Fourth party logistics routing problem model with fuzzy duration time and cost discount

In this paper, from the viewpoint of a fourth party logistics (4PL) provider, a multi-source single-destination 4PL routing problem with fuzzy duration time and cost discount (M-S 4PLRPFC) is described considering the comprehensive ability of 3PL suppliers and nodes. A chance-constrained programming model is established for the M-S 4PLRPFC. Next, a memetic algorithm (MA) with a fuzzy simulation method is designed to solve the problem. Based on a set of problem instances as the test bed, experiments are performed to compare the performance of the proposed MA with those of the enumeration method and a standard genetic algorithm (SGA). The experimental results show that the proposed MA obtains the same results as the enumeration method and that it is than the SGA.