Time-Dependent Holding Cost in Inventory Models for Deteriorating Items: A Linear and Nonlinear Approach

This study presents a dynamic inventory model, which includes time-dependent product deterioration and holding cost variations. The model assumes exponential product deterioration, one merchant with multiple consumers, and no shortages or lead times. It also assumes the products that are deteriorated will not be repaired or replaced, which happens only at the end of the inventory cycle. The dynamics of the inventory are represented using differential equations subject to certain boundary conditions that take into account demand and product deterioration, defined over discrete time periods. The framework measures the total inventory cost — the cost associated with sales, holding, deterioration, and ordering — from both the consumer perspective and the merchant perspective as collaborative approach, and noncollaborative approach. The numerical study of the inventories measures the total profit using a variety of parameter values to show the effect of different rates of the deterioration, with the associated holding cost and ordering costs. The numerical study also used a sensitivity study to assess the effect of varying the parameters and phenomena visually and contingently displayed total inventory cost and profit maximization. This inventory model contributes to the academic body of literature in inventory management of a framework that can manage time-related deterioration of inventories. The overall significance of the findings will add value to strategic decision-making in commercial enterprises where perishable or degradable products are produced, aimed at increasing efficiency and cost-effectiveness in the inventory.