As Table 1 shows no single existing approaches meets all the requirements for a strategic decision support system for enterprise adaptation. DSM systems [ 9 ] are effective for macro-analysis but suffer a loss of detail at the level of robot kinematics or 3D sensor operation, which levels out the advantages of the event-driven approach when attempting to take these aspects into account. Quasi-continuous simulators [ 8 ] provide the necessary detail but their application is limited to individual cells and the process of iterating over variants requires manual labor. 3. The concept of the proposed decision support system based on virtual test benches Virtual Test Benches and Hybrid Modeling. Under the current conditions the use of the concept of virtual test benches and associated experimental digital twins developed by Rossman, Schluze, and their colleagues is considered the most promising approach to creating the required decision support system [16]. This approach has significant potential due to the ability to combine various modeling paradigms including discrete-event and quasi-continuous modeling within a single simulation environment by linking them to digital twins [16]. The concept of virtual test benches involves holistic modeling of a system in virtual reality, as opposed to the isolated treatment of separate subsystems. These subsystems can be represented with varying degree of detail to meet the requirements. A key advantage of virtual test benches is their ability to integrate a wide range of modeling methods into a single environment, including solids dynamics, discrete-event simulation, finite element analysis and energy efficiency analysis of industrial robots. In addition to simulation, these virtual test benches can congregate information from various subject areas. For example, Delbrugger et al. demonstrated the feasibility of incorporating building information models originated from construction design into an enterprise virtual test bench with subsequent automatic employment of semantic information for path planning of mobile robots and simulated personnel [11]. Figure 2 shows the conceptual architecture of the proposed 3D simulation DSS based on a virtual test bench. Integration of virtual reality technologies into decision support systems. An important aspect of experimental digital twins and virtual test benches is the integration of modern virtual reality (VR) technologies for human-machine interaction. This approach has proven effective in facilitating the understanding of complex systems by specialists from various disciplines through high-quality 3D visualization and informative visual metaphors together with optimization methods. Within the framework of the proposed decision support system virtual reality performs three key functions: • Immersive visualization – a 1:1 scale representation of the production system with the ability to freely move and observe technological processes from any point in space. • Interactive experimentation – an ability to interact directly with elements of the virtual enterprise, change equipment parameters and instantly observe the results of the changes. • Collaborative decision-making – support for the joint work of several specialists in a common virtual space to reach consensus decisions on production reconfiguration. Figure 3 shows a detailed architecture for integrating a VR component into the proposed DSS. Figure 3. Architecture for VR technologies integration into the DSS for production planning The developed framework supports various interaction scenarios with the virtual enterprise model for decision makers. The main types of interactions implemented in the modern VR systems for industrial planning are summarized in Table 2. Table 2. Types of user interaction with the virtual production environment Type of interaction Description Technical implementation Application in planning Navigation and visibility Free overview of the virtual workshop, inspection of equipment from different angles Transition between scenes, smooth movement (using the joystick), scaling ("fly-by-fly") Initial layout overview, identification of collisions and bottlenecks Object manipulation Capturing, moving, rotating, installing equipment Capture with controllers with feedback (visual and haptic) Equipment layout, workstations’ ergonomics check Parameters’ change Setting up equipment operating modes, setting speeds, loading Voice commands, virtual controls and menus Optimization of operating modes, performance analysis Scenario modeling Running predefined scenarios ("what-if"), comparing options Select from a virtual menu, voice activation Production performance evaluation, alternative configuration assessment, incident situation analysis Collaborative work Multiple users co-locating, discussing solutions Avatars with pose and gesture transmission, voice communication Collective decision-making, coordination of changes Annotation and markup Applying virtual notes, comments, and instructions Drawing in space, placing text labels Recording comments, transferring tasks, documenting decisions The effectiveness of VR integration into production planning processes is confirmed by a number of industrial implementations. For example, BMW Group is actively developing the "Virtual Factory" concept based on the NVIDIA Omniverse platform, which has reduced the time for collision detection from 4 weeks to 3 days and predicts planning costs reduction up to 30% [7]. Northrop Grumman has developed the HIVE (Highly Immersive Virtual Environment) system, which combines motion capture with Siemens Process Simulate for the ergonomic analysis of assembly operations [2]. In the VITAMINE_5G research project, a virtual reality environment was created for decentralized monitoring of additive production processes. [11]. 