mcm1997B Mix Well For Fruitful Discussions 开会决策美国数学建模 - matlab数学建模

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标题：mcm1997B Mix Well For Fruitful Discussions 开会决策美国数学建模
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所属分类: 数学建模资源类型：文档文件大小: 5.57 KB 上传时间: 2019-08-19 21:00:24 下载次数: 905 资源积分：1分提供者: jiqiren 20190819090108134

内容：
(MCM 1997B)

Small group meetings for the discussion of important issues, particularly long-rang planning, are gaining popularity. It is believed that large groups discourage productive discussion and that a dominant personality will usually control and direct the discussion. Thus, in corporate board meetings the board will meet in small groups to discuss issues before meeting as a whole. These smaller groups still run 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 each group.

A meeting of a Tostal Corporation will be attended by 29 Board Members of which nine are in-horse members (i.e., corporate employees). The meeting is to be an all-day affair with three sessions scheduled for the morning and four for the afternoon. Each session will take 45 minutes, beginning on the hour from 9:00 A.M. to 4:00 P.M., with lunch scheduled at noon. Each morning session will consist of six discussions group with each discussion group led by one of the corporation's six senior officers. None of these of officers are board members. Thus each senior officer will lead three different discussion groups. The sessions will consist of only four discussion groups.

The president of the corporation wants a list of board-member assignments to discussion group for each of seven sessions. The assignments should achieve as much of a mix of members as much as possible. The ideal assignment would have each board member with each other board member in a discussion group the same number of times while minimizing common membership of groups for the different sessions.

The assignments should also satisfy the following criteria:

1.For the morning sessions, no board member should be in the same senior officer's discussion group twice.

2.No discussion group should contain a disproportionate number of in-house members.

Give a list of assignments for members 1-9 and 10-29 and officers 1-6. Indicate how well the criteria in the precious paragraphs are met. Since it is possible that some board members will cancel at the last minute or that some not scheduled will show up, an algorithm that the secretary could use to adjust the assignments with an user to make assignments for future meetings involving different levels of participation for each type of attendee.

为取得富有成果的讨论怎样搭配与会成员(美国竞赛1997年B题)

为讨论重要问题，特别是长远规划问题而召开小组讨论会正变得愈来愈普遍。人们相信有很多人参加的会妨碍有成果的讨论，甚至一位占支配地位的人能控制并操纵会议的讨论。因此，在公司的董事会议中在召集全体董事会议之前会先开一些讨论有关事务的小组会议。这些规模较小的小组会议仍然有被某个占支配地位的人控制的危险。为降低这种危险，常用的办法是安排每个小组开几次会，每次会有不同的人参加.

An Tostal公司的一次会议的参加者为29位公司董事会成员，其中9位是在职董事(即公司的雇员)。会议要开一天，每个小组上午开3段。下午开4段。每段会议开45分钟，从上午9：00到下午4：00每整点开始开会，中午12：00午餐。上午的每段会议都有6个小组讨论会，每个小组讨论会都由公司的一位资深高级职员来主持讨论，这些资深高级职员都不是董事会的成员。因此，每资深高级职员都要主持3个不同的小组讨论会。这些资深高级职员不参加下午的讨论会，而且下午的每段会议只有4个不同的小组讨论会。

公司董事长要一份公司董事参加7段会议的每个小组讨论会酌分配名单。这份搭配名单要尽可能多地把董事均匀搭配。理想的搭配应是每一位董事和其他每一位董事一起参加小组讨论会的次数相同，与此同时要使不同段的小组中在一起开过会的董事数达到最小。

名单中的搭配还应满足下列两个准则：

①在上午的讨论会上，不允许一位董事参加由同一位资深高级职员主持的两次会议。

②每个分组讨论会都不应有不成比例的在职董事参加。

给出一张1-9号在职董事、10一29号董事、1-6号公司资深高级职员的搭配名单。说明该名单在多大程度上满足了前面提出的各种要求和准则。因为有的董事可能在最后一刻宣布不参加会议，也可能不在名单上的董事将出席会议，因此一个能使秘书在一小时前得到变更与会与否通知的情况下来调整搭配的算法定会得到赏识。如果算法还能用于涉及不同水平的与会者参加的未来的会议中每类与会者搭配的话，那就更理想了。

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mcm1997B Mix Well For Fruitful Discussions 开会决策 .doc