A bi-level programming for logistics network design with system-optimized flows

This paper proposes a bi-level programming for a logistics network design problem with system-optimized flows. We applied the Wardrop's second principle to the logistics network design problem. A system-optimized logistics network design problem can be formulated as a bi-level program. For the system-optimized flows, a user equilibrium traffic assignment problem with marginal costs can be solved at the lower level problem. Due to the non-differentiability of the perturbed solutions in system-optimized flows, we present a novel solution algorithm to efficiently solve the logistics network design problem. By using the subgradients of the objective function, a new projection method is proposed with global convergence. Numerical calculations are implemented using a grid-size hypothetical network and comparisons are made with other alternatives in solving the logistics network design problem. Numerical results disclose that the proposed method has successful solved the logistics network design problem and achieved significant performance both in computational efficacy and cost reduction when compared to other alternatives. (C) 2009 Elsevier Inc. All rights reserved.