Optimum operational schedule and accounts receivable financing in a production supply chain considering hierarchical industrial status and uncertain yield

• Investigated operational decisions and accounts receivable financing decisions. • Optimized decisions for the SME, CE and CB under hierarchical industrial status. • Addressed uncertain yield and market demand in production supply chain finance. • Proposed a nonlinear model to integratively determine loan quota and interest rate. • Provided implications and suggestions on improving financing circumstance of SMEs. Consider a production supply chain system, in which a small- and medium-sized enterprise (SME) supplies products to and has accounts receivable (AR) from a core enterprise (CE), and the SME collateralizes the AR to a commercial bank (CB) for a loan to make production. We address and model hierarchical industrial status of the SME, CE, and CB and the uncertainties in SME's production yield and market demand. The production decisions on the order quantity of the CE and the production quantity of the SME are determined through a Stackelberg game, and the AR loan contract that specifies the loan quota and interest rate is determined by the CB by means of optimizing its expected profit while satisfying the requirements from the SME. We derive the analytical optimal conditions for these decisions and demonstrate the effects of the market value of AR, upper bound of loan interest rate, production yield uncertainty, and market demand uncertainty on the operational decisions and the AR loan contract through sensitivity analysis. The analytical approach and results and numerical findings provide decision tools and advice for production schedules and loan application of the SME as well as suggestions for intervention of macro regulations.