4. Multi-criteria optimization of enterprise configurations To enable automatic combination of simulated variants in non-trivial problems optimization algorithms are applied, since the number of possible configurations increases exponentially with the number of variation points. Due to the fact the selected optimization algorithm must be applicable to an arbitrary enterprise model, and an analytical representation of the objective function is generally unavailable, black-box optimization algorithms are preferred. Conflicting objectives typical for enterprise planning and adaptation tasks explains the application of multicriteria algorithms of this group with more detailed reviews presented in the papers. The interaction of modules describes the data flow in the process of searching for an optimal solution. The task of configuration search can be formalized as follows. Let C be a set of all possible configurations of an industrial enterprise and represent a vector of parameters describing the structure and operating modes of the production system: С = (p 1 , p 2 , …, p n ), where pi are either discrete (e.g., equipment type, number of machines) or continuous (e.g., conveyor speed, processing temperature) parameters. To evaluate a configuration quality, a vector criterion (objective function) F(c) is used, which associates each configuration c with a set of k key performance indicators (KPIs): $$\:\text{F}\left(\text{c}\right)=\left(\genfrac{}{}{0pt}{}{{f}_{1}\left(\text{c}\right)}{\begin{array}{c}{f}_{2}\left(\text{c}\right)\\\:\dots\:\\\:{f}_{k}\left(c\right)\end{array}}\right)$$ Within the production planning, the components of the vector F(c) may include (but are not limited to): f1(c) — production volume (units); f2(c) — production program costs (monetary units); f3(c) — production cycle time (hours); f4(c) — equipment utilization rate (%); f5(c) — production inventories (units). It is assumed that all fi(c) indicators are reduced to a form where a lower value is preferable (i.e., a minimization problem is being solved). If any indicator needs to be maximized (e.g., productivity), it can be taken either with the opposite sign or transformed. Since improving one indicator often leads to a degradation in another (for example, increasing production volume may increase inventory or production costs), we cannot search for a single "perfect" solution. Instead, we seek a set of compromise solutions. The multi-criteria optimization task then consists of finding a set of Pareto-optimal configurations P*, which is formally defined as follows: $$\:{\varvec{P}}^{\varvec{*}}=\{\varvec{c}\in\:\varvec{C}\mid\:\nexists\:\varvec{c}\varvec{{\prime\:}}\in\:\varvec{C}:\varvec{F}(\varvec{c}\varvec{{\prime\:}})\prec\:\varvec{F}(\varvec{c}\left)\right\}$$ where the symbol ≺ denotes the Pareto dominance relationship. According to the formula, vector F(c') dominates vector F(c) if c' is not worse than c in any of the indicators and c' is strictly better in at least one indicator. In other words, configuration c' is better than configuration c if it is not inferior to it in any indicator and is superior in at least one. The set P* is called the Pareto set (or Pareto-optimal frontier). Any configuration not belonging to P* can be improved in at least one indicator without degrading the others. It is important to emphasize that the function F(c) is not defined analytically. The value of F(c) for a specific configuration c can only be obtained as a result of a computational experiment using a simulation model (virtual test bench). This is the so-called black-box optimization problem. Considering the complexity and stochastic nature of the objective function (the simulation result), the use of gradient methods is impossible. In this context, metaheuristic algorithms, such as evolutionary algorithms [ 5 , 19 ], are preferable. To speed up convergence, surrogate modeling can be used [ 14 ], where based on previously conducted experiments, an approximation of the objective function F(c) landscape is constructed and the promising candidates are selected for simulation on a virtual test bench. The end user of the system is the decision maker, who is not required to be an expert in either simulation modeling or optimization. Therefore, the interface must translate complex optimization results into an intuitive clear form. Interactive radial charts (radar diagrams) are an effective tool for visualizing multidimensional data [ 15 , 16 ]. The diagram displays multiple broken lines, each representing a separate enterprise configuration from the Pareto-optimal set. Interactive control elements (sliders or threshold values on the axes) allow decision makers to dynamically filter the displayed configurations. For example, by setting a minimum acceptable performance level, the user immediately sees which Pareto-optimal solutions satisfy this condition and how other indicators change. This approach proposed in [ 16 – 18 ] enables decision makers to explore trade-offs and select a configuration based on their strategic priorities. 5. Conclusion and future research directions This paper proposes a concept for a three-dimensional decision support system designed for adaptive planning of industrial enterprises. Its novelty lies in the integration of hybrid modeling methods (virtual test benches), automatic generation of configuration variants and multi-criteria optimization in a single tool designed for the end user—a strategic decision maker. The analysis proved that the existing commercial and academic solutions cover only certain aspects of the problem failing to provide a comprehensive approach. The proposed architecture and formalized statement of the optimization problem (1) provide the basis for the practical implementation of such a DSS. Further research will focus on: 1. Developing protocols for seamless interaction between heterogeneous computing modules (DES and quasi-continuous) within a single virtual test bench. 2. Studying the effectiveness of various multi-criteria optimization algorithms (NSGA-II, MOPSO, etc.) and surrogate modeling methods for solving industrial enterprise planning problems. 3. Development and validation of a system prototype using real production cases to evaluate the economic impact of the proposed approach. 4. Development of intuitive clear visualization methods beyond radial diagrams to handle the uncertainty and stochasticity of modeling results. Implementation of the proposed concept will improve the validity and speed of decision-making when reconfiguring production systems, which is a critical factor for competitiveness for the modern industry. Statements & Declarations Acknowledgments This work was supported by the Ministry of Science and Higher Education of the Russian Federation under project №70-2025-000835 from 04 June 2025. Availability of Data and Materials No datasets were generated or analyzed during the current study All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Nezhmetdinov R.A., Kovalev I.A.. Charuyskaya M.A., Kryzhanovskaya A.S., Bilchuk M.A. The first draft of the manuscript was written by Nezhmetdinov R.A. and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.” This work was supported by the Ministry of Science and Higher Education of the Russian Federation under project №70-2025-000835 from 04 June 2025. The authors have no relevant financial or non-financial interests to disclose. References J. C. Nöcker: Zustandsbasierte Fabrikplanung: Zugl.: Aachen, Techn. Hochsch., Diss., 2012. 