求解多准则决策问题指标权重的二次规划方法

在多准则决策过程中,由于信息不完全从而造成准则权重系数不能完全确定并最终导致决策困难的现象经常存在。针对此类问题,分析并形式化描述了三类准则权重约束,即基本约束关系、由经验判断给定的不完备权重约束关系、由数据包络分析方法确定的DEA有效性所隐含的权重约束关系。综合以上约束并以所有可选方案到理想解的距离平方和最小为目标建立了二次规划模型,通过转化为线性规划模型进行求解从而求得最佳权重,该权重可作为理想解法的基础。最后通过项目招标的实例验证了本方法的有效性。

Quadratic programming approach to determine the weights in multiple criteria decision making problems

It is not uncommon during the process of multiple criteria decision making that the weights of criteria cannot be completely determined due to the partial information,which results in the difficulty of decision.To solve this problem,first,three types of constraints on weights are differentiated and formerly described.They consist of the basic constraints,the imperfection constraints originating from the judgment by experience,and the implicit constraints due to the DEA efficiency determined by the DEA approach.Then a quadratic programming model is constructed by synthesizing all these constraints,in which the minimum square sum of distance to the ideal solution of all alternatives serves as the objective.This model can then be transformed to a linear programming model and be solved to get the prefect weights that are the basis of the TOPSIS approach.Finally,an example about the project bidding is given to show the feasibility and effectiveness of this method.