When operating in highly competitive business environments, contemporary manufacturing firms must persistently find ways to fulfill timely orders with quality ensured merchandise, manage the unanticipated fabrication disruptions, and minimize total operating expenses. To address the aforementioned concerns, this study explores the optimal runtime decision for a manufacturing system featuring an expedited fabrication rate, random equipment failures, and scrap. Specifically, the proposed study considers an expedited rate that is linked to higher setup and unit costs. The fabrication process is subject to random failure and scrap rates. The failure instance follows a Poisson distribution, is repaired right away, and the fabrication of interrupted batch resumes when the equipment is restored. The defective goods are identified and scrapped. Mathematical modeling and optimization method are used to find the total system cost and the optimal runtime of the problem. The applicability and sensitivity analyses of research outcome are illustrated through a numerical example. Diverse critical information regarding the individual/joint impacts of variations in stochastic time-to-failure, expedited rate, and random scrap on the optimal runtime decision, total system expenses, different cost components, and machine utilization, can now be revealed to assist in in-depth problem analyses and decision makings.

This study employs mathematical modeling to explore the effects of overtime option, rework, and discontinuous end-item issuing policy on the economic manufacturing quantity (EMQ) model. Conventional EMQ model assumed that all products fabricated are of good quality and are issued under continuous policy. In real world, however, nonconforming items are randomly produced, due to diverse unexpected factors in fabrication process. When finished items are to be distributed to outside locations, discontinuous multi-shipment policy is often used rather than continuous rule. In addition, with the intention of increasing short-term capacity or shortening replenishment cycle length to smooth the production planning, adopting overtime option can be an effective strategy. To cope with the aforementioned features in real production systems, this study incorporates overtime option, rework, and multi-shipment policy into the EMQ model and explores their joint effects on optimal lot size and number of shipments, and on other relevant system parameters. Mathematical modeling and Hessian matrix equations enable us to derive the optimal policies to the problem. Through the use of numerical example, the applicability of research result is exhibited and a variety of significant effects of these features on the proposed system are revealed.