Optimization models for calculating the best size for passenger carrying vehicles in urban areas were popular during the 1980s. These studies were abandoned in the '90s concluding that it was more efficient to use smaller buses at higher frequencies.This article returns to this controversial question, starting from the point of view that any calculation of bus size can only be made after considering the demand for each of the routes on the system. Therefore, an optimization model for sizing the buses and setting frequencies on each route in the system is proposed in accordance with the premises detailed below. The proposed model is a bi-level optimization model with constraints on bus capacity. The model allows buses of different sizes to be assigned to public transport routes optimizing the headways on each route in accordance with observed levels of demand. At the upper level the model considers the optimization of the system's social and operating costs, these are understood to be the sum of the user's and operator's costs. At the lower level there is an assignment model for public transport with constraints on vehicle capacity which balances the flows for bus sizes and headways at each iteration. By graphically representing the results of the model applied to a real case, a series of useful conclusions are reached for the management and planning of a fleet of public transport vehicles.

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SUMMARY This article presents a bi‐level optimization model to assign optimal bus sizes and frequencies to public transport routes. The upper level problem of the proposed model minimizes a cost function representing the costs of the users and operators, and the lower level solves a public transport assignment model subject to a capacity constraint. The article discusses the benefits of using either Hooke–Jeeves or tabu search algorithms for solving the bi‐level model. Following the real‐case application to the city of Santander (Spain), it is concluded that both algorithms lead to very similar solutions. It has also been shown that when both algorithms start from the same homogenous solution, the convergence speed of tabu search is almost 50% quicker than that of Hooke–Jeeves, making tabu search more attractive if there is a need to solve a problem many times and for large networks. Copyright © 2012 John Wiley & Sons, Ltd.

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