 Homogeneous optimal fleetI. Gertsbakh and Yuri Gurevich Transportation Research Part B: Methodological, 1982, vol. 16, issue 6, 459-470 Abstract: The structure of chains in the optimal chain decomposition of a periodic schedule S is investigated. A finite oriented graph termed the Linis Graph (LG) is defined which serves as the key for this investigation. The edges of the LG are trip-types of S and the vertices of the LG represent terminals. It is proved that there is an Euler cycle for a connected LG satisfying natural precedence relations between arrival and departure times. Expansion of this cycle in a real time gives a "master-chain" of trips which, being repeated periodically, gives an infinite periodic chain. Time-shifted periodic replication of this chain allows obtaining a group of twin-type periodic chains forming an optimal fleet over S. It is proved that if the LG has m connected components then there is an optimal fleet consisting of m groups of similar periodic chains. It is shown that if the graph of terminals is connected and the LG is disconnected then it is possible to obtain a twin-type fleet over S by adding to S "dummy" trip-types. A general approach to constructing a twin-type fleet of minimal size for this case is described. The relation of the theory developed to the so-called center problem is discussed. Date: 1982 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:transb:v:16:y:1982:i:6:p:459-470 Ordering information: This journal article can be ordered from Access Statistics for this article Transportation Research Part B: Methodological is currently edited by Fred Mannering More articles in Transportation Research Part B: Methodological from Elsevier |
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