A deterministic inventory model with quadratic demand, linear deterioration, time-dependent holding cost, and trade credit

This study presents a deterministic inventory model incorporating realistic and dynamic system characteristics such as quadratic demand, time-dependent linear deterioration, and linearly increasing holding costs. The model further accounts for trade credit, allowing the buyer a delay period to settle payments without incurring interest. The primary objective is to minimize the total average cost by optimizing the replenishment cycle length. Inventory depletion over time is governed by a first-order linear differential equation that simultaneously considers both demand and deterioration effects. An explicit expression for the inventory level is derived using integrating factors, and cost functions are formulated to include ordering, holding, and interest costs (if the replenishment cycle exceeds the trade credit period). Sensitivity analysis is performed to examine the impact of variations in key parameters such as demand rate, deterioration coefficient, holding cost rates, and credit period on the optimal cycle time and total cost. Numerical results indicate that parameters like holding cost and demand rate significantly affect both the cost and cycle length, while the trade credit period has a noticeable influence only when the cycle time exceeds the credit period. The model provides valuable insights into real-world inventory management scenarios where demand, cost, and deterioration evolve over time. Graphs and tables support the results, confirming the model’s robustness and applicability for effective decision-making in supply chain environments.