An efficient Imperialistic Competitive Algorithm for the closed-loop supply chains considering pricing for product, and fleet of heterogeneous vehicles

 This paper investigates a pricing multi-period, closed-loop supply chains (CLSCs) with two echelons of producers and customers. Products are delivered to customers might be defective which are picked up and gathered in the collection center and will be fixed if it is possible and will be returned to the chain. Otherwise, they are sold as waste. This problem is determining price and distribution of the product, supplying the material, and routing the vehicles with simultaneous pick-up and delivery in order to maximize the profit. A fleet of heterogeneous vehicles is routed to deliver the products from producers to customers and to pick up defective products from the customers and shipped them to the collection-repair center. The objective function is maximization of the profit. Total cost is consisted of defective products ’costs, ordering cost, cost of holding in producers and collection-repair center, transportation costs, and the cost of assigning place for collection-repair center. This problem has been known as Np-hard, therefore two meta-heuristic algorithms namely genetic algorithm (GA) and Imperialist competitive algorithm (ICA) are applied to solve the random generated test problems. Computational results reveal that GA is better than ICA statistically based on RPD metric and reach to solutions with high quality.