An EPQ-based optimization approach to variable-rate screening in supply chain production systems

Abstract

This study presents a comprehensive framework for optimizing the Economic Production Quantity (EPQ) with variable screening rates under two distinct inspection scenarios: Sufficient-Inspection-Rate (IRS) and Insufficient-Inspection-Rate (IRI). In the IRS scenario, the production system employs a high screening rate exceeding the production rate, enabling immediate inspection post-production to segregate imperfect and perfect items. Conversely, the IRI scenario features a slower screening rate relative to production, with inspection occurring post-production completion. The study incorporates inspection costs, and the percentage of imperfect items detected using decreasing exponential functions dependent on screening rate. A Sequential Quadratic Programming (SQP) approach is employed to solve both nonlinear models efficiently.

The analysis demonstrates that adopting a high screening rate (Model I) offers significant production efficiency and cost-effectiveness advantages. For instance, the total cost under the IRS scenario is approximately $394,522, which is notably lower than that of the IRI scenario. A comprehensive sensitivity analysis shows that holding cost, defect rate, and inspection parameters significantly influence both the production quantity and total cost, with the IRI scenario being more sensitive to these changes. These findings underscore the importance of selecting appropriate inspection strategies based on operational constraints and cost dynamics.