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

► An approximately equivalent single-level formulation for a bi-level discrete network design problem. ► An MILP formulation for discrete network design problem, handling side constraints. ► An efficient unimodular linear approximation scheme for nonlinear travel time function. Discrete network desi...

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Bibliographic Details
Published in:Transportation research. Part E, Logistics and transportation review Vol. 47; no. 5; pp. 623 - 640
Main Authors: Farvaresh, Hamid, Sepehri, Mohammad Mehdi
Format: Journal Article
Language:English
Published: Exeter Elsevier India Pvt Ltd 01.09.2011
Elsevier
Elsevier Sequoia S.A
Series:Transportation Research Part E: Logistics and Transportation Review
Subjects:
Approximation
Bi-level programming
Discrete network design problem
Discrete network design problem Bi-level programming Transportation network Multi-commodity flows
Formulations
Ganzzahlige Optimierung
Güterverkehr
Integer programming
Linear programming
Mathematical analysis
Mathematical functions
Mathematical problems
Mixed integer
Multi-commodity flows
Networks
Nonlinearity
Time functions
Transportation
Transportation network
Validation studies
Verkehrsinfrastruktur
Verkehrsplanung
Multi-commodity flows
Bi-level programming
Discrete network design problem
Transportation network
ISSN:1366-5545, 1878-5794
Online Access:Get full text
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Summary:► An approximately equivalent single-level formulation for a bi-level discrete network design problem. ► An MILP formulation for discrete network design problem, handling side constraints. ► An efficient unimodular linear approximation scheme for nonlinear travel time function. 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.
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ISSN:1366-5545
1878-5794
DOI:10.1016/j.tre.2011.02.001