1. Aufl. Vol. 2012,6. Edition Wissenschaft Apprimus. Aachen: ApprimusVerl., 2012. Slack, N., Operations management/ N. Slack, A. Brandon-Jones, R. Johnston. - Italy: Pearson, 2013. -713p Andreev, V.N., Charuyskaya, M.A., Kryzhanovskaya, A.S. et al. Application of intelligent engineering in the planning of cyber-physical production systems. Int J Adv Manuf Technol 115, 117–123 (2021). Heilala J, Montonen J, Järvinen P, Kivikunnas S (2010) Developing simulation-based Decision Support Systems for customer-driven manufacturing operation planning. In: Proceedings of the 2010 Winter Simulation Conference (WSC), pp 1-12 Trigueiro de Sousa Junior W, Barra Montevechi JA, de Carvalho Miranda R, Teberga Campos A (2019) Discrete simulation-based optimization methods for industrial engineering problems: A systematic literature review. Computers & Industrial Engineering 128:1-12. Kritzinger, W., Karner, M., Traar, G., Henjes, J., & Sihn, W. (2018). Digital Twin in manufacturing: A categorical literature review and classification. *IFAC-PapersOnLine, 51*(11), 1016-1022. DOI: 10.1016/j.ifacol.2018.08.474 T. Bauernhansl, J. Krüger, G. Reinhart, et al.: WGP-Standpunkt Industrie 4.0. Tech. rep. Wissenschaftliche Gesellschaft für Produktionstechnik WGP e.V., 2016. url: https://www.ipa.fraunhofer.de/content/dam/ipa/de/documents/ Presse / Presseinformationen / 2016 / Juni / WGP _ Standpunkt _ Industrie _ 40 . pdf P. Goodall, R. Sharpe, and A. West: A data-driven simulation to support remanufacturing operations. In: Computers in Industry 105 (2019), pp. 48–60. issn: 0166-3615. doi: 10.1016/j.compind.2018.11.001 (cit. on p. 28). Nezhmetdinov RA, Charuiskaya MA, Kovalev IA (2023) Enterprise Development Planning and AI-Based Technological Forecasting. Russian Engineering Research 43(10):1284–1288. M. Schluse, M. Priggemeyer, L. Atorf, et al.: Experimentable Digital Twins - Streamlining Simulation-based Systems Engineering for Industry 4.0. In: IEEE Transactions on Industrial Informatics (2018), p. 1. Schluse, M., Priggemeyer, M., Atorf, L., & Rossmann, J. (2018). Experimentable Digital Twins - Streamlining Simulation-based Systems Engineering for Industry 4.0. IEEE Transactions on Industrial Informatics, 14(4), 1722-1731. DOI: 10.1109/TII.2018.2804917 Roßmann, H.-J. (Betreuer), & Rumpe, B. (Betreuer). (2022). Parallele Simulation interagierender Digitaler Zwillinge in Virtuellen Testbeds (Dissertation). RWTH Aachen University. Delbrügger, T., Lenz, L. T., & Rossmann, J. (2017). From BIM to digital twin: A holistic approach for building and production system simulation. In Proceedings of the 2017 Winter Simulation Conference (WSC) (pp. 1-12). IEEE. DOI: 10.1109/WSC.2017.8247973 Hülsmann, M., & Windt, K. (Eds.). (2007). Understanding Autonomous Cooperation and Control in Logistics: The Impact of Autonomy on Management, Information, Communication and Material Flow. Springer. Information Visualization: Perception for Design, Ware, C., 2013, Elsevier Science Schluse M., Priggemeyer M., Atorf L., Rossmann J. Experimentable Digital Twins — Streamlining Simulation-based Systems Engineering for Industry 4.0 // IEEE Transactions on Industrial Informatics. – 2018. – Vol. 14, No. 4. – P. 1722-1731. – DOI: 10.1109/TII.2018.2804917. Nezhmetdinov R, Kovalev I, Chumak R (2023) Modeling the Interaction of Technological Objects at Production Sites in a Virtual Reality Environment. In: 2023 International Russian Automation Conference (RusAutoCon), IEEE, pp 900–904. Chumak RR, Nezhmetdinov RA, Nezhmetdinova RA, Nikitin DV (2025) Approaches to the Implementation of Simulators for Training Engineering Personnel Using Virtual Reality Technologies. Russian Engineering Research 45(3):392–397. Nezhmetdinov RA, Kovalev IA, Charuiskaya MA, Kryzhanovskaya AS (2023) Architectural Solutions and Design Models for a System of Intelligent Forecasting and Assessment of Promising Technologies in Industry. In: 2023 International Russian Automation Conference (RusAutoCon), IEEE, pp 494–498. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9606058","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":636245179,"identity":"9fafe37d-fef9-4528-8990-fb43dffa1e04","order_by":0,"name":"Ramil Nezhmetdinov","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVRIiWNgGAWjYNACAws5EHXgAQlaJIzBWhJIsEYisQFEEaXFnL334acbBRLp88MOPwTaYien20BAi2XPcWPpHAOJ3I230wyAWpKNzQ4Q0GJwI40BomV2AkjLgcRtBLXcf8b8G6gl3XB2+gcitdxgYwPZkiAPJInUciaNzRqoxXCDdE7BgQQDYvxy/Bjz7Zw/NvLys9M3f/hQYSdHUAtCL1ilAbHKQUC+gRTVo2AUjIJRMKIAAFfHQaYomZyiAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0001-8734-0224","institution":"Moscow State University of Technology STANKIN Institute of Information Systems and Technologies: Moskovskij gosudarstvennyj tehnologiceskij universitet STANKIN Institut informacionnyh sistem i tehnologij","correspondingAuthor":true,"prefix":"","firstName":"Ramil","middleName":"","lastName":"Nezhmetdinov","suffix":""}],"badges":[],"createdAt":"2026-05-04 08:42:55","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9606058/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9606058/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109454858,"identity":"ed567aea-ecf3-4b62-b9c9-360cc0c89dc5","added_by":"auto","created_at":"2026-05-18 09:49:24","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":278453,"visible":true,"origin":"","legend":"\u003cp\u003eClassification of digital representations based on the nature of data flows\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-9606058/v1/e117e701b505df17377a7ec2.png"},{"id":109799743,"identity":"2806c41b-8db9-4dac-a9d0-1f6ebd3b46d6","added_by":"auto","created_at":"2026-05-22 15:33:37","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":199242,"visible":true,"origin":"","legend":"\u003cp\u003eConceptual architecture of the proposed 3D simulation DSS\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-9606058/v1/8eaf4d0816dafc47315b4728.png"},{"id":109454860,"identity":"97fdb237-deb4-4c94-8e67-15b6faf9b0ca","added_by":"auto","created_at":"2026-05-18 09:49:24","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":324940,"visible":true,"origin":"","legend":"\u003cp\u003eArchitecture for VR technologies integration into the DSS for production planning\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-9606058/v1/02b7402fb76ed0d6e7dd779e.png"},{"id":109759672,"identity":"01f1b40c-e2d7-4d37-9660-a6822e5919d4","added_by":"auto","created_at":"2026-05-22 07:27:31","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":185518,"visible":true,"origin":"","legend":"\u003cp\u003eAn example of the Pareto front configurations visualization using an interactive radial diagram.