A chance-constrained programming of Fourth-Party Logistics routing problem with fuzzy duration time

In the last ten years, Fourth Party Logistics (4PL) has been attracting more and more attention in many relative fields. In this paper, a 4PL Routing Problem (4PLPR) with fuzzy duration time is presented where the fuzzy numbers are used to describe the uncertainty of the duration time. After the description of 4PLRP, a chance-constrained programming for it is established according to the credibility theory. And a crisp equivalent is derived when fuzzy variables are characterized by triangular fuzzy numbers. Then genetic algorithm embedded K th shortest path algorithm with special initialization is designed. Finally, an extensive computational analysis is presented and the numerical results show that which route should be selected in order to get minimum cost in the due date.