Bus service optimisation with fuel saving objective and various financial constraints

A model for optimal bus service in urban areas is presented. Following the recent increasing environmental concerns the model takes, as objective function, the total (bus and car modes) reduction of fuel consumption. The optimal service level, price and bus size are determined subject to the operator financial constraint and the capacity constraint. Two formulations of the financial constraint are considered: subsidy as fraction of costs and subsidy as fixed amount. Bus-km and average revenue per passenger carried are used as proxies for service level and price, respectively. Bus demand varies with the generalised cost of bus travel according to a constant elasticity. Transfers of passengers from car to bus are a given fraction of the demand newly attracted from bus. Model solution requires only one algebraic equation to be solved for one of the service variables, the remaining being provided in closed form. A selection of the results for a case study shows the variations at optimum of bus service variables with the operating parameters. The conditions under which bus policies based on service level and price are effective to save fuel and the different policy implications deriving from the two financial constraint formulations are highlighted.