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-9606058/v1/38e04ee07b8927b8cd71ebc7.png"},{"id":109799745,"identity":"2a32e9bc-c606-4a88-a56c-a4ab9131f475","added_by":"auto","created_at":"2026-05-22 15:33:42","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1025056,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9606058/v1/f42265d9-7b4d-4883-b635-51f21563de54.pdf"}],"financialInterests":"","formattedTitle":"Elaboration of a Concept for a Simulation-Based Modelling and Decision Support System Employing Virtual Reality Technology for Adaptive Planning in Industrial Enterprises","fulltext":[{"header":"1. INTRODUCTION","content":"\u003cp\u003eModern industrial enterprises operate under high rates of external environmental dynamics, which requires production systems to be flexible [1]. Production flexibility is considered as a system\u0026apos;s ability to change the range of manufactured products comprising both mastered and innovative, the volume of output and the delivery time of products to consumers [2]. Achieving target key performance indicators (output volume, production cycle duration, production costs and inventory) under these conditions is impossible without the effective decision support system [3].\u003c/p\u003e\n\u003cp\u003eThe analysis of modern DSS for design and operational planning presented in [4, 5] indicates a shift towards hybrid methods that combine simulation modeling, optimization algorithms and advanced visualization tools. Heylala et al. [4] emphasize the need to create user-friendly interfaces and integrate heterogeneous modeling methods. Trigueiro de Souza J\u0026uacute;nior et al. [5] suggest the predominance of metaheuristic algorithms (43.1% are for the evolutionary algorithms) in solving stochastic optimization problems of planning (36.4% of the problems considered) and logistics (16.7%).\u003c/p\u003e\n\u003cp\u003eThe concept of digital twins is rapidly advancing in parallel with the development of optimization methods. According to Kritzinger\u0026apos;s classification [6], a digital twin is characterized by a fully automated bidirectional data flow between a physical object and its virtual model (Figure 1). However, for strategic planning purposes, according to the author, the behavioral adequacy of the model is as critically important as the automation of data flows, it implies the use of a detailed three-dimensional simulation [7, 8].\u003c/p\u003e\n\u003cp\u003eDespite the progress in certain areas, there is a gap between deterministic engineering calculations (e.g., in Matlab/Modelica-type environments), abstract discrete-event simulation (DES) and detailed technological processes 3D visualization [9, 10]. Existing three-dimensional simulation DSS have significant limitations:\u003c/p\u003e\n\u003cp\u003e1. Lack of functionality for automatic modeling a combinatorial set of enterprise entities design alternatives.\u003c/p\u003e\n\u003cp\u003e2. Insufficient support for automated procedures of optimal solutions searchthat handle complex combinations of the alternatives.\u003c/p\u003e\n\u003cp\u003e3. The user interface is designed for the analytical engineer rather than the strategic decision maker (SDM).\u003c/p\u003e\n\u003cp\u003eThe purpose of this article is to elaborate a conceptual architecture for a three-dimensional simulation DSS that eliminates these limitations and is intended to support decision making in the adaptive planning of industrial enterprises.\u003c/p\u003e"},{"header":"2. EXISTING APPROACHES ANALYSIS AND PROBLEM STATEMENT","content":"\u003cp\u003eThe analysis made by the authors allows to classify existing approaches to developing DSS for industrial enterprises by the level of abstraction and scope of application. The results are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparative Analysis of Modeling Approaches in DSS for Enterprise Modeling\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eApproach/System type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAbstraction level\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSphere of usage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3D-visualization\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eVariant optimization\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFocus on decision makers\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eDAU systems (Matlab, Modelica)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHigh\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDesign of units and control systems\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLow/conditional\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLimited\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNo (engineers)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eDiscrete-event simulation (DES) (AnyLogic, Plant Simulation, Delmia)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMedium (processes, queues)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFlow analysis, logistics, macro-planning\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMedium/simplified\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAverage (requires integration)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePartially (preparation and production planning)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eQuasi-continuous 3D simulators (Process Simulate, 3D Experience)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLow (kinematics, operations)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSimulation of equipment behavior and human factors for site inspection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHigh\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLow (manual