Building a sustainability in a two-echelon closed loop supply chains: a mathematical approach for permissible delay in payment and backlogging

This paper develops a supply chain framework where payments take place with permissible delays. Unlike other studies, the is modelled as closed-loop system, in which returning products incorporated into classical models and full backorder permitted. Among most important research questions order amount of members to maximize Retailer delays profit chains. The study determines portion time interval inventory system experiences shortage optimal replenishment frequency. Ultimately, it was shown that, if delay from supplier retailer increases, also increases. For all three proposed models, closed-form solution developed algorithm presented. Applying coordinated model considerably increases total earned by whole SC well members. An example our bottle for drink producer. Another military oriented. Furthermore, elaborates feasibility suggested means some numerical examples discusses results using sensitivity analysis.