An Inventory Control Model for Deteriorating Items with Probabilistic Demand Under Delay In Payment and Budget Constraint

Abstract

This study develops an inventory control model for products that experience degradation under probabilistic demand by simultaneously combining delays in permitted payments and budget constraints. In a real operational setting, inventory decisions are increasingly challenged by demand uncertainty, declining product quality, financial constraints, and payment policies offered by suppliers. To overcome this complexity, the probabilistic inventory model is formulated with the aim of minimizing the total cost of inventory per unit of time, which consists of ordering costs, warehouse storage costs, quality degradation costs, shortage costs, and financial storage costs, while taking into account the interest earned during the credit period. This model considers two payment scenarios: when the allowable payment delay occurs before the end of the recharge cycle and when the delay exceeds the length of the cycle. The decision variables in this study are  optimal order lot sizes, safety stock, and reorder points, as well as budget constraints imposed to ensure financial feasibility. Numerical experiments show that extending payment delays beyond the recharge cycle significantly reduces total costs by eliminating financial storage costs. Further sensitivity analysis revealed that the total cost and optimal order quantity were highly sensitive to the cost of ordering, the level of demand, and the rate of damage, while financial parameters showed a relatively marginal influence. These results confirm that the proposed model provides a more realistic and robust decision-support framework for the inventory management of damaged products under conditions of demand uncertainty and financial constraints.