selection)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNo (technologists)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eProposed approach\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHybrid\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAdaptive enterprise planning\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHigh (detailed)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHigh (automatic)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAs Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows no single existing approaches meets all the requirements for a strategic decision support system for enterprise adaptation. DSM systems [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] are effective for macro-analysis but suffer a loss of detail at the level of robot kinematics or 3D sensor operation, which levels out the advantages of the event-driven approach when attempting to take these aspects into account. Quasi-continuous simulators [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] provide the necessary detail but their application is limited to individual cells and the process of iterating over variants requires manual labor.\u003c/p\u003e"},{"header":"3. The concept of the proposed decision support system based on virtual test benches","content":"\u003cp\u003e\u003cstrong\u003eVirtual Test Benches and Hybrid Modeling.\u003c/strong\u003e Under the current conditions the use of the concept of virtual test benches and associated experimental digital twins developed by Rossman, Schluze, and their colleagues is considered the most promising approach to creating the required decision support system [16]. This approach has significant potential due to the ability to combine various modeling paradigms including discrete-event and quasi-continuous modeling within a single simulation environment by linking them to digital twins [16].\u003c/p\u003e\n\u003cp\u003eThe concept of virtual test benches involves holistic modeling of a system in virtual reality, as opposed to the isolated treatment of separate subsystems. These subsystems can be represented with varying degree of detail to meet the requirements. A key advantage of virtual test benches is their ability to integrate a wide range of modeling methods into a single environment, including solids dynamics, discrete-event simulation, finite element analysis and energy efficiency analysis of industrial robots. In addition to simulation, these virtual test benches can congregate information from various subject areas. For example, Delbrugger et al. demonstrated the feasibility of incorporating building information models originated from construction design into an enterprise virtual test bench with subsequent automatic employment of semantic information for path planning of mobile robots and simulated personnel [11].\u003c/p\u003e\n\u003cp\u003eFigure 2 shows the conceptual architecture of the proposed 3D simulation DSS based on a virtual test bench.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eIntegration of virtual reality technologies into decision support systems.\u0026nbsp;\u003c/strong\u003eAn important aspect of experimental digital twins and virtual test benches is the integration of modern virtual reality (VR) technologies for human-machine interaction. This approach has proven effective in facilitating the understanding of complex systems by specialists from various disciplines through high-quality 3D visualization and informative visual metaphors together with optimization methods.\u003c/p\u003e\n\u003cp\u003eWithin the framework of the proposed decision support system virtual reality performs three key functions:\u003c/p\u003e\n\u003cp\u003e\u0026bull; Immersive visualization \u0026ndash; a 1:1 scale representation of the production system with the ability to freely move and observe technological processes from any point in space.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Interactive experimentation \u0026ndash; an ability to interact directly with elements of the virtual enterprise, change equipment parameters and instantly observe the results of the changes.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Collaborative decision-making \u0026ndash; support for the joint work of several specialists in a common virtual space to reach consensus decisions on production reconfiguration.\u003c/p\u003e\n\u003cp\u003eFigure 3 shows a detailed architecture for integrating a VR component into the proposed DSS.\u003c/p\u003e\n\u003cp\u003eFigure 3. Architecture for VR technologies integration into the DSS for production planning\u003c/p\u003e\n\u003cp\u003eThe developed framework supports various interaction scenarios with the virtual enterprise model for decision makers. The main types of interactions implemented in the modern VR systems for industrial planning are summarized in Table 2.\u003c/p\u003e\n\u003cp\u003eTable 2. Types of user interaction with the virtual production environment\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eType of interaction\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eDescription\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eTechnical implementation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eApplication in planning\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eNavigation and visibility\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eFree overview of the virtual workshop, inspection of equipment from different angles\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eTransition between scenes, smooth movement (using the joystick), scaling (\u0026quot;fly-by-fly\u0026quot;)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eInitial layout overview, identification of collisions and bottlenecks\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eObject manipulation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eCapturing, moving, rotating, installing equipment\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eCapture with controllers with feedback (visual and haptic)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eEquipment layout, workstations\u0026rsquo; ergonomics check\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eParameters\u0026rsquo; change\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eSetting up equipment operating modes, setting speeds, loading\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eVoice commands, virtual