multi-objective optimization for multi-product multi-period four echelon supply chain problems under uncertainty

The multi-objective optimization for a multi-product multi-period four-echelon supply chain network consisting of manufacturing plants, distribution centers (dcs) and retailers each with uncertain services and uncertain customer nodes are aimed in this paper. the two objectives are minimization of the total supply chain cost and maximization of the average number of products dispatched to customers. the decision variables are the number and the locations of reliable dcs and retailers, the optimum number of items produced by plants, the optimum quantity of transported products, the optimum inventory of products at dcs, retailers and plants, and the optimum shortage quantity of the customer nodes. the problem is first formulated into the framework of a constrained multi-objective mixed integer linear programming model. after that, the problem is solved by using meta-heuristic algorithms that are multi-objective genetic algorithm (moga), fast non-dominated sorting genetic algorithms (nsga-ii) and epsilon constraint methods via the matlab software to select the best in terms of the total supply chain cost and the total expected number of products dispatched to customers simultaneously. at the end, the performance of the proposed multi-objective optimization model of multi-product multi-period four-echelon supply chain network design is validated through three realizations and an innumerable of various analyses in a real world case study of bangladesh. the obtained outcomes and their analyses recognize the efficiency and applicability of the proposed model under uncertainty.