  We study a vehicle-based hub network design problem (HNDPv) with the main
applications in freight distribution and parcel delivery systems, where the
economies of scale stem from the effective utilization of vehicles that move
consolidated freight. The HNDPv is a generalization of the classical single
allocation hub location problem, in which the transportation costs are stepwise
functions of the number (and type) of vehicles that move the demand. We present
the quadratic mixed-integer programming formulation of the problem and its
linear reformulation. Exploiting the special structures of the linearized
model, we develop a branch-and-cut method based on Benders decomposition with
solely feasibility subproblems. We derive closed-form solutions for the extreme
rays of the feasibility subproblems that improve the efficiency of the proposed
algorithm through generating stronger feasibility cuts. We also address the
HNDPv under demand uncertainty and show the flexibility of our solution
methodology in handling the stochastic variant of the problem. To evaluate the
efficiency of our models and solution approaches, we perform extensive
computational experiments on uncapacitated and capacitated instances of the
problem derived from the classical Australian Post dataset. The results show a
considerable advantage of using HNDPv compared to the classical HLP with
constant discount factors in terms of vehicle utilization and total
transportation costs. Our computational experiments also demonstrate the
efficiency of our proposed solution method in solving large-scale problem
instances.
