Investigation of the impact of force majeure circumstances as a market instability factor on the flexibility and sustainability of engineering SMEs

INTRODUCTION: Modern manufacturing operates under complex natural, economic, and political conditions. Small and medium-sized enterprises (SMEs), as the most flexible representatives of the engineering industry, small and medium-sized enterprises (SMEs) must account for potential stress factors in their current and future development. Research indicates that enterprises must respond rapidly to such stressors to maintain competitiveness and stability in domestic and international markets. Management decisions to ensure SME resilience should adopt a comprehensive approach, considering economic indicators such as productivity, product quality, logistics, and cost, as well as social aspects like employee safety, workplace conditions, and resource-efficient technologies. This study develops and analyzes a mathematical model describing the impact of various stress factors on the stability of SMEs in the engineering sector under force majeure conditions. The research identifies key stressors, formulates a mathematical model to assess their influence on enterprise resilience, and evaluates the model’s effectiveness over time. The integral flexibility functional serves as the foundation for this model, incorporating market fluctuations, production costs, and force majeure impacts, including quarantine restrictions and enterprise relocation. To optimize this functional, the study employs the automated planning method PPLAN, which is rooted in artificial intelligence. This approach enables the generation of adaptive strategies to mitigate stress factors affecting SME stability. The findings reveal that relocation due to force majeure is the most detrimental factor, leaving minimal time for recovery actions, while demand fluctuations exert a more cyclical influence. The proposed methodology provides a structured framework for enhancing SME resilience in dynamic and unpredictable environments OBJECTIVES: The objective of this paper is to develop a mathematical model that quantifies the impact of stress factors on the stability of small and medium-sized enterprises (SMEs) in the engineering sector under force majeure conditions. The study aims to identify key external and internal stressors, construct a functional model based on the integral flexibility approach, and optimize enterprise resilience strategies using artificial intelligence-based automated planning. By analyzing the model’s effectiveness over time, the research provides a structured framework for enhancing SME adaptability and sustainability in dynamic and unpredictable environments. METHODS: The research employs techniques derived from social network analysis to model and analyze the stability of small and medium-sized enterprises (SMEs) in the machine engineering industry under stress and force majeure conditions. Specifically, the study uses a mathematical model that integrates stress factors like market demand and supply fluctuations, relocation, and quarantine restrictions. The optimization of this model is achieved through automatic planning methods based on the PPLAN approach, which enables the consideration of various anti-stress measures and their impacts on the stability of SMEs over time. Additionally, 3D technologies are identified as critical tools for enhancing the flexibility and adaptability of production processes during external stresses. RESULTS: The main results of this paper include the development of a mathematical model for analyzing the impact of stress factors on the stability of SMEs in the machine engineering sector. Additionally, optimizing the model using the PPLAN method demonstrated the effectiveness of 3D technologies in enhancing the adaptability and resilience of SMEs under force majeure conditions. CONCLUSION: This paper concludes that integrating 3D technologies and using the PPLAN optimization method can significantly improve the stability and adaptability of SMEs in the machine engineering sector during stress and force majeure events.