多次分组会议安排的最佳混合方案

本文在仔细分析问题条件和要求的基础上,运用了运筹学、图论、矩阵理论和置换等方面的知识和技巧,建立了一个布尔规划模型。

An Assignment Model for Fruitful Discussion

We are asked to solve a practical problem**giving a list of assignment for meeting. On the base of analyzing the conditions and requirements, using the knowledges and skills of operational reseach, graph theory, theory of matrix and permutation and so on we present the Boolean programming model. Because the objective function of the model is nonlinear,and there are too many variables in the model,it is quite difficult to solve it with the general methods of the integer programming. We give a iterative algorithm to solve our model: Firstly, we use the greedy algorithm to get the initial feasible solution . Then we use the principle of local optimizing, iterate repeatedly to approach the optimal solution . Finally we get a satisfisfactory result. We believe that our algorithm solve the given problem quite well. To the possibility of the state that some board members will cancel at the last minute or that some not scheduled will show up, we give an adjust method. By using this method, we can give the new assignments quickly on the base of the original assignments. The strength of the adjust method is that it makes the least change of the assignments . In the course of designing and resolving the model above, the ideas and skills have generality. So it is easy to be extended. We aim at the requirements of the problem to extend our model and establish the general model for the assignments of actual meeting. The parameters such as the sum of the members, the number of the types of attendee and the different of levels of participation are also able to change. The model and the algorithm can always give quite good solution. The model has the following advantages:(1) It solves the given problem successfully. And it can give a group of quite optimized solution quickly.(2) The model is of universal significance. It can give quite good solution according to different parameters in different cases.(3) In the course of solving problem, we use much thought of optimizing and mathematics skills so that we solve the problem of integer nonlinear programming of several variables successfuly.lt has a lot of application.