Advertisement

Aggregation techniques for frequency assignment in public transportation

  • Benjamin OttoEmail author
Original Paper
  • 33 Downloads

Abstract

In public transportation, frequency assignment is a sub-problem of line planning which is responsible for assigning each route of a line a certain frequency with which they are serviced by vehicles. Frequency assignment is among the most important decision problems for optimizing the waiting times in a transportation network and is often a very complex matter. This paper focuses on different aggregation techniques for reducing the computational effort to obtain (near-)optimal line frequencies. In detail, the influence of different model formulations and strategies for customer input data aggregation are investigated. For this purpose, six models are provided, their computational complexity is investigated and suitable mixed-integer mathematical programs are developed. These models vary in the levels of line utilization detail and predict the resulting travel times. Both aggregation techniques are evaluated according to their influence on the solution quality, which is determined by the transport suppliers’ point of view as forecast accuracy of the weighted number of customers using the transport. This comprehensive computational study reveals that some model formulations reduce the computational effort considerably by only small losses in line frequency quality. Furthermore, dramatically compressed customer data lead to (near-)optimal line frequencies.

Keywords

Public transportation Line planning Frequency assignment Revenue maximization Aggregation techniques 

References

  1. Aarts H, Verplanken B, Knippenberg A (1998) Predicting behavior from actions in the past: repeated decision making or a matter of habit? J Appl Soc Psychol 28(15):1355–1374Google Scholar
  2. Assad AA (1980) Models for rail transportation. Transp Res Part A Policy Pract 14:205–220Google Scholar
  3. Berliner Verkehrsbetriebe (ed) (2016) Annual report 2015. Berliner Verkehrsbetriebe, BerlinGoogle Scholar
  4. Black A (1990) The Chicago area transportation study: a case study of rational planning. J Plan Educ Res 10(1):27–37Google Scholar
  5. Borndörfer R, Grötschel M, Pfetsch ME (2008) Models for line planning in public transport. In: Hickman M, Mirchandani P, Voß S (eds) Computer-aided systems in public transport, vol 600. Lecture notes in economics and mathematical systems. Springer, New York, pp 363–378Google Scholar
  6. Bruno G, Gendreau M, Laporte G (2002) A heuristic for the location of a rapid transit line. Comput Oper Res 29(1):1–12Google Scholar
  7. Bussieck MR (1998) Optimal lines in public rail transport. Ph.D. thesis, TU Braunschweig, GermanyGoogle Scholar
  8. Bussieck MR, Kreuzer P, Zimmermann UT (1997) Optimal lines for railway systems. Eur J Oper Res 96(1):54–63Google Scholar
  9. Caprara A, Kroon L, Monaci M, Peeters M, Toth P (2007) Passenger railway optimization. In: Barnhart C, Laporte G (eds) Transportation. Handbooks in operations research & management science, vol 14. North Holland, Amsterdam, pp 129–187Google Scholar
  10. Caprara A, Kroon L, Toth P (2011) Optimization problems in passenger railway systems. In: Cochran J, Cox L, Keskinocak P, Kharoufed J, Smith JC (eds.) Wiley encyclopedia of operations research and management science, vol 6. Wiley, New York, pp 3896–3905.  https://doi.org/10.1002/9780470400531.eorms0647 Google Scholar
  11. Ceder A, Wilson NH (1986) Bus network design. Transp Res Part B Methodol 20(4):331–344Google Scholar
  12. Chowdhury S, Chien S (2001) Optimization of transfer coordination for intermodal transit networks. Transportation Research Board Annual Meeting, Washington, DCGoogle Scholar
  13. Chua TA (1984) The planning of urban bus routes and frequencies: a survey. Transportation 12(2):147–172Google Scholar
  14. Constantin I, Florian M (1995) Optimizing frequencies in a transit network: a nonlinear bi-level programming approach. Int Trans Oper Res 2(2):149–164Google Scholar
  15. Cordeau JF, Toth P, Vigo D (1998) A survey of optimization models for train routing and scheduling. Transp Sci 32:380–404Google Scholar
  16. Desaulniers G, Hickman MD (2007) Public transit. In: Barnhart C, Laporte G (eds) Transportation. Handbooks in operations research & management science, vol 14. North Holland, Amsterdam, pp 69–127Google Scholar
  17. Dufourd H, Gendreau M, Laporte G (1996) Locating a transit line using tabu search. Locat Sci 4(1):1–19Google Scholar
  18. Elbassioni K, Raman R, Ray S, Sitters R (2009) On profit-maximizing pricing for the highway and tollbooth problems. In: Mavronicolas M, Papadopoulou VG (eds) Algorithmic game theory, vol 5814. Lecture notes in computer science. Springer, New York, pp 275–286Google Scholar
