Model and algorithm for 4PLRP with uncertain delivery time

To address the challenge of logistics routing decision under uncertain environment, this paper studies a fourth party logistics routing problem (4PLRP) with uncertain delivery time (4PLRPU). A novel 4PLRPU model based on uncertainty theory is proposed by describing the delivery time of a third party logistics (3PL) provider as an uncertain variable. After that, the model is transformed into an equivalent deterministic model, and several improved genetic algorithms are designed to get solutions. To handle the problem of infeasible solutions in the proposed 4PLRPU, an improved node-based genetic algorithm (INGA) and an improved distance-based genetic algorithm (IDGA) are developed to reduce the computing time required to repair infeasible solutions, and an improved genetic algorithm based on the simple graph and Dijkstra algorithm (SDGA) is proposed to avoid the generation of infeasible solutions. Numerical experiments are conducted to investigate the performance of the proposed algorithms and verify the effectiveness of the proposed 4PLRPU model. The results show that INGA and SDGA are more effective than the standard genetic algorithm and IDGA at solving large-scale problems. Additionally, compared with the expected value model, the 4PLRPU model is more robust. (C) 2015 Elsevier Inc. All rights reserved.