Design of a fuzzy bi-objective reliable p-hub center problem

Nowadays in all shipment delivery systems, most of customers are looking for companies that offer fast and reliable delivery service as well as guarantee when deliveries will be made. With variability in travel time, the configuration of the hub-and-spoke network is vital to meet the delivery service requirement. For this purpose, a bi-objective stochastic p-hub center problem is considered to investigate the effect of delivery service requirement on the configuration of the hub-and-spoke network with fuzzy parameters, in which hub operational nodes may disrupt and fail to operate shipments. Since delivery time of the shipments is the sum of transit time over the links and spent time at the hubs, spent times with fuzzy arrival of shipments are calculated by utilizing a fuzzy M/M/1 queuing system. In order to solve large-sized instances of the presented mathematical model, two meta-heuristic algorithms, namely SA and self-adaptive DE (SADE) are developed and their performances are evaluated using a proposed lower bound approach. Computational experiments are provided to demonstrate the effectiveness of the proposed model and solution approaches. Finally, a real transportation case is studied.