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master's thesis
Network optimization in railway transport planning
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:138780
Jusup, Matej
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Jusup, M. (2017). Network optimization in railway transport planning (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:138780

Jusup, Matej. "Network optimization in railway transport planning." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:138780

Jusup, Matej. "Network optimization in railway transport planning." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:138780

Jusup, M. (2017). 'Network optimization in railway transport planning', Master's thesis, University of Zagreb, Faculty of Science, accessed 22 March 2025, https://urn.nsk.hr/urn:nbn:hr:217:138780

Jusup M. Network optimization in railway transport planning [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2025 March 22] Available at: https://urn.nsk.hr/urn:nbn:hr:217:138780

M. Jusup, "Network optimization in railway transport planning", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:138780

Metadata
TitleNetwork optimization in railway transport planning
AuthorMatej Jusup
MentorMarko Vrdoljak (mentor)
MentorAndreas Dress (mentor)
VIAF: 19759435
Committee memberMarko Vrdoljak (predsjednik povjerenstva)
Committee memberVjekoslav Kovač (član povjerenstva)
Committee memberMaja Starčević (član povjerenstva)
Committee memberMiljenko Marušić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-02-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
This work is dealing with train timetabling problem. In the first chapter, one can find an introduction to network flows which is needed for understanding deeper concepts later on. Namely, basic graph theory definitions are stated as well as core problems like the minimum cost flow and shortest path problem. Furthermore, two equivalent representations of network flows are described, including some useful properties connected to each of them. At the end of the chapter, linear programming and... More simplex method are introduced into some detail. In the second chapter more complex theory is introduced. At the beginning, multi-commodity flow problem is stated and few solutions approaches are briefly described. Once we settled for one of them, the rest of the chapter is dealing with Lagrangian relaxation and column generation techniques. Since column generation is the main result needed for solving our problem, some finer results, like determining lower and upper bounds, are stated. In the last, third chapter, one can find a model for representing train timetabling problem for a single line network. That model was introduced by Valentina Cacchiani in her Ph.D. thesis. In this work, periodicity of timetable is assumed because it makes computations way quicker, as well as it has some other benefits. At the end, one can find an algorithm based on column generation technique for solving introduced model. That algorithm is based on 6 steps, and after reading this work, one should be able to fully understand each of them. Less
Abstract (croatian)
Ovaj rad bavi se problemom rasporeda vožnje u željezničkom prometu. U prvom poglavlju nalazi se uvod u mrežne tokove koji je potreban za razumijevanje naprednijih koncepata. Konkretno, iskazane su osnovne definicije teorije grafova kao i neki temeljni problemi poput problema najjeftinijeg toka i problema najkraćeg puta. Nadalje, opisana su dva ekvivalenta prikaza mrežnih tokova, uključujući neka korisna svojstva za svaki od njih. Na kraju poglavlja, linearno programiranje i simpleks... More metoda, objašnjeni su na razini razumijevanja. U drugom poglavlju nalazi se naprednija teorija koja se nadovezuje na prvo poglavlje. Na početku poglavlja prikazan je problem više dobara, kao i nekoliko pristupa rješavanju navedenog problema. Nakon što smo se odlučili za jedan od pristupa, ostatak poglavlja bavi se Lagrangeovom relaksacijom i metodom generacije stupaca. Kako je upravo metoda generacije stupaca najvažniji rezultat za rješavanje našega problema, napredniji rezultati vezani uz određivanje donjih i gornjih granica su detaljno objasnjeni. U posljednjem, trećem poglavlju, nalazi se model za prikazivanje problema rasporeda vožnje za mreže s jednom tračnicom. Navedeni model prvi puta je predstavljen u doktorskom radu Valentine Cacchiani. U ovom radu također pretpostavljamo periodičnost rasporeda vožnje kako bismo, između ostalih, ostvarili prednost poput bržeg vremena računanja. Na kraju rada nalazi se algoritam, temeljen na metodi generacije stupaca, za rješavanje predstavljenog modela. Navedeni algoritam sastoji se od 6 koraka, od kojih je svaki detaljno opisan u ovome radu. Less
Keywords
Keywords (croatian)
Languageenglish
URN:NBNurn:nbn:hr:217:138780
Study programmeTitle: Mathematical Statistics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2018-02-27 13:01:58
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