Models and algorithms for the screen line-based traffic-counting location problems

We consider an overlooked, but important, practical problem about the optimal selection of cordon–screen lines for traffic census study in road networks. The problem can be stated as: (1) how to select the optimal locations of a given number of counting stations to separate as many origin–destination (O–D) pairs as possible, (2) how to determine the minimum number of counting stations and their locations required for separating all O–D pairs. Here, an O–D pair is said to be separated if trips between this O–D pair are entirely intercepted by the current traffic-counting stations. The problems of interest are formulated as integer linear-programming models. After exploring the relaxed linear-programming problems and their dual problems, a solution scheme that combines a shortest path-based column generation procedure and a branch-and-bound technique is developed to find an optimal counting location solution. The proposed models and algorithms are illustrated with numerical examples and compared with the genetic algorithm.