controls and menus\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eOptimization of operating modes, performance analysis\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eScenario modeling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eRunning predefined scenarios (\u0026quot;what-if\u0026quot;), comparing options\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eSelect from a virtual menu, voice activation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eProduction performance evaluation, alternative configuration assessment, incident situation analysis\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eCollaborative work\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eMultiple users co-locating, discussing solutions\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eAvatars with pose and gesture transmission, voice communication\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eCollective decision-making, coordination of changes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eAnnotation and markup\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eApplying virtual notes, comments, and instructions\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eDrawing in space, placing text labels\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eRecording comments, transferring tasks, documenting decisions\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThe effectiveness of VR integration into production planning processes is confirmed by a number of industrial implementations. For example, BMW Group is actively developing the \u0026quot;Virtual Factory\u0026quot; concept based on the NVIDIA Omniverse platform, which has reduced the time for collision detection from 4 weeks to 3 days and predicts planning costs reduction up to 30% [7]. Northrop Grumman has developed the HIVE (Highly Immersive Virtual Environment) system, which combines motion capture with Siemens Process Simulate for the ergonomic analysis of assembly operations [2]. In the VITAMINE_5G research project, a virtual reality environment was created for decentralized monitoring of additive production processes. [11].\u003c/p\u003e"},{"header":"4. Multi-criteria optimization of enterprise configurations","content":"\u003cp\u003eTo enable automatic combination of simulated variants in non-trivial problems optimization algorithms are applied, since the number of possible configurations increases exponentially with the number of variation points. Due to the fact the selected optimization algorithm must be applicable to an arbitrary enterprise model, and an analytical representation of the objective function is generally unavailable, black-box optimization algorithms are preferred. Conflicting objectives typical for enterprise planning and adaptation tasks explains the application of multicriteria algorithms of this group with more detailed reviews presented in the papers. The interaction of modules describes the data flow in the process of searching for an optimal solution. The task of configuration search can be formalized as follows.\u003c/p\u003e \u003cp\u003eLet C be a set of all possible configurations of an industrial enterprise and represent a vector of parameters describing the structure and operating modes of the production system:\u003c/p\u003e \u003cp\u003eС = (p\u003csub\u003e1\u003c/sub\u003e, p\u003csub\u003e2\u003c/sub\u003e, \u0026hellip;, p\u003csub\u003en\u003c/sub\u003e),\u003c/p\u003e \u003cp\u003ewhere pi are either discrete (e.g., equipment type, number of machines) or continuous (e.g., conveyor speed, processing temperature) parameters.\u003c/p\u003e \u003cp\u003eTo evaluate a configuration quality, a vector criterion (objective function) F(c) is used, which associates each configuration c with a set of k key performance indicators (KPIs):\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\text{F}\\left(\\text{c}\\right)=\\left(\\genfrac{}{}{0pt}{}{{f}_{1}\\left(\\text{c}\\right)}{\\begin{array}{c}{f}_{2}\\left(\\text{c}\\right)\\\\\\:\\dots\\:\\\\\\:{f}_{k}\\left(c\\right)\\end{array}}\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWithin the production planning, the components of the vector F(c) may include (but are not limited to):\u003c/p\u003e \u003cp\u003ef1(c) \u0026mdash; production volume (units);\u003c/p\u003e \u003cp\u003ef2(c) \u0026mdash; production program costs (monetary units);\u003c/p\u003e \u003cp\u003ef3(c) \u0026mdash; production cycle time (hours);\u003c/p\u003e \u003cp\u003ef4(c) \u0026mdash; equipment utilization rate (%);\u003c/p\u003e \u003cp\u003ef5(c) \u0026mdash; production inventories (units).\u003c/p\u003e \u003cp\u003eIt is assumed that all fi(c) indicators are reduced to a form where a lower value is preferable (i.e., a minimization problem is being solved). If any indicator needs to be maximized (e.g., productivity), it can be taken either with the opposite sign or transformed.\u003c/p\u003e \u003cp\u003eSince improving one indicator often leads to a degradation in another (for example, increasing production volume may increase inventory or production costs), we cannot search for a single \"perfect\" solution. Instead, we seek a set of compromise solutions. The multi-criteria optimization task then consists of finding a set of Pareto-optimal configurations P*, which is formally defined as follows:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:{\\varvec{P}}^{\\varvec{*}}=\\{\\varvec{c}\\in\\:\\varvec{C}\\mid\\:\\nexists\\:\\varvec{c}\\varvec{{\\prime\\:}}\\in\\:\\varvec{C}:\\varvec{F}(\\varvec{c}\\varvec{{\\prime\\:}})\\prec\\:\\varvec{F}(\\varvec{c}\\left)\\right\\}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere the symbol ≺ denotes the Pareto dominance relationship.\u003c/p\u003e \u003cp\u003eAccording to the formula, vector F(c') dominates vector F(c) if c' is not worse than c in any of the indicators and c' is strictly better in at least one indicator. In other words, configuration c' is better than configuration c if it is not inferior to it in any indicator and is superior in at least one. The set P* is called the Pareto set (or Pareto-optimal frontier). Any configuration not belonging to P* can be improved in at least one indicator without degrading the others.