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