Optimal production cycle time for multi-item FPR model with rework and multi-shipment policy

This paper determines the optimal common production cycle time for a multi-item finite production rate (FPR) model with rework and multi-shipment policy. The classic FPR model considers production planning for a single product with perfect quality production and a continuous issuing policy. However, in real life production environments, vendors often plan to produce multiple products in turn on a single machine in order to maximize the machine utilization. Also, due to various uncontrollable factors, generation of nonconforming items in any given production run is inevitable. It is also common for vendors to adopt multiple/periodic delivery policy for distributing their finished goods to customers. In this study, it is assumed that all nonconforming items can be reworked and repaired in the same cycle when regular production ends at additional cost per each reworked item. Our objective is to determine the optimal common production cycle time that minimizes the long-run average cost per unit time and to study the effect of rework on the optimal common cycle time for such a specific multi-item FPR model with rework and multi-shipment policy. Mathematical modeling is used, and the expected system cost for the proposed model is derived and proved to be convex. Finally, a closed-form optimal cycle time is obtained. A numerical example and sensitivity analysis is provided to show the practical use of our obtained results