Takustraße 7 Konrad-Zuse-Zentrum D-14195 Berlin-Dahlem fur¨ Informationstechnik Berlin Germany SATOSHI ITO1,YUJI SHINANO2 Calculation of clinch and elimination numbers for sports leagues with multiple tiebreaking criteria 2 The Institute of Statistical Mathematics and the Graduate University for Advanced Studies, 10-3 Midoricho, Tachikawa, Tokyo 190-8562, Japan,
[email protected] 3 Zuse Insitute Berlin, Takustr. 7, 14195 Berlin, Germany,
[email protected] The work of the first author was supported by JSPS KAKENHI Grant Number 15K00041. The work for this article has been partly conducted within the Research Campus MODAL funded by the German Federal Ministry of Education and Research (BMBF grant number 05M14ZAM). ZIB-Report 18-51 (September 2018) Herausgegeben vom Konrad-Zuse-Zentrum f¨urInformationstechnik Berlin Takustraße 7 D-14195 Berlin-Dahlem Telefon: 030-84185-0 Telefax: 030-84185-125 e-mail:
[email protected] URL: http://www.zib.de ZIB-Report (Print) ISSN 1438-0064 ZIB-Report (Internet) ISSN 2192-7782 Calculation of clinch and elimination numbers for sports leagues with multiple tiebreaking criteria Satoshi Ito, Yuji Shinano The Institute of Statistical Mathematics and the Graduate University for Advanced Studies, 10-3 Midoricho, Tachikawa, Tokyo 190-8562, Japan Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany
[email protected],
[email protected] September 27, 2018 Abstract The clinch (elimination) number is a minimal number of future wins (losses) needed to clinch (to be eliminated from) a specified place in a sports league. Several optimization models and computational results are shown in this paper for calculating clinch and elimination numbers in the presence of predefined multiple tiebreaking criteria.