The Transit Route Arc-Node Service Maximization problem
This article presents a new method for determining optimal transit routes. The Transit Route Arc-Node Service Maximization model is a mathematical model that maximizes the service value of a route, rather than minimizing cost. Cost (distance) is considered as a budget constraint on the extent of the...
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| Published in: | European journal of operational research Vol. 208; no. 1; pp. 46 - 56 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Amsterdam
Elsevier B.V
2011
Elsevier Elsevier Sequoia S.A |
| Series: | European Journal of Operational Research |
| Subjects: | |
| ISSN: | 0377-2217, 1872-6860 |
| Online Access: | Get full text |
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| Abstract | This article presents a new method for determining optimal transit routes. The Transit Route Arc-Node Service Maximization model is a mathematical model that maximizes the service value of a route, rather than minimizing cost. Cost (distance) is considered as a budget constraint on the extent of the route. The mathematical formulation modifies and exploits the structure of linear programming problems designed for the traveling salesman problem. An innovative divide-and-conquer solution procedure is presented that not only makes the transit routing problem tractable, but also provides a range of high-quality alternate routes for consideration, some of which have substantially varying geometries. Variant formulations are provided for several common transit route types. The model is tested through its application to an existing street network in Richardson, TX. Optimal numeric results are obtained for several problem instances, and these results demonstrate that increased route cost is not correlated with increased service provision. |
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| AbstractList | This article presents a new method for determining optimal transit routes. The Transit Route Arc-Node Service Maximization model is a mathematical model that maximizes the service value of a route, rather than minimizing cost. Cost (distance) is considered as a budget constraint on the extent of the route. The mathematical formulation modifies and exploits the structure of linear programming problems designed for the traveling salesman problem. An innovative divide-and-conquer solution procedure is presented that not only makes the transit routing problem tractable, but also provides a range of high-quality alternate routes for consideration, some of which have substantially varying geometries. Variant formulations are provided for several common transit route types. The model is tested through its application to an existing street network in Richardson, TX. Optimal numeric results are obtained for several problem instances, and these results demonstrate that increased route cost is not correlated with increased service provision. [PUBLICATION ABSTRACT] This article presents a new method for determining optimal transit routes. The Transit Route Arc-Node Service Maximization model is a mathematical model that maximizes the service value of a route, rather than minimizing cost. Cost (distance) is considered as a budget constraint on the extent of the route. The mathematical formulation modifies and exploits the structure of linear programming problems designed for the traveling salesman problem. An innovative divide-and-conquer solution procedure is presented that not only makes the transit routing problem tractable, but also provides a range of high-quality alternate routes for consideration, some of which have substantially varying geometries. Variant formulations are provided for several common transit route types. The model is tested through its application to an existing street network in Richardson, TX. Optimal numeric results are obtained for several problem instances, and these results demonstrate that increased route cost is not correlated with increased service provision. |
| Author | Curtin, Kevin M. Biba, Steve |
| Author_xml | – sequence: 1 givenname: Kevin M. surname: Curtin fullname: Curtin, Kevin M. email: curtin@gmu.edu organization: Department of Geography and GeoInformation Science (MS 6C3), George Mason University, 4400 University Drive, Fairfax, VA 22030, USA – sequence: 2 givenname: Steve surname: Biba fullname: Biba, Steve organization: Public Affairs (GR 31), University of Texas at Dallas, P.O. Box 830688, Richardson, TX 75083, USA |
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| Keywords | Integer programming Routing Transit Transportation Network optimization Location Costs Linear structure Travelling salesman problem Modeling Urban district network Street Budget Localization Divide and conquer method Optimal flow |
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| SubjectTerms | Applied sciences Buildings. Public works Divide & conquer algorithms Exact sciences and technology Flows in networks. Combinatorial problems Integer programming Linear programming Location Logistics Mathematical models Mathematical programming Network optimization Operational research and scientific management Operational research. Management science Route optimization Routing Routing Transportation Integer programming Network optimization Transit Location Studies Transit Transportation Transportation problem (Operations research) Traveling salesman problem Urban development |
| Title | The Transit Route Arc-Node Service Maximization problem |
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