\u003c/p\u003e \u003cp\u003eIt is important to emphasize that the function F(c) is not defined analytically. The value of F(c) for a specific configuration c can only be obtained as a result of a computational experiment using a simulation model (virtual test bench). This is the so-called black-box optimization problem. Considering the complexity and stochastic nature of the objective function (the simulation result), the use of gradient methods is impossible. In this context, metaheuristic algorithms, such as evolutionary algorithms [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], are preferable.\u003c/p\u003e \u003cp\u003eTo speed up convergence, surrogate modeling can be used [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], where based on previously conducted experiments, an approximation of the objective function F(c) landscape is constructed and the promising candidates are selected for simulation on a virtual test bench.\u003c/p\u003e \u003cp\u003eThe end user of the system is the decision maker, who is not required to be an expert in either simulation modeling or optimization. Therefore, the interface must translate complex optimization results into an intuitive clear form. Interactive radial charts (radar diagrams) are an effective tool for visualizing multidimensional data [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe diagram displays multiple broken lines, each representing a separate enterprise configuration from the Pareto-optimal set. Interactive control elements (sliders or threshold values on the axes) allow decision makers to dynamically filter the displayed configurations. For example, by setting a minimum acceptable performance level, the user immediately sees which Pareto-optimal solutions satisfy this condition and how other indicators change. This approach proposed in [\u003cspan additionalcitationids=\"CR17\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] enables decision makers to explore trade-offs and select a configuration based on their strategic priorities.\u003c/p\u003e"},{"header":"5. Conclusion and future research directions","content":"\u003cp\u003eThis paper proposes a concept for a three-dimensional decision support system designed for adaptive planning of industrial enterprises. Its novelty lies in the integration of hybrid modeling methods (virtual test benches), automatic generation of configuration variants and multi-criteria optimization in a single tool designed for the end user—a strategic decision maker.\u003c/p\u003e\n\u003cp\u003eThe analysis proved that the existing commercial and academic solutions cover only certain aspects of the problem failing to provide a comprehensive approach. The proposed architecture and formalized statement of the optimization problem (1) provide the basis for the practical implementation of such a DSS.\u003c/p\u003e\n\u003cp\u003eFurther research will focus on:\u003c/p\u003e\n\u003cp\u003e1. Developing protocols for seamless interaction between heterogeneous computing modules (DES and quasi-continuous) within a single virtual test bench.\u003c/p\u003e\n\u003cp\u003e2. Studying the effectiveness of various multi-criteria optimization algorithms (NSGA-II, MOPSO, etc.) and surrogate modeling methods for solving industrial enterprise planning problems.\u003c/p\u003e\n\u003cp\u003e3. Development and validation of a system prototype using real production cases to evaluate the economic impact of the proposed approach.\u003c/p\u003e\n\u003cp\u003e4. Development of intuitive clear visualization methods beyond radial diagrams to handle the uncertainty and stochasticity of modeling results.\u003c/p\u003e\n\u003cp\u003eImplementation of the proposed concept will improve the validity and speed of decision-making when reconfiguring production systems, which is a critical factor for competitiveness for the modern industry.\u003c/p\u003e"},{"header":"Statements \u0026 Declarations","content":"\u003cp\u003eAcknowledgments\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Ministry of Science and Higher Education of the Russian Federation under project №70-2025-000835 from 04 June 2025.\u003c/p\u003e\n\u003cp\u003eAvailability of Data and Materials\u003c/p\u003e\n\u003cp\u003eNo datasets were generated or analyzed during the current study\u003c/p\u003e\n\u003cp\u003eAll authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Nezhmetdinov R.A., Kovalev I.A.. Charuyskaya M.A., Kryzhanovskaya A.S., Bilchuk M.A. The first draft of the manuscript was written by Nezhmetdinov R.A. and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.\u0026rdquo;\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Ministry of Science and Higher Education of the Russian Federation under project №70-2025-000835 from 04 June 2025.\u003c/p\u003e\n\u003cp\u003eThe authors have no relevant financial or non-financial interests to disclose.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eJ. C. N\u0026ouml;cker: Zustandsbasierte Fabrikplanung: Zugl.: Aachen, Techn. Hochsch., Diss., 2012. 1. Aufl. Vol. 2012,6. Edition Wissenschaft Apprimus. Aachen: ApprimusVerl., 2012.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eSlack, N., Operations management/ N. Slack, A. Brandon-Jones, R. Johnston. - Italy: Pearson, 2013. -713p\u003c/li\u003e\n \u003cli\u003eAndreev, V.N., Charuyskaya, M.A., Kryzhanovskaya, A.S.\u0026nbsp;et al.\u0026nbsp;Application of intelligent engineering in the planning of cyber-physical production systems.\u0026nbsp;Int J Adv Manuf Technol\u0026nbsp;115, 117\u0026ndash;123 (2021).\u003c/li\u003e\n \u003cli\u003eHeilala J, Montonen J, J\u0026auml;rvinen P, Kivikunnas S (2010) Developing simulation-based Decision Support Systems for customer-driven manufacturing operation planning. In: Proceedings of the 2010 Winter Simulation Conference (WSC), pp 1-12\u003c/li\u003e\n \u003cli\u003eTrigueiro de Sousa Junior W, Barra Montevechi JA, de Carvalho Miranda R, Teberga Campos A (2019) Discrete simulation-based optimization methods for industrial engineering problems: A systematic literature review. Computers \u0026amp; Industrial Engineering 128:1-12.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eKritzinger, W., Karner, M., Traar, G., Henjes, J., \u0026amp; Sihn, W. (2018). Digital Twin in manufacturing: A categorical literature review and classification.