Deterministic and probabilistic inventory models with quadratic deterioration and exponential demand

Abstract

This study presents a comprehensive analysis of deterministic and probabilistic inventory models considering quadratic deterioration rates and exponential demand growth. The models integrate holding and deterioration costs to evaluate total inventory expenses under both certain and uncertain conditions. The deterministic model provides insights into inventory dynamics and fixed demand and deterioration parameters, while the probabilistic model accounts for stochastic variations. Sensitivity analyses are conducted to examine the effect of deterioration coefficients, demand growth rates, and cost parameters on total costs. Results show that probabilistic models yield higher total costs due to uncertainty, emphasizing the importance of robust inventory management strategies. Heat maps and cost curves further illustrate the interaction between holding and deterioration costs. This analysis aids decision makers in selecting appropriate inventory policies to minimize costs and manage risk effectively.