An EPQ model with a random breakdown, rework, and a discontinuous issuing policy

This study attempts to determine the optimal production run time for an economic production quantity (EPQ) model with a Poisson breakdown rate, the rework of nonconforming items, and multi-delivery of finished products. It is assumed that nonconforming items can be randomly produced and repaired through a rework process added at the end of the production process. Production equipment is subject to a random breakdown, which follows a Poisson distribution. When a breakdown occurs, the machine immediately goes under repair and adopts an abort/resume inventory control policy. Under this policy, the production of the interrupted lot instantaneously resumes when the machine is repaired and restored. Upon completion of the rework process, n fixed quantity installments of the finished batch are delivered to the customer at a fixed interval of time. Mathematical modelling together with a numerical analysis is used in this study. Theorems on the convexity of the expected system cost function and bounds of production uptime are proposed and proved. A recursive searching algorithm is developed to find the optimal replenishment uptime within the bounds. Finally, a numerical example is provided to demonstrate the practical usage of the study results.