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<p>This study introduces an advanced stochastic differential equation (SDE)-based inventory model for managing perishable goods under demand uncertainty, product deterioration, and shortage-induced lost sales. Addressing the limitations of conventional deterministic frameworks, the proposed model integrates seasonally varying, stock-dependent demand influenced by both Brownian motion and discrete external disruptions. These disruptions, classified by their timing and impact, allow for a nuanced representation of real-world events that cause sudden demand surges or collapses. The inventory depletion is modeled through a continuous-time process incorporating time-dependent deterioration, with shortages accounted for through a lost sales cost structure, reflecting realistic consumer behavior in perishable goods markets. The model evaluates multiple event scenarios across the inventory cycle and employs a Monte Carlo simulation to estimate the average total cost (ATC), including holding, deterioration, and lost sales costs. Results demonstrate that incorporating stochasticity and disruption into inventory decision-making significantly improves cost-efficiency and system resilience. This work contributes a rigorous and adaptable framework suited for dynamic, uncertainty-prone supply chains, offering valuable implications for operational strategy and risk-aware inventory control in global markets.</p>

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Uncertain event-based inventory model with stochastic differential equation framework for perishable goods with deterioration and shortages

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Sourav Nath,
  • Sumit Saha

摘要

This study introduces an advanced stochastic differential equation (SDE)-based inventory model for managing perishable goods under demand uncertainty, product deterioration, and shortage-induced lost sales. Addressing the limitations of conventional deterministic frameworks, the proposed model integrates seasonally varying, stock-dependent demand influenced by both Brownian motion and discrete external disruptions. These disruptions, classified by their timing and impact, allow for a nuanced representation of real-world events that cause sudden demand surges or collapses. The inventory depletion is modeled through a continuous-time process incorporating time-dependent deterioration, with shortages accounted for through a lost sales cost structure, reflecting realistic consumer behavior in perishable goods markets. The model evaluates multiple event scenarios across the inventory cycle and employs a Monte Carlo simulation to estimate the average total cost (ATC), including holding, deterioration, and lost sales costs. Results demonstrate that incorporating stochasticity and disruption into inventory decision-making significantly improves cost-efficiency and system resilience. This work contributes a rigorous and adaptable framework suited for dynamic, uncertainty-prone supply chains, offering valuable implications for operational strategy and risk-aware inventory control in global markets.