期刊
TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW
卷 47, 期 5, 页码 623-640出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.tre.2011.02.001
关键词
Discrete network design problem; Bi-level programming; Transportation network; Multi-commodity flows
Discrete network design problem (DNDP) is generally formulated as a bi-level programming. In this paper, a single-level mixed integer linear programming (SL-MILP) formulation for bi-level DNDP is presented. To cope with the dependency of node-link adjacency matrix on new links, travel time function is appropriately modified. The nonlinearity of the travel time function is also removed by means of a convex-combination based linear approximation which takes advantage of a unimodular structure. Two valid inequalities is developed which shorten computation time significantly. The validity of the proposed formulation is examined by two test problems. SL-MILP is able to provide optimal solution. (C) 2011 Elsevier Ltd. All rights reserved.
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