Two Meta-heuristic Algorithms for a Capacitated Inventory-location Problem in Multi-echelon Supply Chain

Document Type : Research Paper


Department of Industrial Engineering, Alzahra University, Tehran, Iran


In this study, we propose a model to minimize the inventory and location costs of a supply chain, including a production plant, warehouses and retailers. The production plant distributes a single product to retailers through warehouses. The model determines the location of warehouses, allocates retailers to the warehouses and indicates the length of order intervals at warehouses and retailers. To ensure the order quantity is lower than the warehouses’ capacity, we consider the capacity constraints. Unlike the exciting researches, we investigate the limitation on the number of established warehouses. We formulize the problem as a nonlinear mixed-integer model and propose two efficient meta-heuristic algorithms including a genetic algorithm (GA) and an evolutionary simulated annealing algorithm (ESA) to solve it. To improve the proposed algorithms, in generating populations, a new heuristic method which produces feasible solutions is designed. The Taquchi method is used for tuning the parameters of the proposed algorithms. The small size numerical examples are solved and sensitivity analysis is done to demonstrate the influential theoretical results. We evaluate the proposed algorithms by comparing the solutions of them with the optimal solution obtained by the Lingo 11. Further, we investigate the efficiency of the proposed algorithms by solving numerical examples in different sizes and depict the percentage gaps between the best solution values and the average objective values of them. Results reveal that both the GA and ESA are efficient for solving the proposed model, but the ESA outperforms the GA on the optimal solution, computing time and stability.