Benders Decomposition for the Design of a Hub and Shuttle Public Transit System

The BusPlus project aims at improving the off-peak hours public transit service in Canberra, Australia. To address the difficulty of covering a large geographic area, proposes a hub and shuttle model consisting of a combination of a few high-frequency bus routes between key hubs and a large number of shuttles that bring passengers from their origin to the closest hub and take them from their last bus stop to their destination. This paper focuses on the design of the bus network and proposes an efficient solving method to this multimodal network design problem based on the Benders decomposition method. Starting from a mixed-integer programming (MIP) formulation of the problem, the paper presents a Benders decomposition approach using dedicated solution techniques for solving independent subproblems, Pareto-optimal cuts, cut bundling, and core point update. Computational results on real-world data from Canberra’s public transit system justify the design choices and show that the approach outperforms the MIP...

[1]  Andreas T. Ernst,et al.  Hub Arc Location Problems: Part II - Formulations and Optimal Algorithms , 2005, Manag. Sci..

[2]  Gilbert Laporte,et al.  Benders Decomposition for Large-Scale Uncapacitated Hub Location , 2011, Oper. Res..

[3]  Iván A. Contreras,et al.  Exact and heuristic algorithms for the design of hub networks with multiple lines , 2015, Eur. J. Oper. Res..

[4]  Ehsan Nikbakhsh,et al.  Hub location problems: A review of models, classification, solution techniques, and applications , 2013, Comput. Ind. Eng..

[5]  Ricardo Saraiva de Camargo,et al.  Benders decomposition for the uncapacitated multiple allocation hub location problem , 2008, Comput. Oper. Res..

[6]  Thomas L. Magnanti,et al.  Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria , 1981, Oper. Res..

[7]  Chang-ho Lee,et al.  Topological design of a two-level network with ring-star configuration , 1993, Comput. Oper. Res..

[8]  Sibel A. Alumur,et al.  Network hub location problems: The state of the art , 2008, Eur. J. Oper. Res..

[9]  Iván A. Contreras,et al.  The Hub Line Location Problem , 2015, Transp. Sci..

[10]  Ricardo Saraiva de Camargo,et al.  An improved Benders decomposition algorithm for the tree of hubs location problem , 2013, Eur. J. Oper. Res..

[11]  James F. Campbell Hub location for time definite transportation , 2009, Comput. Oper. Res..

[12]  S. L. Hakimi,et al.  Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph , 1964 .

[13]  Ravindra K. Ahuja,et al.  Network Flows , 2011 .

[14]  Sebastian Bocker,et al.  Exact and heuristic algorithms for Cograph Editing , 2017, 1711.05839.

[15]  Andreas T. Ernst,et al.  Hub Arc Location Problems: Part I - Introduction and Results , 2005, Manag. Sci..

[16]  J. Birge,et al.  A multicut algorithm for two-stage stochastic linear programs , 1988 .

[17]  Patricia Jaramillo,et al.  Urban rapid transit network design: accelerated Benders decomposition , 2009, Ann. Oper. Res..

[18]  Harvey J. Miller,et al.  THE HUB NETWORK DESIGN PROBLEM: A REVIEW AND SYNTHESIS. , 1994 .

[19]  G. Ghiani,et al.  A multi-modal approach to the location of a rapid transit line , 1998 .

[20]  Jacques F. Benders,et al.  Partitioning procedures for solving mixed-variables programming problems , 2005, Comput. Manag. Sci..

[21]  Fang Lu Integrated airline scheduling : models and algorithms , 1997 .

[22]  Hande Yaman,et al.  Star p-hub median problem with modular arc capacities , 2008, Comput. Oper. Res..

[23]  Thomas L. Magnanti,et al.  Tailoring Benders decomposition for uncapacitated network design , 1986 .

[24]  Nikolaos Papadakos,et al.  Practical enhancements to the Magnanti-Wong method , 2008, Oper. Res. Lett..

[25]  Stefan Nickel,et al.  Hub Location Problems in Urban Traffic Networks , 2001 .

[26]  Morton E. O'Kelly,et al.  The Location of Interacting Hub Facilities , 1986, Transp. Sci..

[27]  Michel Gendreau,et al.  LOCATING RAPID TRANSIT LINES , 1995 .

[28]  A. M. Geoffrion,et al.  Multicommodity Distribution System Design by Benders Decomposition , 1974 .

[29]  J. F. Benders Partitioning procedures for solving mixed-variables programming problems , 1962 .

[30]  Martine Labbé,et al.  Solving the hub location problem in a star–star network , 2008, Networks.

[31]  Morton E. O'Kelly,et al.  Twenty-Five Years of Hub Location Research , 2012, Transp. Sci..

[32]  Iván A. Contreras,et al.  Tight bounds from a path based formulation for the tree of hub location problem , 2009, Comput. Oper. Res..

[33]  M. Labbé,et al.  Solving the hub location problem in a star–star network , 2008 .