In a recent paper, Chiu et al. (2014) utilized mathematical modeling and differential calculus to determine the common production cycle time that minimizes total production, inventory, and delivery costs for a multi-item economic production quantity (EPQ) model with scrap, rework, and multi-delivery. The present study proposes an algebraic approach substituting the use of differential calculus on the system cost function for deriving the optimal common cycle time in the aforementioned multi-item EPQ model. This simplified approach may enable managing practitioners to resolve real multi-item EPQ models more effectively.

This paper is concerned with determining the optimal common production cycle policy for a multi-item economic production quantity (EPQ) model with scrap, rework and multiple deliveries. The classic EPQ model considers the optimal replenishment quantity of single product under a perfect production assumption and a continuous inventory issuing policy. However, in real life production planning, manufacturing firms often plan to have multiple products made in turn on a single machine in order to maximize the machine utilization. Also, dealing with random defective items during the production run seems to be an inevitable task, and the multi-delivery policy is commonly adopted for distributing finished items to customers. In this study, we assume a portion of nonconforming items is scrap and the other portion of them can be reworked and repaired in the same production cycle with additional cost. The objective is to determine an optimal common production cycle time that minimizes the long-run average cost per unit time for such a specific multi-item EPQ model with scrap, rework and multi-delivery policy. Mathematical modeling and analysis is used and a closed-form optimal common cycle time for multi-item production planning is obtained. A numerical example is provided to demonstrate the practical usage of research result.