Bi-Level Mathematical Programming Model for Locating Bus Stops and Optimizing Frequencies

Document Type

Journal Article

Publication Date


Subject Area

economics - operating costs, infrastructure - stop, mode - bus, operations - frequency, operations - traffic, policy - congestion, ridership - demand


Traffic congestion, Supply and demand, Stop (Public transportation), Site selection, Simulation, Service frequency, Programming (Mathematics), Placement (Location), Optimization theory, Optimization, Optimisation, Operating costs, Mathematical programming, Mathematical analysis, Location, Locating, Gridlock (Traffic), Cost of operation, Computer simulation, Bus stops, Bilevel programming, Behavioral models


This paper proposes a model for locating bus stops and optimizing bus frequencies in congested local public transport networks. The analysis addresses the issue of reducing the overall costs of operating a transport system, including costs associated with provision of services and bus stop construction, using a bi-level mathematical programming method. The upper level defines the overall cost of the system, which must be kept to a minimum taking into account operational restrictions, and the lower level defines a behavioral model for system users. The suggested model mixes optimization and simulation and allows supply and demand to be linked; this ensures consistency between equilibrium flows and bus frequencies and between equilibrium flows and the distances between bus stops calculated at each iteration of the algorithm.