Optimization of unsubsidized and subsidized customized bus services

This paper develops a model that considers both peak and off-peak demands. The optimal operating strategy is determined by maximizing the social welfare of unsubsidized and subsidized customized bus systems. Headway, fare, and fleet size are decision variables. Three plans are formulated for the subsidized case. Social welfare, fares, and actual demands for three plans at various subsidy levels are then compared. An improved particle swarm optimization (PSO) algorithm is designed by dynamically adjusting parameters in the update rule, combining the brainstorming algorithm mutation strategy. Results indicate that off-peak fares are consistently lower than peak fares. To attract a wide range of passengers, adopting a subsidy plan that partially compensates for operating costs is preferable. Furthermore, government subsidy programs help generate enhanced social benefits. The findings derived from numerical examples can be used as planning guides for customized bus systems.