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<p>This paper develops two Economic Order Quantity (EOQ) models within a unified optimization framework to examine inventory systems under realistic operational conditions. The proposed two models incorporate quadratic price-dependent demand to capture nonlinear customer behaviour, along with inspection processes for defective items and a learning mechanism with carbon tax that improves operational efficiency over time. The first model (Case 1) represents a baseline system excluding deterioration, inflation, and carbon emission costs, while the second model (Case 2) extends the framework by integrating imperfect item deterioration, inflationary effects, and environmental (carbon) costs. The objective is to jointly determine the optimal selling price and replenishment cycle that maximize total profit. A comparative analysis reveals that Case 1 yields lower profitability and is highly sensitive to shorter replenishment cycles, which increase ordering costs. In contrast, Case 2, despite incorporating additional cost factors, achieves significantly higher total profit and provides a more realistic representation of practical inventory systems. The inclusion of deterioration and sustainability considerations substantially improves economic performance and decision reliability. For finding optimal decision variables- the selling price and replenishment cycle, were determined by maximizing the total profit function for both inventory models by classical optimization technique is utilised. Sensitivity analysis demonstrates that learning rate and price sensitivity are critical parameters influencing optimal decisions and profitability. Numerical results further indicate that a lower optimal selling price in the extended mode (Case-2) stimulates demand, leading to higher overall profit. The results show that the extended model (Case 2) ($ 77,725.43), which incorporates operational factors (learning, inspection, deterioration, and inflation) together with environmental considerations (carbon tax and emission costs), generates approximately 6.6 times higher optimal profit than the baseline model (Case 1) ($ 11,727.23), demonstrating the value of holistic decision-making in modern inventory management.</p>

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Optimizing Sustainable Inventory with Deterioration, Learning, and Carbon Tax Under Time-price Sensitive Quadratic Demand and Inflationary Environment

  • 期刊论文

  • 发表日期：

    2026年7月3日

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  • Vrushali A. Surve,
  • Monika K. Naik

摘要

This paper develops two Economic Order Quantity (EOQ) models within a unified optimization framework to examine inventory systems under realistic operational conditions. The proposed two models incorporate quadratic price-dependent demand to capture nonlinear customer behaviour, along with inspection processes for defective items and a learning mechanism with carbon tax that improves operational efficiency over time. The first model (Case 1) represents a baseline system excluding deterioration, inflation, and carbon emission costs, while the second model (Case 2) extends the framework by integrating imperfect item deterioration, inflationary effects, and environmental (carbon) costs. The objective is to jointly determine the optimal selling price and replenishment cycle that maximize total profit. A comparative analysis reveals that Case 1 yields lower profitability and is highly sensitive to shorter replenishment cycles, which increase ordering costs. In contrast, Case 2, despite incorporating additional cost factors, achieves significantly higher total profit and provides a more realistic representation of practical inventory systems. The inclusion of deterioration and sustainability considerations substantially improves economic performance and decision reliability. For finding optimal decision variables- the selling price and replenishment cycle, were determined by maximizing the total profit function for both inventory models by classical optimization technique is utilised. Sensitivity analysis demonstrates that learning rate and price sensitivity are critical parameters influencing optimal decisions and profitability. Numerical results further indicate that a lower optimal selling price in the extended mode (Case-2) stimulates demand, leading to higher overall profit. The results show that the extended model (Case 2) ($ 77,725.43), which incorporates operational factors (learning, inspection, deterioration, and inflation) together with environmental considerations (carbon tax and emission costs), generates approximately 6.6 times higher optimal profit than the baseline model (Case 1) ($ 11,727.23), demonstrating the value of holistic decision-making in modern inventory management.