This paper studies the optimal production run time in an economic manufacturing quantity (EMQ) model with imperfect rework and Poisson machine breakdowns under abort/resume (A/R) control policy. In most realistic manufacturing processes, generation of defective items and random machine breakdowns are inevitable. In this study, a random defective rate is assumed and all defective items produced are reworked when regular production ends. The rework process is assumed to be imperfect. A proportion of reworked items fail during the reworking and become scrap. The system is subject to random breakdowns. The A/R inventory control policy is adopted when breakdowns occur, under such a policy, and the production of the interrupted lot will be immediately resumed when the machine is fixed and restored. Mathematical modelling is used and the integrated long-run average production-inventory cost per unit time is derived. Theorems on conditional convexity and on bounds of optimal production run times are proposed and proved. A recursive searching algorithm is developed for locating the optimal run time within the bounds, which minimizes the expected production-inventory costs. A numerical example with sensitivity analysis is provided to give insight into the operational planning and control of such a realistic production system.

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.