Stochastic Hierarchical Multimodal Hub Location Problem for Cargo Delivery Systems: Formulation and Algorithm

This study aims at developing a stochastic hierarchical multimodal hub location modeling framework for cargo delivery systems to capture uncertainty in hub construction cost and travel time at the strategic level. From a ring-star-star type network design perspective, a stochastic model is established to formulate this problem formally via the expected value and chance-constrained programming techniques. In particular, three types of chance constraints are proposed to ensure that the on-time delivery with pre-specified confidence levels in their respective layer networks. For normal distributions, the original stochastic model can be reformulated as a crisp equivalent mixed-integer linear programming (MILP) model by invoking the central limit theorem. Since the number of constraints and variables increases drastically with the size of cargo delivery distribution network, a memetic algorithm (MA) is designed. This algorithm incorporates genetic search and local intensification to obtain optimal/near-optimal solutions for realistic instance size within a reasonable time limit. For general distributions, it is difficult to convert the stochastic model into its deterministic counterpart. Hence, a hybrid methodology is further designed by combining the MA and Monte Carlo (MC) simulation to solve the proposed stochastic model. To demonstrate the properties of the proposed model and the performance of the designed algorithm, a series of numerical experiments are set up based on the Civil Aeronautics Board (CAB) and Turkish network data sets. Computational results indicate as the confidence level increases, the airport hubs are located further apart in the cargo delivery distribution network for gaining a greater time advantage. In addition, comparative results demonstrate that the MA algorithm proposed herein performs better than the genetic algorithm (GA) in terms of computing speed and quality of the solution.