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Urban public transit network optimization with flexible demand. (English) Zbl 1308.90019
Summary: A new optimization approach is introduced for designing a public transit network. The main innovation of this paper is that the demand for public transit is endogenous. We maximize the total number of expected public transit passengers subject to a budget constraint. The demand depends on the established routes and their frequencies. A binary logit model is applied to simulate the behavior of the potential customers where the expected utility for public transit depends on in-vehicle time, waiting time, and access time. The expected waiting time depends on the frequency of the transit routes. The approach has been tested for the City of Dresden in Germany. The computational experiments show that the approach is applicable to real-world situations.
MSC:
90B06 Transportation, logistics and supply chain management
90B10 Deterministic network models in operations research
90B15 Stochastic network models in operations research
90C10 Integer programming
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[1] Balcombe R, Mackett R, Paulley N, Preston J, Shires J, Titheridge H, Wardman M, White P (2004) The demand for public transport: a practical guide · Zbl 1305.90251
[2] Ben-Akiva M, Lerman S (1985) Discrete choice analysis: theory and application to travel demand. The MIT Press, New York
[3] Borndörfer, R; Grötschel, M; Pfetsch, ME, A column-generation approach to line planning in public transport, Transp Sci, 41, 123-132, (2007)
[4] Borndörfer, R; Grötschel, M; Pfetsch, ME; Fandel, G (ed.); Trockel, W (ed.); Hickman, M (ed.); Mirchandani, P (ed.); Voß, S (ed.), Models for line planning in public transport, No. 600, 363-378, (2008), Berlin · Zbl 1169.90314
[5] Bussieck MR (1998) Optimal lines in public transport. Ph.D. thesis, Technische Universität Braunschweig
[6] Bussieck, MR; Lindner, T; Lübbecke, ME, A fast algorithm for near cost optimal line plans, Math Methods Oper Res, 59, p205-220, (2004) · Zbl 1138.90434
[7] Chriqui, C; Robillard, P, Common bus lines, Transp Sci, 9, 115-121, (1975)
[8] Claessens, MT; Dijk, NM; Zwaneveld, PJ, Cost optimal allocation of rail passenger lines, Eur J Oper Res, 110, 474-489, (1998) · Zbl 0948.90097
[9] Dienst H (1978) Linienplanung im spurgeführten Personenverkehr mit Hilfe eines heuristischen Verfahrens. Ph.D. thesis, Technische Universität Braunschweig · Zbl 1209.90042
[10] Goossens JW (2004) Models and algorithms for railway line planning problems. Ph.D. thesis, Universität Maastricht
[11] Guihaire, V; Hao, JK, Transit network design and scheduling: a global review, Transp Res Part A Policy Pract, 42, 1251-1273, (2008)
[12] Haase, K; Müller, S, Management of school locations allowing for free school choice, Omega, 41, 847-855, (2013)
[13] Haase, K; Müller, S, A comparison of linear reformulations for multinomial logit choice probabilities in facility location models, Eur J Oper Res, 232, 689-691, (2014) · Zbl 1305.90251
[14] Haase K, Müller S (2014) Insights into clients’ choice in preventive health care facility location planning. OR Spectr (accepted for publicatiton) · Zbl 1308.90017
[15] Kepaptsoglou, K; Karlaftis, M, Transit route network design problem: review, J Transp Eng, 135, 491-505, (2009)
[16] Klier, MJ; Haase, K; Kalcsics, J (ed.); Nickel, S (ed.), Line optimization in public transport systems, 473-478, (2008), Berlin · Zbl 1209.90042
[17] Müller, S; Haase, K; Kless, S, A multiperiod school location planning approach with free school choice, Environ Plan A, 41, 2929-2945, (2009)
[18] Nachtigall, K; Jerosch, K; Fischetti, M (ed.); Widmayer, P (ed.), Simultaneous network line planning and traffic assignment, (2008), Germany · Zbl 1247.90058
[19] Oltrogge C (1994) Linienplanung für mehrstufige Bedienungssysteme im öffentlichen Personenverkehr. Ph.D. thesis, Technische Universität Braunschweig · Zbl 1209.90042
[20] Patz A (1925) Die richtige Auswahl von Verkehrslinien bei großen Straßenbahnnetzen. Verkehrstechnik 50/51
[21] Paulley N, Balcombe R, Mackett R, Titheridge H, Preston J, Wardman M, Shires J, White P (2006) The demand for public transport: the effects of fares, quality of service, income and car ownership. Transp Policy 13(4):295-306 (innovation and integration in urban transport policy)
[22] Schöbel A (2011) Line planning in public transportation: models and methods. OR Spectr 1-20. doi:10.1007/s00291-011-0251-6
[23] Scholl S (2005) Customer-oriented line planning. Ph.D. thesis, Technische Universität Kaiserslautern
[24] Shimamoto H, Schmöcker JD, Kurauchi F (2012) Optimisation of a bus network configuration considering the common lines problem. In: 91st annual meeting of Transportation Research Board, pp 1-19
[25] Tscharaktschiew, S; Hirte, G, Should subsidies to urban passenger transport be increased? A spatial CGE analysis for a German metropolitan area, Transp Res Part A Policy Pract, 46, 285-309, (2012)
[26] Wardman, M, Public transport values of time, Transp Policy, 11, 363-377, (2004)
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