MCM Problem A
1997 MCM Problem B
Small group meetings are gaining popularity for the discussion of
important issues, particularly long range planning. It is believed that
large groups stymie productive discussion and a dominant personality
will usually control and direct the discussion.
Thus in Corporation Board meetings the Board will meet in small
groups to discuss issues before meeting as a whole. These smaller groups
still run the risk of control by a dominant personality.
In an attempt to reduce this danger it is common to schedule
several sessions with a different mix of people in the groups.
A meeting of An Tostal Corporation will be attended by 29 Board
Members of which 9 are in-house members (ie. employees of the
corporation). The meeting
is to be an all-day affair with 3 sessions scheduled for the morning and
4 for the afternoon. The
sessions will each be 45 minutes, beginning on the hour from 9:00 AM to
4:00 PM with lunch scheduled at noon Each morning session will consist
of six discussion groups with each discussion group led by one of the
Corporation's six senior officers. None of these officers are Board
members. Thus each senior officer will lead three different discussion
groups. The senior officers
will not be involved in the afternoon sessions and each of these
sessions will consist of only four different discussion groups.
The president wants a list of board member assignments to discussion groups for each of the seven sessions. The assignments should achieve as much mix of the members as possible. The ideal assignment would have each board member in a discussion group with each other board member the same number of times while minimizing common membership of groups for the different sessions.