Mathematical modelling for a fabrication–inventory problem with scrap, an acceptable stock-out level, stochastic failures and a multi-shipment policy

While planning for batch manufacturing, determining the optimal runtime that minimizes total system costs is equally important and so is maintaining high product quality, keeping the batch process environment free of disruption, and ensuring timely delivery of end products to meet market demand. Owing to the imperfect nature of the fabrication process, both the production of random scrap and machine failures are inevitable and require special treatment. Permitting an acceptable level of shortages with backordering is often considered an effective approach to reduce inventory costs and lower the total system costs. Moreover, for delivering end products, a periodic multi-shipment policy is commonly adopted in real supply chain systems. To cope with the aforementioned realistic factors, this study explores a fabrication–inventory problem that considers scrap items, an acceptable level of stock outs with backordering, stochastic machine failures, and a multi-shipment policy. A mathematical model is built to accurately represent the problem. An optimization method along with an algorithm is presented to derive optimal production uptime that minimizes total system costs. Using a numerical example, we demonstrate that this precise model and its solution process can not only provide an optimal decision, but also reveal diverse and valuable system characteristics including (1) details of cost components of the system and (2) the individual and joint impact of system factors, such as product quality, service-level constraints, machine failures, number of deliveries, and uptime in the proposed problem. Without such an in-depth exploration, these important system characteristics remain inaccessible and unknown to production managers