Supply chain with random yield and financing

In this paper, we consider a supply chain consisting of a well-capitalized manufacturer, a well-capitalized and reliable supplier, and a capital-constrained and unreliable supplier with random yield. The interactive relationship among them is modeled as a Stackelberg game with the manufacturer as the leader and the suppliers as the followers. The optimal production quantity of the suppliers and ordering quantity of the manufacturer are derived. We investigate the manufacturer's optimal sourcing strategy considering a fixed interest rate. The analytical model shows that when external financing is available, the optimal sourcing strategy depends on the interest rate threshold. Specifically, if the interest rate is lower than the threshold, the unreliable channel dominates; otherwise, the reliable channel dominates. When financing is not available and the supply price of the reliable supplier is high, dual-channel sourcing is the optimal choice. Computational studies are performed to explore the impacts of the initial capital and the interest rate on the optimal decisions and profits. It shows capital constraint does not always decrease the attraction of the unreliable supplier for the manufacturer. Actually the attraction of using an unreliable supplier can increase if the interest rate is low or the initial capital of the unreliable supplier is small. Several extensions are considered in this paper. We show the attraction of the unreliable supplier for the manufacturer will increase if the sourcing price from the unreliable supplier is endogenously determined by the manufacturer or the demand is random.