Stochastic Resilience in Operations Management Using Ito Diffusion and Gamma Catastrophe Processes

Abstract

This study introduces a novel Ito diffusion model for operations management, addressing the challenge of maintaining resilience in supply chains and production networks against unpredictable disruptions. The model incorporates a general catastrophe process with a low occurrence rate, using stochastic methods to represent disruption magnitudes as gamma distribution variables. It provides an analytical framework detailing the process's mean, variance, and sample path. Applying this model across various operational scenarios demonstrates its practical significance. By examining the impacts of disruptions on operational efficiency, the model offers insights into disruption dynamics, crucial for resilience planning and risk mitigation. The findings enhance logistics networks' resilience and efficiency, aiding decision-makers in navigating disruptions. This research presents a practical tool for decision-making in operations management and sets the stage for future research with complex variables and emerging technologies to enhance predictive strength in a dynamic environment.