A credibility-based fuzzy programming model for the hierarchical multimodal hub location problem with time uncertainty in cargo delivery systems

This paper studies the fuzzy hierarchical multimodal hub location problem for cargo delivery systems. It differs from traditional hub location problem in two ways. First, this paper constructs a hierarchical multimodal hub-and-spoke distribution network for the cargo delivery systems, which involves two transportation modes (road and air), two types of hubs (ground and airport) and three corresponding layers. Second, this paper develops a credibility-based fuzzy programming model capturing the uncertainty in travel time and handling time of the cargo delivery systems. This new model aims to minimize the latest arrival time (travel time plus handling time) for delivering cargoes from each pair of origin and destination nodes under diverse credibility of chance constraints. Under mild assumptions, the original model can be turned into an equivalent deterministic integer linear programming model. However, even for small instances of the problem, the equivalent model becomes too hard to be tackled by a general solver, e.g., CPLEX. This fact motivates the development of a two-stage heuristic procedure, wherein the first stage for the hub location subproblem is solved by a variable neighborhood search algorithm. These location solutions are then embedded into the second-stage process for the link assignment subproblem based on a shortest path method. To verify the proposed model and method, extensive numerical experiments are conducted on the well-known Turkish network data set.