A Hybrid Meta-Heuristic algorithm for optimization location-routing problem of facilities in four echelon supply chain

During the last three decades, the concept of integrated decision making in the supply chain becomes one of the essential aspects of supply chain management (SCM). This concept explores the interdependence between facility location, flow allocation between facilities, transportation system structure, and inventory control system. This study presents a new form of the location-routing problem of facilities under uncertainty in a supply chain network for deteriorating items through taking environmental considerations, cost, and procurement time and customer satisfaction into account, to simultaneously minimize total system costs, maximal delivery time and emissions across the entire network and maximize customer satisfaction. The research problem is formulated in a mixed-integer nonlinear multi-objective programming. In order to solve the model, the combination of the two Benders decomposition algorithm and Lagrange multiplier liberalization, as well as the combination of red deer algorithm and annealing simulation, was proposed. For validation, the results of the proposed algorithm in different size examples are compared with the results of the exact method solution by MATLAB software. The mean error of the proposed algorithm for the objective function is less than 4% compared to the exact method in solving the sample problems. Besides, the results of the algorithm performance are investigated based on standard indices. The computational results show the efficiency of the algorithm for a wide range of problems with different sizes. The location decisions are interdependent, and the process of determining the optimal values of these variables interact together, which can lead to an optimal system with the least possible costs.