comparing multi-objective meta-heuristics for multi- commodity supply chain design problem with partial coverage

A three-echelon multi-commodity supply chain including manufacturers, distribution centers (dcs) and customers is considered. customers may be partially or fully covered by the dcs which should be opened in some candidate locations. a two-objective model is developed to find the locations of dcs and the flows of commodities in the whole supply chain considering a pre-determined number of dcs. the first objective function minimizes the total operation costs including transportation, inventory holding, production and site opening costs while the second objective maximizes the customers’ partial coverages. since the presented problem is np-hard in nature, three metaheuristic algorithms of nsga-ii, nrga and mopso are developed to find the pareto-optimal solutions and are compared using some standard criteria for multi-objective algorithms. numerical examples are designed to assess the performance of the model and the developed metaheuristic algorithms. considering different criteria for comparing the algorithms, the superiority of some algorithms against others are reported.