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<p>When a supplier announces an impending price increase, buyers of perishable products face a complex trade-off: the cost-saving benefit of a large, special advance order must be balanced against the associated holding costs and losses from product deterioration. Traditional special order quantity models are limited by the restrictive assumption of zero inventory at both the start and end of the special-order period, and they often ignore deterioration altogether. This study bridges this gap by developing a unified analytical framework comprising four distinct economic order quantity (EOQ) models for deteriorating items that accommodate all possible real-world inventory states. Specifically, our models allow inventory to be positive or negative (backorders) at both the beginning and the end of the special-order cycle. For each of the four scenarios, we derive closed-form expressions for the total cost and establish a solution procedure to determine the optimal special-order quantity and the resulting maximum savings. Numerical examples validate the models and demonstrate their practical application, while a sensitivity analysis provides key managerial insights. The results show that the proposed models offer a more flexible and realistic decision-support tool for inventory managers, enabling significant cost reduction compared to policies that ignore deterioration or assume idealized inventory conditions.</p>

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Perishable special economic order quantity with price increase at known specific time

  • 期刊论文

  • 发表日期：

    2026年4月4日

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  • Ata Allah Taleizadeh,
  • Alireza Birjandi,
  • Jalal Delaram

摘要

When a supplier announces an impending price increase, buyers of perishable products face a complex trade-off: the cost-saving benefit of a large, special advance order must be balanced against the associated holding costs and losses from product deterioration. Traditional special order quantity models are limited by the restrictive assumption of zero inventory at both the start and end of the special-order period, and they often ignore deterioration altogether. This study bridges this gap by developing a unified analytical framework comprising four distinct economic order quantity (EOQ) models for deteriorating items that accommodate all possible real-world inventory states. Specifically, our models allow inventory to be positive or negative (backorders) at both the beginning and the end of the special-order cycle. For each of the four scenarios, we derive closed-form expressions for the total cost and establish a solution procedure to determine the optimal special-order quantity and the resulting maximum savings. Numerical examples validate the models and demonstrate their practical application, while a sensitivity analysis provides key managerial insights. The results show that the proposed models offer a more flexible and realistic decision-support tool for inventory managers, enabling significant cost reduction compared to policies that ignore deterioration or assume idealized inventory conditions.