Optimizing an FPR-based supplier-retailer integrated problem with an outsourcer, rework, expedited rate, and probabilistic breakdown

Internal supply chains exist in many global enterprises, where manufacturing tasks and sales jobs operate separately, but the management needs to integrate their financial performance reports. In addition, the fabrication planning must meet specific operational goals, such as meeting external clients’ requirements on quality and short order due dates, avoiding internal fabricating interruptions due to inevitable equipment breakdowns, and minimizing overall manufacturing and stock holding costs. Motivated by helping multinational corporations deal with the issues mentioned earlier, this study aims to optimize a finite production rate (FPR)-based supplier-retailer cooperative problem with multi-shipment, rework, subcontracting, probabilistic failure, and expedited rate. Wherein using an outsourcer and expedited-rate help shorten the needed batch producing time significantly; the rework of defects and corrective action on unanticipated breakdown assist in up-keeping the quality and avoiding fabricating delay. We develop an FPR-based model to cautiously represent the considered manufacturing features and activities involved in transporting end products and retailers’ stock holding. Model’s formulating and investigating assists us in gaining the function of operating costs. In addition, optimization procedures with a proposed algorithm help us verify its convexity and decide the model’s best fabricating runtime solution. Finally, we validate how this study works and what important information our model can disclose using a numerical example to facilitate management’s decision-making to end our work.