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<p>This study develops a dynamic economic production model for an inventory system with two distinct demand patterns influenced by real-world complexities. The first demand function incorporates price sensitivity and memory effects, while the second integrates selling price, time, and memory influences, capturing realistic market dynamics. The model accounts for partial backlogging with lost sales, ensuring practical relevance. The governing Caputo fractional differential and Riemann-Liouville integral equations are solved via Laplace transforms to capture memory-dependent dynamics effectively. The total profit function is optimized using the Firefly Algorithm (FOA), a robust metaheuristic for complex inventory problems. Numerical simulations and graphical analyses highlight the impact of critical parameters−including memory, price sensitivity, decay, and backlogging rates−on profit maximization. This research offers managerial insights into optimal pricing and production, demonstrating how memory effects and dynamic demand structures influence optimal production and pricing strategies. By integrating advanced demand models with FOA optimization, this study advances decision-making in inventory and supply chain management.</p>

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Optimization of fractional-order EPQ models with memory-dependent demand and shortage dynamics

  • 期刊论文

  • 发表日期：

    2025年10月23日

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  • Poonam Yadav,
  • Vijender Yadav,
  • Trilok Mathur,
  • Chandra Shekhar

摘要

This study develops a dynamic economic production model for an inventory system with two distinct demand patterns influenced by real-world complexities. The first demand function incorporates price sensitivity and memory effects, while the second integrates selling price, time, and memory influences, capturing realistic market dynamics. The model accounts for partial backlogging with lost sales, ensuring practical relevance. The governing Caputo fractional differential and Riemann-Liouville integral equations are solved via Laplace transforms to capture memory-dependent dynamics effectively. The total profit function is optimized using the Firefly Algorithm (FOA), a robust metaheuristic for complex inventory problems. Numerical simulations and graphical analyses highlight the impact of critical parameters−including memory, price sensitivity, decay, and backlogging rates−on profit maximization. This research offers managerial insights into optimal pricing and production, demonstrating how memory effects and dynamic demand structures influence optimal production and pricing strategies. By integrating advanced demand models with FOA optimization, this study advances decision-making in inventory and supply chain management.