Title: Finding optimal realignments in sports leagues using a branch-and-cut-and-price approach

Authors: Xiaoyun Ji, John E. Mitchell

Addresses: Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th St., Troy, NY 12180, USA. ' Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th St., Troy, NY 12180, USA

Abstract: The sports team realignment problem can be modelled as k-way equipartition: given a complete graph K_n = (V, E), with edge weight c_e on each edge, partition the vertices V into k divisions that have exactly S vertices, so as to minimise the total weight of the edges that have both endpoints in the same division. In this paper, we discuss solving k-way equipartition problem using branch-and-price scheme. We demonstrated the necessity of cutting planes for this problem and suggested an effective way of adding cutting planes in the branch-and-price framework. We solved the pricing subproblem as an integer programming problem. Using this method, we found the optimal realignment solution for three major professional sports leagues in North America (basketball, hockey, football). We also present computational results on some larger randomly generated microaggregation problems.

Keywords: graph equipartition; branch-and-price; clustering; microaggregation; sports team realignment; NBA; National Basketball Association; National Hockey League; NHL; National Football League; NFL; sports leagues.

DOI: 10.1504/IJOR.2005.007436

International Journal of Operational Research, 2005 Vol.1 No.1/2, pp.101 - 122

Published online: 20 Jul 2005 *

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