Optimization of costs, time and transportation system's reliability in a four-echelon supply chain network; using mixed integer linear programming

The effectiveness and efficiency of each organization is the result of management performance and its supply chain structure. In order to optimizing the total costs, lead time and transportation system's reliability in all levels of supply chain network, a multi-objective mixed integer linear programming has been used in this paper. This mathematical modeling has addressed the design of a four-echelon supply chain structure, including multiple suppliers, multiple manufacturers, multiple distributors, and several customers. Optimizing costs has been considered based on the uncertainty of customers' demand. Also, the shortage of products is eligible in the mathematical modeling. In this paper, the uncertain demand is converted to deterministic by using Chance - Constrained Programming (CCP) approach. Due to the complexity of the model structure in large sizes, this paper has also proposed a meta-heuristic algorithm called Non-Dominated Sorting Genetic Algorithm (NSGAII) as a solving method and the results have been analyzed. Finally, in order to validate the efficiency of the proposed meta-heuristic method, we compared the results in both the exact solution of the model and the proposed algorithm in small sizes.