When making a batch production decision for a buyer-vendor coordination system, the management must simultaneously consider the operating expenses incurred in in-house manufacturing and inventory, finished goods’ shipping, and stock holding at the retailer end. Achieving the operational goals of desirable quality, minimal production disruption, and shortening fabrication time help minimize overall in-house operating costs and maximize customer satisfaction. This work builds an operating cost minimization model for buyer-vendor coordination batch system with scrap, breakdowns, overtime, multi-shipment, and an external source to assist the management in optimizing their production-delivery plan. Removing inevitable scrap items ensures product quality, and correction action on stochastic equipment breakdown prevents unacceptable production delays. Implementing partial overtime and adopting an external source expedites in-house manufacturing time. Model construction and cost analysis enable us to decide the operating expense function. Then, we verify the function’s convexity and decide our model’s best manufacturing runtime with the differential calculus and a proposed algorithm. Furthermore, the numerical demonstrations are used to exhibit our work’s applicability and show what kinds of crucial in-depth information can be disclosed and made accessible to the production planners for their decision-making.

Manufacturing firms operating in today’s competitive global markets must continuously find the appropriate manufacturing scheme and strategies to effectively meet customer needs for various types of quality of merchandise under the constraints of short order lead-time and limited in-house capacity. Inspired by the offering of a decision-making model to aid smooth manufacturers’ operations, this study builds an analytical model to expose the influence of the outsourcing of common parts, postponement policies, overtime options, and random scrapped items on the optimal replenishment decision and various crucial system performance indices of the multiproduct problem. A two-stage fabrication scheme is presented to handle the products’ commonality and the uptime-reduced strategies to satisfy the short amount of time before the due dates of customers’ orders. A screening process helps identify and remove faulty items to ensure the finished lot’s anticipated quality. Mathematical derivation assists us in finding the manufacturing relevant total cost function. The differential calculus helps optimize the cost function and determine the optimal stock-replenishing rotation cycle policy. Lastly, a simulated numerical illustration helps validate our research result’s applicability and demonstrate the model’s capability to disclose the crucial managerial insights and facilitate manufacturing-relevant decision making.