Solution algorithm for the bilevel linear programming formulation of the network design problem

The urban traffic continuous network design problem is concerned with the modification of an existing road network, with given demand from each origin to each destination. The objective is to minimize total system costs consisting of system travel costs and investment costs, While accounting for the route choice behavior of network users. LeBlanc and Boyce (1986)first gave an explicit formulation of the continuous network design problem as a bilevel linear programming model, but no acceptable bilevel. linear programming algorithm is found to solve the model proposed. In this paper, by using the duality theory to express the relationship between the extreme points of the feasible region of the follower's dual problem and the optimal solution of the bilevel linear programming problem, a new solution algorithm with global convergence for bilevel linear programming problem is proposed. Moreover, the applications of the new algorithm are illustrated with two simple examples.