Retailer’s optimal replenishment policy in a two-echelon supply chain under two-part delay in payments and disruption in delivery

Now-a-days, the risks associated with transportation have received special attention among the global traders due to the unusual circumstances such as terrorist attack, earth quake, mishandling in transport, shipping damage, misplacing products etc. A mathematical model for an inventory system under such transport risk conditions is highly useful to run the supply chain (SC) smoothly and it paves the way to minimize the total cost incurred. In business, many suppliers offer two-part delay in payments, say $$ (\alpha /M_{1} ,{\text{ net }}M_{2} ) $$ ( α / M 1 , net M 2 ) , in order to attract their retailers. This paper investigates retailer’s inventory system in a SC under the random effect of risk in delivery from a supplier to the retailer. Here, the supplier offers two-part trade credit to his retailer and the retailer in turn offers a full credit period to the customers. The total cost incurred at the retailer’s inventory system is minimized and the optimal replenishment policies are determined. Mathematical theorems are developed and numerical examples are presented to illustrate the sensitivity analysis of inventory key parameters.