Sustainable EOQ and EPQ models for a two-echelon multi-product supply chain with return policy

In this work, a new model is developed to determine optimum sustainable economic order quantity (EOQ) and economic production quantity (EPQ) values for multiple products of a supply chain with two echelons, consist of a retailer and a supplier, considering product return policy. Based on a literature review on previous related works in sustainable inventory area, 17 different sustainability cost functions, in three types of economic, environmental and social, are defined to form the profit functions of the retailer and the supplier as the main members of the chain. We formulate the profit function of each members of the chain using direct accounting approach as a careful method, considering sustainability costs and return policy to produce and supply multiple products. Two different scenarios for product return are studied considering return amount as a variable or a given parameter. After a numerical example according to an Iranian supply chain that supplies various petrochemical products, a sensitivity analysis related to three parameters of the problem that imposed return functions of products has been conducted. The results show that the total profit amount of each members of the sustainable supply chain is sensitive on the return parameters with different rates.