Supply chain contract design under financial constraints and bankruptcy costs

We study contract design and coordination of a supply chain with one supplier and one retailer, both of which are capital constrained and in need of short-term financing for their operations. Competitively priced bank loans are available, and the failure of loan repayment leads to bankruptcy, where default costs may include variable (proportional to the firm's sales) and fixed costs. Without default costs, it is known that simple contracts (e.g., revenue-sharing, buyback, and quantity discount) can coordinate and allocate profits arbitrarily in the chain. With only variable default costs, buyback contracts remain coordinating and equivalent to revenuesharing contracts but are Pareto dominated by revenue-sharing contracts when fixed default costs are present. Thus, for general bankruptcy costs, contracts without buyback terms are of most interest. Quantity discount contracts fail to coordinate the supply chain, since a necessary condition for coordination is to proportionally reallocate debt obligations within the channel. With only variable default costs and with high fixed default costs exhibiting substantial economies-of-scale, revenue-sharing contracts with working capital coordination continue to coordinate the chain. Unexpectedly, for fixed default costs with small economies-of-scale effects, the two-firm system under a revenue-sharing contract with working capital coordination might have higher expected profit than the one-firm system. Our results provide support for the use of revenue-sharing contracts with working capital coordination for decentralized management of supply chains when there are bankruptcy risks and default costs.