A comparative study of deterministic and probabilistic inventory control model

Abstract

In modern inventory systems, managing the dual challenges of variable demand and item. deterioration is critical for minimizing operational costs. This study proposes two inventory models deterministic and probabilistic incorporating a logarithmic demand function and a quadratic deterioration rate under constant holding cost conditions. The deterministic model assumes complete certainty in system parameters, while the probabilistic model integrates demand variability by incorporating safety stock to achieve desired service levels. Mathematical models are developed using differential equations and solved for optimal inventory policies. Sensitivity analysis on key parameters such as deterioration rate, holding cost, and demand variability reveals critical insights. Results show that the probabilistic model offers greater resilience against demand uncertainty but at the cost of slightly higher holding costs. In contrast, the deterministic model is optimal under highly stable demand conditions. This study provides practical guidance for selecting appropriate inventory strategies based on operational environments, contributing valuable insights to both academic research and industrial practice.