  19. Evans JR (1983) A network decomposition/aggregation procedure for a class of multicommodity transportation problems. Networks 13(2):197–205Google Scholar
  20. Francis RL, Lowe TJ, Rayco MB, Tamir A (2003) Exploiting self-canceling demand point aggregation error for some planar rectilinear median location problems. Nav Res Logist 50(6):614–637Google Scholar
  21. Frank L, Bradley M, Kavage S, Chapman J, Lawton TK (2008) Urban form, travel time, and cost relationships with tour complexity and mode choice. Transportation 35(1):37–54Google Scholar
  22. Furth PG, Wilson NH (1981) Setting frequencies on bus routes: theory and practice. Transp Res Rec 818:1–7Google Scholar
  23. Gao Z, Sun H, Shan LL (2004) A continuous equilibrium network design model and algorithm for transit systems. Transp Res Part B Methodol 38(3):235–250Google Scholar
  24. Garg N, Vazirani VV, Yannakakis M (1997) Primal-dual approximation algorithms for integral flow and multicut in trees. Algorithmica 18(1):3–20Google Scholar
  25. Goossens J-W (2004) Models and algorithms for railway line planning problems. Dissertation, Maastricht UniversityGoogle Scholar
  26. Goossens J-W, Van Hoesel S, Kroon L (2004) A branch-and-cut approach for solving railway line-planning problems. Transp Sci 38(3):379–393Google Scholar
  27. Groß DRP, Hamacher HW, Horn S, Schöbel A (2009) Stop location design in public transportation networks: covering and accessibility objectives. Top 17(2):335–346Google Scholar
  28. Guihaire V, Hao JK (2008) Transit network design and scheduling. A global review. Transp Res Part A Policy Pract 42(10):1251–1273Google Scholar
  29. Hamacher HW, Liebers A, Schöbel A, Wagner D, Wagner F (2001) Locating new stops in a railway network. Electron Notes Theor Comput Sci 50(1):229–242Google Scholar
  30. Han AF, Wilson NH (1982) The allocation of buses in heavily utilized networks with overlapping routes. Transp Res Part B Methodol 16(3):221–232Google Scholar
  31. Hu TC (1969) Integer programming and network flows. Addison-Wesley, ReadingGoogle Scholar
  32. Huisman D, Kroon LG, Lentink RM, Vromans MJCM (2005) Operations research in passenger railway transportation. Statistica Neerlandica 59(4):467–497Google Scholar
  33. Ibarra-Rojas OJ, Delgado F, Giesen R, Muñoz JC (2015) Planning, operation, and control of bus transport systems. A literature review. Transp Res Part B Methodol 77:38–75Google Scholar
  34. Klier MJ, Haase K (2008) Line optimization in public transport systems. In: Kalcsics J, Nickel S (eds) Operations research proceedings 2007. Springer, Berlin, pp 473–478Google Scholar
  35. LeBlanc LJ (1988) Transit system network design. Transp Res Part B Methodol 22(5):383–390Google Scholar
  36. Martínez H, Mauttone A, Urquhart ME (2014) Frequency optimization in public transportation systems: formulation and metaheuristic approach. Eur J Oper Res 236(1):27–36Google Scholar
  37. Rogers DF, Plante RD, Wong RT, Evans JR (1991) Aggregation and disaggregation techniques and methodology in optimization. Oper Res 39(4):553–582Google Scholar
  38. Ryals L (2008) Determining the indirect value of a customer. J Mark Manag 24(7–8):847–864Google Scholar
  39. Salzborn FJ (1972) Optimum bus scheduling. Transp Sci 6(2):137–148Google Scholar
  40. Schéele S (1980) A supply model for public transit services. Transp Res Part B Methodol 14(1):133–146Google Scholar
  41. Schöbel A (2006) Optimization in public transportation: stop location, delay management and tariff zone design in a public transportation network. Springer, New YorkGoogle Scholar
  42. Schöbel A (2012) Line planning in public transportation: models and methods. OR Spectr 34(3):491–510Google Scholar
  43. Schöbel A, Scholl S (2005) Line planning with minimal travelling time. In: Kroon LG, Möhring RH (eds) 5th workshop on algorithmic methods and models for optimization of railways (ATMOS 2005). Dagstuhl Publishing, Saarbrücken, pp 1–16Google Scholar
  44. Spiess H, Florian M (1989) Optimal strategies: a new assignment model for transit networks. Transp Res Part B Methodol 23(2):83–102Google Scholar
  45. Verband Deutscher Verkehrsunternehmen (ed) (2015) Annual report for 2014/2015. Verband Deutscher Verkehrsunternehmen e.V., CologneGoogle Scholar
  46. Yu B, Yang Z, Yao J (2010) Genetic algorithm for bus frequency optimization. J Transp Eng 136(6):576–583Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Lehrstuhl für Operations ManagementFriedrich-Schiller-Universität JenaJenaGermany

Personalised recommendations