a multi-objective model for the location routing problem with fuzzy travel times and due dates

in this study the location routing problem with fuzzy parameters is taken into account, this problem involves determining the location of the depots and routing of the vehicles in order to serve the customers. in this study a location routing problem with fuzzy travel times and due dates is considered and two objective models are proposed. the considered objectives are minimizing the total costs of the network and minimizing the total weighted tardiness. the costs of the network include the fixed installation costs and the transportation costs. in order to solve this problem a mathematical model is proposed. however since this problem is categorized into np-hard problem; the mathematical model cannot be solved efficiently. therefore meta-heuristic algorithms are proposed to efficiently solve this problem.