Accelerating Benders decomposition for stochastic incomplete multimodal hub location problem in many-to-many transportation and distribution systems

To customize the hub location model for application in many-to-many transportation and distribution systems, this study introduces a stochastic incomplete multimodal hub location problem with multiple assignments and delivery-time restrictions. This problem explicitly considers the mode-specific hub and link, incomplete inter-hub connectivity, multiple-assignment pattern of demand nodes to hubs and two types of uncertainties in an expected cost-minimization context with delivery-time restrictions. Using a filtering technique, this study first presents a sophisticated path-based formulation for the problem with uncertain demand embedded in a two-stage stochastic programming framework. More importantly, the stochastic demand model is proven to be equivalent to the corresponding deterministic expected value problem (EVP), which can be solved to optimality using Gurobi. By considering the uncertainty in transportation cost, this study further proposes an associated two-stage stochastic program, in which the EVP equivalence does not hold. To solve the stochastic transportation cost version efficiently, the study implements an improved Benders decomposition algorithm by adopting a sample average approximation approach and a dualization strategy. To accelerate the convergence of the proposed Benders decomposition algorithm, this study also presents a multi-cut reformulation and a cut-loop stabilization strategy for Benders acceleration. Numerical experiments based on the well-studied Turkish network and AP dataset corroborate the advantages of the proposed models and the effectiveness of the developed approaches. Some key managerial insights are summarized to effectively guide incomplete, multimodal hub network designs against uncertainty in many-to-many transportation and distribution practices.