会议安排数学模型.ppt

摘要 在这里，我们给出了一个求解该模型的迭代算法：首先，我们使用贪婪算法求得问题的初始可行解；然后，我们利用局部优化的原理，反复迭代，逐步逼近最优解；最终，我们可得到一个满意解。 我们认为，我们的算法相当好地解决了提出的问题。 对于有些委员可能临时缺席或者有些未被安排的人员出席会议的情况，我们也给出了一个调整算法。利用它，我们能够在原来的安排表的基础上，快速地得到新的安排方案。这种调整算法的优点在于它能够最少地改动安排方案来满足新的要求，从而更具有实际意义。 由于在前述的模型建立与求解的过程中，所使用的思想方法和技巧具有一般性，因此，模型很容易推广。我们针对题目的要求推广了模型，建立了一般会议安排模型。模型中的参数，例如参加会议的人数、与会者的类型数和参与的不同层次数均是可变的。该模型及算法均能够得出相当好的结果。 本模型有以下优点： (1)它相当成功地解决了提出的问题,并能够迅速地求出一组相当优化的解。 (2)本模型具有普遍的意义，能针对不同情况，根据不同参数，得到令人满意的结果。 (3)在模型求解过程中,运用了大量的优化思想和数学技巧，相当好地解决了多变量非线性整数规划问题,具有较大的应用价值。 Problem B: Mix Well For Fruitful Discussions Small group meeting for the discussion of important issues, particularly long-range 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 the risk of control by a dominant personality. In an attempt to reduce this dangue it is common to schedule several sessions with a diffent mix of people in each group. Problem B: Mix Well For Fruitful Discussions A meeting of An Tostal Corporation will be attended by 29 Board Members of which nine are in-house 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 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. Problem B: Mix Well For Fruitful D