A single-level mixed integer linear formulation for a bi-level discrete network design problem

Hamid Farvaresh and Mohammad Mehdi Sepehri

Transportation Research Part E: Logistics and Transportation Review, 2011, vol. 47, issue 5, 623-640

Abstract: 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.

Keywords: Discrete; network; design; problem; Bi-level; programming; Transportation; network; Multi-commodity; flows (search for similar items in EconPapers)
Date: 2011
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