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Public Transport

, Volume 11, Issue 2, pp 321–340 | Cite as

Locating key stations of a metro network using bi-objective programming: discrete and continuous demand mode

  • Seyed Sina MohriEmail author
  • Meisam Akbarzadeh
Original Paper
  • 19 Downloads

Abstract

This study proposes two bi-objective optimization problems for locating key stations of a metro network in both discrete and continuous demand modes. Traditionally, designing a metro network based on optimization techniques consists of two approaches. The first approach locates a number of alignments and their stations simultaneously, while the second approach involves locating key stations, designing a core network, and locating secondary stations. In locating key stations processed by a single objective model, the number of produced and attracted trips to the key stations is maximized. This paper considers a second objective for this stage to maximize the coverage of key stations on origin/destination (OD) trips. A fuzzy goal programming model is established to solve the bi-objective model and provide some Pareto-optimal solutions. The previous single objective model and the proposed model with continuous demand mode are applied to a real network. Results show that the proposed model significantly increases the coverage of key stations on OD trips with only a slight reduction in the number of produced and attracted trips.

Keywords

Rail rapid transit Metro network design Fuzzy goal programming 

List of symbols

Sets/Indices

\(S\)

The set of proposed stations

\(D\)

The set of demand points

\(C\)

The set of demand areas

\(L\)

The set of catchment levels

\(s,s^{\prime}\)

The index for proposed stations

\(i,j\)

The index for demand points/areas

\(l,l^{\prime}\)

The index for catchment levels

Input parameters

\(w_{s}\)

The coverage of station s of network demand points

\(w_{ij}^{{ss^{\prime}}}\)

The coverage of stations s and \(s^{\prime}\) of demand flow i to j where s and \(s^{\prime}\) are situated around the demand points/areas i and j, respectively

\(w^{{ss^{\prime}}}\)

The coverage of stations s and \(s^{\prime}\) of total demand flows

\(P\)

The number of key stations in the network

\(\theta_{l}\)

The cover intensity at the catchment level l

\(v_{i}\)

The total number of trip production and attraction in the demand point i

\(v_{ij}\)

The demand flow from point/area i to point/area j

\(\delta_{isl}\)

A binary input parameter, which is equal to one, if station i belongs to catchment level l of station s, and zero, otherwise

\(d_{{ss^{\prime}}}\)

The Euclidian distance between stations s and \(s^{\prime}\)

\(d_{min}\)

The minimum permitted Euclidian distance between two key stations

\(\beta\)

A constant value based on the gravity model

\(a_{i}\)

The total area of demand area i

\(a_{isl}\)

The common area of demand area i and catchment area l of station s

Decision variables

\(Z_{s}\)

A binary decision variable; it is equal to one if station s is selected as key station; otherwise it is equal to zero

\(Y^{{ss^{\prime}}}\)

A binary decision variable; it is equal to one if both stations s and \(s^{\prime}\) are selected as key stations; otherwise it is equal to zero

Notes

Acknowledgements

The authors are grateful for the helpful comments of two anonymous referees that have allowed us to improve upon the original version. The authors also acknowledge the help of Dr. Hossein Haghshenas from the Isfahan University of Technology for making the data set available for this study.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Transportation EngineeringIsfahan University of TechnologyIsfahanIran

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