Optimal ordering policy in a two-echelon supply chain model with variable backorder and demand uncertainty

The paper investigates a two-echelon production-delivery supply chain model for products with stochastic demand and backorder-lost sales mixture under trade-credit financing. manufacturer delivers the retailer’s order quantity in number of equal-sized shipments. replenishment lead-time is such that it can be crashed to minimum duration at an additional cost treated as investment. Shortages inventory are allowed occur partially backlogged backlogging rate dependent on customer’s waiting time. Moreover, offers retailer credit period which less than reorder interval. formulated find optimal solutions quantity, safety factor, lead time, shipments from light both distribution-free known distribution functions. Two solution algorithms provided obtain decisions integrated system. effects controllable backorder financing illustrated through numerical examples.