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 study explores the effect of delayed differentiation on a multiproduct vendor-buyer integrated inventory system with rework to identify its potential benefits and provide managers with in-depth information for operational decision-making. The main considerations of the proposed study include a multiproduct fabrication plan to increase machine utilization, a rework process to ensure product quality, and a multi-shipment policy to distribute the end products. In addition, these products sharing an intermediate part for which a two-stage fabrication scheme is adopted, wherein the common parts are produced at the first stage and the end products are manufactured at the second stage. The aim is to reduce the overall system costs and shorten the replenishment cycle time. Mathematical modeling and optimization methods were employed to derive the closed-form optimal replenishment cycle time and delivery decisions. We demonstrated the applicability of our research results through numerical examples and revealed that for both linear and nonlinear relationships between the common intermediate part's completion rate α and its practical value at α, our proposed two-stage production scheme with delayed differentiation is considerably beneficial vis-à-vis single-stage schemes in saving overall system costs and reducing the replenishment cycle time.

This study is concerned with the replenishment-shipment decision for a multi-customer finite production rate (FPR) model with quality assurance and discontinuous deliveries. We consider that a product is manufactured by a producer and all items are screened for quality control purpose. Nonconforming items will be picked up and categorized as scrap or repairable items. The reworking will be done right after the regular production in each replenishment cycle. After the entire lot is quality assured, multiple shipments will be delivered synchronously to multi-customer in each cycle. Each customer has its own annual product demand, unit stock holding cost, as well as fixed and variable product delivery costs. Mathematical modeling along with Hessian matrix equations is employed to solve the proposed model. A closed-form optimal replenishment-shipment policy for such a specific integrated FPR model is obtained. A numerical example is provided to show the practical applicability of the obtained results.

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.

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