\u0026nbsp;*IFAC-PapersOnLine, 51*(11), 1016-1022. DOI: 10.1016/j.ifacol.2018.08.474\u003c/li\u003e\n \u003cli\u003eT. Bauernhansl, J. Kr\u0026uuml;ger, G. Reinhart, et al.: WGP-Standpunkt Industrie 4.0. Tech. rep. Wissenschaftliche Gesellschaft f\u0026uuml;r Produktionstechnik WGP e.V., 2016. url: https://www.ipa.fraunhofer.de/content/dam/ipa/de/documents/ Presse / Presseinformationen / 2016 / Juni / WGP _ Standpunkt _ Industrie _ 40 . pdf\u003c/li\u003e\n \u003cli\u003eP. Goodall, R. Sharpe, and A. West: A data-driven simulation to support remanufacturing operations. In: Computers in Industry 105 (2019), pp. 48\u0026ndash;60. issn: 0166-3615. doi: 10.1016/j.compind.2018.11.001 (cit. on p. 28).\u003c/li\u003e\n \u003cli\u003eNezhmetdinov RA, Charuiskaya MA, Kovalev IA (2023) Enterprise Development Planning and AI-Based Technological Forecasting. Russian Engineering Research 43(10):1284\u0026ndash;1288.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eM. Schluse, M. Priggemeyer, L. Atorf, et al.: Experimentable Digital Twins - Streamlining Simulation-based Systems Engineering for Industry 4.0. In: IEEE Transactions on Industrial Informatics (2018), p. 1.\u003c/li\u003e\n \u003cli\u003eSchluse, M., Priggemeyer, M., Atorf, L., \u0026amp; Rossmann, J. (2018). Experimentable Digital Twins - Streamlining Simulation-based Systems Engineering for Industry 4.0.\u0026nbsp;IEEE Transactions on Industrial Informatics, 14(4), 1722-1731. DOI: 10.1109/TII.2018.2804917\u003c/li\u003e\n \u003cli\u003eRo\u0026szlig;mann, H.-J. (Betreuer), \u0026amp; Rumpe, B. (Betreuer). (2022).\u0026nbsp;Parallele Simulation interagierender Digitaler Zwillinge in Virtuellen Testbeds\u0026nbsp;(Dissertation). RWTH Aachen University.\u003c/li\u003e\n \u003cli\u003eDelbr\u0026uuml;gger, T., Lenz, L. T., \u0026amp; Rossmann, J. (2017).\u0026nbsp;From BIM to digital twin: A holistic approach for building and production system simulation. In\u0026nbsp;Proceedings of the 2017 Winter Simulation Conference (WSC)\u0026nbsp;(pp. 1-12). IEEE. DOI: 10.1109/WSC.2017.8247973\u003c/li\u003e\n \u003cli\u003eH\u0026uuml;lsmann, M., \u0026amp; Windt, K. (Eds.). (2007).\u0026nbsp;Understanding Autonomous Cooperation and Control in Logistics: The Impact of Autonomy on Management, Information, Communication and Material Flow. Springer.\u003c/li\u003e\n \u003cli\u003eInformation Visualization: Perception for Design, Ware, C., 2013, Elsevier Science\u003c/li\u003e\n \u003cli\u003eSchluse M., Priggemeyer M., Atorf L., Rossmann J.\u0026nbsp;Experimentable Digital Twins \u0026mdash; Streamlining Simulation-based Systems Engineering for Industry 4.0 // IEEE Transactions on Industrial Informatics. \u0026ndash; 2018. \u0026ndash; Vol. 14, No. 4. \u0026ndash; P. 1722-1731. \u0026ndash; DOI: 10.1109/TII.2018.2804917.\u003c/li\u003e\n \u003cli\u003eNezhmetdinov R, Kovalev I, Chumak R (2023) Modeling the Interaction of Technological Objects at Production Sites in a Virtual Reality Environment. In: 2023 International Russian Automation Conference (RusAutoCon), IEEE, pp 900\u0026ndash;904.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eChumak RR, Nezhmetdinov RA, Nezhmetdinova RA, Nikitin DV (2025) Approaches to the Implementation of Simulators for Training Engineering Personnel Using Virtual Reality Technologies. Russian Engineering Research 45(3):392\u0026ndash;397.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eNezhmetdinov RA, Kovalev IA, Charuiskaya MA, Kryzhanovskaya AS (2023) Architectural Solutions and Design Models for a System of Intelligent Forecasting and Assessment of Promising Technologies in Industry. In: 2023 International Russian Automation Conference (RusAutoCon), IEEE, pp 494\u0026ndash;498.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"decision support system (DSS), digital twin, simulation modeling, production flexibility, discrete-event simulation, virtual test bench, multi-criteria optimization, production planning","lastPublishedDoi":"10.21203/rs.3.rs-9606058/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9606058/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn a dynamically changing market environment, industrial enterprises are faced with the need to quickly adapt production systems to achieve key performance indicators. Traditional decision support systems (DSS) often lack sufficient flexibility and visual clarity to analyze multiple alternative configurations of an enterprise. This article presents a conceptual approach for developing a simulation-based modeling DSS with visualization of results in a virtual reality environment designed for enterprise planning. Based on a critical analysis of modern methods (discrete-event simulation (DES), systems based on differential-algebraic equations (DAE), quasi-continuous simulators), their limitations have been identified in the context of modeling and optimizing complex, combinatorially variable design alternatives for enterprise entities. As a solution, an architecture is proposed that integrates the concept of virtual test benches and experimental digital twins. Particular attention is paid to the use of multi-criteria \"black box\" optimization methods in combination with surrogate modeling in search for Pareto-optimal configurations. This paper describes the requirements for a user interface based on interactive radial diagrams, enabling decision makers to effectively navigate the solution space. The proposed approach aims to cover the gap between complex engineering calculations and strategic planning needs, serving as a tool for justified decision-making regarding enterprise configuration under uncertain conditions.\u003c/p\u003e","manuscriptTitle":"Elaboration of a Concept for a Simulation-Based Modelling and Decision Support System Employing Virtual Reality Technology for Adaptive Planning in Industrial Enterprises","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-18 09:49:20","doi":"10.21203/rs.3.rs-9606058/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"cdec4e95-c67b-4496-92d8-c312f7633002","owner":[],"postedDate":"May 18th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Reject, do not transfer","date":"2026-05-17T08:53:48+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2026-05-11T15:01:20+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-05-07T12:44:22+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-05-06T01:49:33+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-05-22T15:29:06+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-18 09:49:20","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9606058","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9606058","identity":"rs-9606058","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}