Mixed-integer programming model and branch-and-price-and-cut algorithm for urban bus network design and timetabling


James C. Chu

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, place - urban, operations - scheduling, planning - network design, planning - methods


Public transit, Network design, Timetable, Branch-and-price-and-cut (BPC), Mixed-integer programming (MIP), Algorithm


This study solves the simultaneous planning problem of network design and timetabling for urban bus systems. An innovative mixed-integer programming (MIP) model is formulated and a parallel branch-and-price-and-cut (BPC) algorithm is proposed to solve the problem. The key idea of the model formulation and the solution algorithm is to represent a bus timetable with a route and a dispatch pattern. An aggregation and greedy algorithm is developed to efficiently solve the pricing subproblem. The cuts of disaggregate coupling inequalities are dynamically added to strengthen the lower bound. A computational study is conducted to evaluate the performance of the proposed methodology. The comparison with alternative solution approaches indicates that the parallel BPC algorithm is superior to solving the MIP formulations with the off-the-shelf MIP solver. Different values of model parameters are also tested, and various statistics of operators and passengers are reported for the cases.


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


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