Optimal managerial decision model in a closed-loop supply chain for a retailer to collect used products with different transfer policy

In recent years, the concerns of environmental and resource issues are growing. Due to a great deal of attention for closed-loop supply chains, collection behaviour of used products from public consumers becomes more and more important. This paper proposes an inventory model for retailer with new products and used products and the retailer is the decision maker who follows the rule of Economic Ordering Quantity (EOQ) model. We assumed that the retailer not only sells products but also collects those sold used products. The proposed problem faced by the retailer is formulated as a cost-minimization problem where the replenishment quantity of new products and the return rate of used products are the decision variables and an efficient iterative algorithm is provided to search for the solution. Furthermore, we extend our model to consider the "not lot for lot policy" inventory model for forward channel and reverse channel and determine the optimal management policy. Finally, we discuss the economical decision modelling for a retailer to analyse the willingness of collecting used products