A note on a symmetrical set covering problem: The lottery problem

In a lottery, n numbers are drawn from a set of m numbers. On a lottery ticket we fill out n numbers. Consider the following problem: what is the minimum number of tickets so that there is at least one ticket with at least p matching numbers? We provide a set-covering formulation for this problem an...

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Veröffentlicht in:	European journal of operational research 2008-04, Vol.186 (1), p.104-110
Hauptverfasser:	Jans, Raf, Degraeve, Zeger
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Exact sciences and technology Integer programming Lotteries Lottery problem Mathematical problems Operational research. Management science Set covering problem Studies Symmetry
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	In a lottery, n numbers are drawn from a set of m numbers. On a lottery ticket we fill out n numbers. Consider the following problem: what is the minimum number of tickets so that there is at least one ticket with at least p matching numbers? We provide a set-covering formulation for this problem and characterize its LP solution. The existence of many symmetrical alternative solutions, makes this a very difficult problem to solve, as our computational results indicate.
ISSN:	0377-2217 1872-6860
DOI:	10.1016/j.ejor.2007.01.039