二层决策问题的灵敏度分析(2)

The Sensitivity of Bilevel Decision Making Problem(2)

二层决策系统包含着两个最优化决策问题,其中上层决策问题的目标值是由下层决策的解所隐含地确定的.本文研究了二层决策问题的另一方面的灵敏度分析问题,讨论了上层决策者的价值系数发生变化而二层决策问题的最优解不变所产生的灵敏度分析问题.为了确定二层决策问题价值系数发生变化的范围,首先我们给出了灵敏度分析的基本方法,结合“k th-best”算法我们又给出了灵敏度分析的操作步骤.在所确定的变化范围内,价值系数的变化,不会引起二层决策问题的全局最优解的变化,从而为决策者提供了相对稳定的决策方案.最后我们给出了数值实例,它表明本文所给出的灵敏度分析的方法是正确的.

The bilevel decision making system involves two optimization problems where the data of the upper level decision making problem is implicitly determined by the solution of the lower one. In this paper, an another research about the sensitivity of the bilevel decision making problem is introduced, we discuss the problem of sensitivity when the price coefficients of the upper level decision making problem are modified and the optimal solution of the bilevel decision making problem is unchangeable. In order to determine the changeable range of the price coefficient,at first, the basic method of the sensitivity is presented, and the procedure of the sensitivity is also provided by using ＂the kth-best＂algorithm. In the range determined by us, the change of the price coefficients can not make the optimal solution of the bilevel decision making problem modify, so it can provide decision makers an relatively stable decision making schema. Last, the changeable range of the price coefficients is demonstrated in an example.