| China has successively implemented and promoted the guidelines on building strong transportation network and developing comprehensive transport network,with the aim of accelerating the coordinated development of various transportation modes,constructing an integrated comprehensive transportation hub system and setting up high-quality comprehensive transport network.The research on multimode-oriented hub location and network design is of great significance for enhancing the effective functions of highway,railway,waterway and air transportation modes and optimizing the layout of comprehensive freight hub and transportation network structure.In this paper,based on the theories of system science,hub location and stochastic programming,an integrated optimization method is presented to comprehensively study the location of hubs and hub arcs,the choice of transportation modes and the allocation of transportation paths in the multimodal cargo transport system under the conditions of deterministic and uncertain information,respectively.The specific research contents are as follows:(1)Multimodal hub location and network design under deterministic information.Firstly,this paper presents an integer programming model by considering multiple modes of transportation,multiple-assignment incomplete hub network,and delivery-time restrictions.This problem aims at minimizing the total costs,including the fixed costs of establishing the hub network and the commodity routing costs.Subsequently,this paper proposes a sophisticated path-based mixed integer linear programming model by using a path filtering technique.Secondly,to solve the large-sized path-based model accurately,this paper implements an improved Benders decomposition algorithm by adopting a strategy for solving subproblems efficiently.This study also presents two acceleration techniques to speed up the Benders decomposition algorithm.Finally,numerical experiments based on the well-studied TR standard dataset and Beijing-Tianjin-Hebei region freight network data corroborate the advantages of the proposed model and the effectiveness of the improved Benders decomposition algorithm.The key observations from the computational results as follows:(i)the delivery time restrictions can effectively improve the transportation service level,and achieve a win-win situation between the economic and service goals;(ii)the multiple-assignment incomplete hub network can reduce the total cost of hub network.(2)Multimodal hub location and network design under uncertain information.Firstly,on the basis of the first research content,two classes of two-stage stochastic programming models under stochastic demand and transportation cost are proposed,respectively.Subsequently,the stochastic demand model is proven to be equivalent to the corresponding deterministic expected value problem(EVP),but the EVP equivalence does not hold for the stochastic transportation model.Secondly,to solve the stochastic transportation cost version efficiently,a Benders decomposition algorithm based on sample average approximate approach is developed.Finally,extensive numerical experiments on the TR standard dataset and Beijing-Tianjin-Hebei freight network data have been carried out to verify the effectiveness of the proposed stochastic programming model and solution method.The value of stochastic solution is also analyzed by the numerical experiments.The key observations from the computational results as follows:(i)the multimodal hub network topology is more sensitive to the stochastic transportation costs than stochastic demand model;(ii)compared with the deterministic model,the stochastic model can effectively resist the impact of uncertain transportation cost and reduce the total cost of the hub network. |