Maximizing net benefits for conventional and flexible bus services

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, planning - route design, planning - service rationalisation, economics - subsidy, economics - operating costs, economics - value of time, economics - pricing, operations - capacity, operations - service span, operations - frequency, ridership - elasticity, ridership - demand, economics - benefits


Public transportation, Conventional bus, Flexible bus, Maximum social welfare, Genetic algorithm, Constrained optimization


Transit ridership is usually sensitive to fares, travel times, waiting times, and access times, among other factors. Therefore, the elasticities of demand with respect to such factors should be considered in modeling bus transit services and must be considered when maximizing net benefits (i.e. “system welfare” = consumer surplus + producer surplus) rather just minimizing costs. In this paper welfare is maximized with elastic demand relations for both conventional (fixed route) and flexible-route services in systems with multiple dissimilar regions and periods. As maximum welfare formulations are usually too complex for exact solutions, they have only been used in a few studies focused on conventional transit services. This limitation is overcome here for both conventional and flexible transit services by using a Real Coded Genetic Algorithm to solve such mixed integer nonlinear welfare maximization problems with constraints on capacities and subsidies. The optimized variables include service type, zone sizes, headways and fares. We also determine the maximum welfare threshold between optimized conventional and flexible services) and explore the effects of subsidies. The proposed planning models should be useful in selecting the service type and optimizing other service characteristics based on local geographic characteristics and financial constraints.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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