Economic Order Quantity under Perishability: Analytical and Iterative Approaches to Cost Minimization

Abstract

Perishability is a critical factor in inventory control that necessitates adjustments to traditional models like the Economic Order Quantity (EOQ). This paper explores the EOQ problem under perishable conditions and employs numerical and analytical methods to derive optimal ordering policies. The study is structured around three cases: (i) calculating EOQ with a fixed percentage of perishable goods, (ii) calculating EOQ with time-based perishability, and (iii) determining the optimal ordering time interval with time-based perishability. To solve the transcendental equations that arise, particularly in cases (ii) and (iii) due to the introduction of time-sensitive decay, the paper utilizes both a numerical iterative method and the Newton-Raphson method.
The numerical method iteratively refines the EOQ or ordering interval until convergence, while the Newton-Raphson method employs derivatives of the cost function to find the optimal solution. The comparison of the two solution methods reveals that while both converge to similar EOQ values, the Newton-Raphson method generally provides a more precise and cost-effective solution, especially in cases with time-dependent perishability.