Financing and coordinating the supply chain with a capital-constrained supplier under yield uncertainty

We consider financing and coordinating issues in a supply chain with one supplier (she) and one manufacturer (he), where the supplier is capital-constrained and her production yield is random. Facing shortage of capital, the supplier may use two financing sources to facilitate her production: bank loan from a commercial bank, or advance payment from the manufacturer. Taking the supply chain with centralized control as a benchmark, we analyze the optimal decisions of the two members in the supply chain. We find that in the optimal decisions, the supplier chooses only one, instead of a combination, of the two financing sources, and the manufacturer is always willing to pay in advance to finance the supplier's production. Furthermore, we propose to use the pay back contract (as well as cost-sharing contract as an extension) for the manufacturer to share the production risk and stimulate the supplier to improve the production yield. Finally, assuming the bargaining process of the supplier and the manufacturer being a Nash bargaining game, we show that the pay back contract under the two sources of financing (bank loan and advance payment) can coordinate the supply chain and flexibly allocate the total profit in the supply chain.