Optimizing payment schemes in a decentralized supply chain: A Stackelberg game with quality investment and bank credit

In reality, supply chain members need to determine the best suitable payment scheme when transacting with their business partners. We investigate the optimization of payment schemes with quality investment and bank credit in a decentralized supply chain consisting of one manufacturer and one retailer, both of which are capital constrained and in need of short-term financing from the bank for their operations. First, we provide a function to describe the market demand by analyzing the impacts of price and quality on the demand. Then, we develop the profit functions of advance payment scheme (APS), normal payment scheme (NPS), and delay payment scheme (DPS) for the capital-constrained manufacturer and retailer. Furthermore, we construct the joint pricing and quality level decision models under APS, NPS, and DPS to determine the optimal profits of the supply chain, manufacturer, and retailer, respectively. On this basis, we conduct theoretical and numerical analyses on the selection of the optimal payment scheme. Our research results in manufacturer Stackelberg game indicate that, the optimal payment scheme from the perspective of supply chain, manufacturer or retailer is not uniquely determined, but generally tends to be DPS. For different perspectives, the optimal payment schemes may be different, and can be affected by the parameters. Especially, for increasing bank rate for the loan of the retailer, the supply chain, manufacturer and retailer generally tend to select DPS. In addition, for increasing bank rate for the loan of the manufacturer, the supply chain and retailer tend to select DPS, but the manufacturer tends to select APS.