An Economic Order Quantity Model for Flawed Units With Quality Screening and Time Dependent Backlogging

This study introduces an Economic Order Quantity (EOQ) model that addresses inventory systems dealing with imperfect quality items, incorporating both quality screening processes and time-dependent backlogging. Recognizing that a proportion of received items may be defective, the model integrates a screening mechanism to identify and separate flawed units before they reach customers. Additionally, the model considers a backlogging scenario where unmet demand is partially backordered, with the backlogging rate being a function of the waiting time until the next replenishment. The objective is to determine the optimal order quantity and backordering level that minimize the total cost, which includes ordering, holding, screening, backordering and shortage costs. Analytical solutions are derived and numerical examples are provided to illustrate the model's applicability. Sensitivity analyses are conducted to examine the impact of key parameters on the optimal solution.