Fourth party logistics routing problem with fuzzy duration time

As fourth party logistics (4PL) has the power to integrate the supply chain, from the beginning of the 21st century, it has attracted more and more attention in many fields. As one of the most important aspects in 4PL, the fourth party logistics routing problem (4PLRP) is very difficult to solve because many issues, such as the selection of third party logistics, cost and time, need to be considered. In this paper, a 4PLRP with fuzzy duration time (4PLRPF) model is presented, which is to find a route of the minimum cost with constraints under uncertain environments, and fuzzy numbers are used to denote the uncertainty of the duration time on each node and arc. Fuzzy programming model is established according to the uncertainty theory. In order to solve the modeled 4PLRPF, a two-step genetic algorithm with the fuzzy simulation is designed to find approximate optimal solutions. Numerical experiments are carried out to investigate the performance of the proposed algorithm on a set of 4PLRPF instances. The experimental results show that the proposed method is a valuable tool for making decisions for the 4PLRPF.