Mathematical models are used in many areas of supply chain management. Here, we present a mixed-integer non-linear programming (MINLP) model to solve a multi-period, closed-loop supply chain (CLSC) with two echelons of producers and customers. To satisfy the customers’ demands, the manufacturer must produce the product,; so, they have to order materials at the beginning of each period for the current or later periods. A fleet of heterogeneous vehicles is routed to deliver the products from the producers to the customers and to pick up defective products from the customers to transport to the collection-repair center. The objective function maximizes the profit, which is equal to total cost minus income. The income is divided into two parts (selling products and wastes), and the total cost consists of the cost of defective product, ordering, holding in producers and collection-repair center, transportation, and assigning place for the collection-repair center. Two numerical examples with their computational results are discussed, and then a solution approach is presented which is analyzed by applying the examples to show the efficiency of the proposed method. The results demonstrate that the approach performances are faster than the MINLP model with negligible gap.
