Outsourcing contracts and ordering decisions of a supply chain under multi-dimensional uncertainties

We consider a supply chain in which a manufacturer with random yield sells the product through a retailer, where the overflowed order of the retailer may be fulfilled by the manufacturer's outsourcing product. The inherent uncertainties include demand uncertainty, yield uncertainty, and outsourcing information asymmetry. Two contingent outsourcing contracts are studied based on whether the delivery lead-time quotation is adopted or not. We study how the two outsourcing contracts affect supply chain decision-makings and profits by introducing a backup supplier with private cost information. By employing backward induction technique, we obtain a closed-form analytical solution for backup supplier selection and ordering decisions. The manufacturer can outsource the retailer's overflowed order to a backup supplier when the actual yield is low. In the presence of multi-dimensional uncertainties, there exists robustness for both outsourcing contracts. Depending on both the yield and the backup supplier's cost type, the manufacturer makes one of three choices to outsource production: choosing both types of the backup supplier, choosing only the low-cost backup supplier, or choosing neither. The outsourcing quantity may be a part or all of the retailer's overflowed order. Unlike the contract without constraint on lead-time, the quotation of the delivery lead-time endows the manufacturer with the ability of revealing the true cost information, thus it can improve the manufacturer's outsourcing profit. However, the quotation of delivery lead-time may make the whole supply chain less efficient.