An Efficient Imperialistic Competitive Algorithm for Closed-loop Supply Chains Considering Pricing for Product and Fleet of Heterogeneous Vehicles

This study investigates multi-period pricing closed-loop supply chains (CLSCs) with two echelons of producers and customers. Products delivered to customers might be defective which would be picked up and gathered in the collection center and fixed if it is possible and returned to the chain. Otherwise, they will be sold as waste materials. This problem determines the price and distribution of the product, supply of the material, and also determines vehicles with simultaneous pick-up and delivery in order to maximize the profit. A fleet of heterogeneous vehicles was 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 was the maximization of the profit. Total cost consisted costs of defective products, ordering cost, the cost of holding in producers and collection-repair center, transportation costs, and the cost of assigning the place for the 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) have been applied to solve the randomly generated test problems. Computational results revealed that GA was statistically better than ICA based on RPD metric reaching solutions with high quality.