A two-stage optimization approach for subscription bus services network design: the China case

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, place - asia, place - urban, economics - profitability, ridership - commuting, ridership - demand, planning - methods, planning - network design


Subscription bus service, Network design optimization, Two-stage optimization model, Two-stage algorithm


Subscription bus services (SBS) is a convenient and low-carbon rapid transport mode for passengers’ daily commute. The network design becomes a vital problem because it closely relates to both operators’ profit and passengers’ daily convenient traveling. In this paper, a two-stage model is formulated to optimize the subscription bus services network design (SBSND). During the first stage we minimize the total service distance and the number of vehicles as a single target objective function; vehicle capacity utilization rate, service time, ratio of service distance and linear distance between origin and destination are limited by means of constraints. During the second stage we share the same objective function and similar constraints used during the first stage, but the parameter settings of the constraints are different. Correspondingly, a two-stage algorithm is also designed to solve the SBSND problem. Firstly, we obtain the possible service lines, match the passengers and bus capacity. Next, we use Dijkstra to obtain the shortest SBS operation lines. Finally, we form the SBS network. The three phases are the main processes about the algorithm during both stages. The comparison between existing SBS in Chengdu city and the optimized SBS shows the high efficiency of the optimization model and algorithm formulated in this paper: the operation line length increases from 250.6 to 300.9 km; only 40 passengers have no SBS after optimization; the average operation time is reduced from 56.8 to 50.2 min.


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