Random Scrap Rate Effect on Multi-Item Finite Production Rate Model with Multi-Shipment Policy

Abstract

This study investigates the effect of random scrap rate on multi-item Finite Production Rate (FPR) model with multi-shipment policy. The classic FPR model considers production planning for single product, a perfect condition during the production run and a continuous inventory issuing policy. However, in real life manufacturing environments, in order to maximize machine utilization, vendors often make plan to produce m products in turn on a single machine. Also, in any given production run due to various different factors, generation of nonconforming items is inevitable. In this study, it is assumed that these defective items cannot be repaired, thus they must be scrapped with an additional cost and delivery of finished products is under a practical multiple shipment policy. Our objective is to determine an optimal common production cycle time that minimizes the long-run average cost per unit time and to investigate the effect of random scrap rate on the optimal common cycle time. Mathematical modeling is employed and renewal reward theorem is used to cope with the variable cycle length. The expected system cost for the proposed multi-item FPR model is derived and its convexity is proved. A closed-form optimal common production cycle time is obtained. A numerical example and sensitivity analysis is provided to demonstrate the practical use of the obtained results.