Two-level trade credit with default risk in the supply chain under stochastic demand

In the business world, both the supplier and the retailer accept the credit to make their business position strong, because the credit not only strengthens their business relationships but also increases the scale of their profits. The long period of credit may increase the demand rate but simultaneously it can also increase the credit risk. This paper investigates the two-echelon supply chain model consisting of a supplier supplying a product to a single retailer, which sells this product to the end customers, under the two-level trade credit policy. The supplier offers the retailer a credit time, and the retailer also provides credit time to the end customers for settling the account. The credit time offered by the retailer is lesser than the credit time offered by the supplier, but they both are facing the default risk. Supplier decides to charge compound interest on the principal amount of the retailer if s/he fails to pay within credit time. Whereas, the retailer faces the uncertain demand from customers that may increase the chance of facing stock-out by the customers, taken as partially backlogged. The demand rate of the supplier is dependent on the two decision variables: a) the quantity of the retailer's order; and b) the credit period offered by the supplier. The main objective of this paper is to determine the distribution-free optimal order quantity of the retailer with an optimal credit period of the supplier, which maximize the profitability of the total supply chain. To find the optimal solution mathematical formulation for the supplier and the retailer has been developed in the solution procedure. Adequate numerical example with uniform distribution has been given to justify the solution procedure. Ultimately, sensitivity analysis of the major parameters, managerial implication, with concluding remarks and future research are discussed