Fuzzy capacitated location-routing problem with simultaneous pickup and delivery demands

In this work, the fuzzy capacitated location-routing problem with simultaneous pickup and delivery demands (FCLRP-SPD) is considered. This problem is a more realistic case of the capacitated location-routing problem and belongs to the reverse logistics. In FCLRP-SPD, a set of customers with simultaneous pickup and delivery demands should be supplied by a fleet of vehicles that start and end their tours at a single depot. In addition, both pickup and delivery demands of customers are fuzzy variables. The objective function is minimizing the routing costs, fixed costs of establishing the depot(s), and employing the vehicles. To model the problem, a fuzzy chance-constrained programming model is designed based upon the fuzzy credibility theory. To solve the FCLRP-SPD, a greedy clustering method (GCM) is developed, which includes four iterative phases. To achieve the best value of two types of parameters of the model, named 'vehicle indexes' and 'depots indexes; and to analyze their influences on the final solution, numerical experiments are carried out. Moreover, the efficiency of the GCM is demonstrated using a standard benchmark set of test problems.