Improper value of the parameter p in robust constraints will result in no feasible solutions while applying stochastic p-robustness optimization approach (p-SRO) to solving facility location problems under uncertainty. Aiming at finding the lowest critical p-value of parameter p and corresponding robust optimal solution, we developed a novel robust optimization approach named as min-p robust optimization approach (min-pRO) for P-median problem (PMP) and fixed cost P-median problem (FPMP). Combined with the nearest allocation strategy, the vertex substitution heuristic algorithm is improved and the influencing factors of the lowest critical p-value are analyzed. The effectiveness and performance of the proposed approach are verified by numerical examples. The results show that the fluctuation range of data is positively correlated with the lowest critical p-value with given number of new facilities. However, the number of new facilities has a different impact on lowest critical p-value with the given fluctuation range of data. As the number of new facilities increases, the lowest critical p-value for PMP and FPMP increases and decreases, respectively.

在应用随机 p 稳健性优化方法 (p-SRO) 解决不确定条件下的设施选址问题时，稳健约束中参数 p 的不正确值将导致没有可行的解决方案。为了找到参数 p 的最低临界 p 值和相应的鲁棒最优解，我们针对 P 中值问题 (PMP) 和固定成本 P 开发了一种新的鲁棒优化方法，称为 min-p 鲁棒优化方法 (min-pRO) -中值问题（FPMP）。结合最近分配策略，改进了顶点替换启发式算法，分析了最低临界p值的影响因素。通过数值例子验证了所提方法的有效性和性能。结果表明，在给定新设施数量的情况下，数据的波动范围与最低临界 p 值呈正相关。但是，在给定的数据波动范围内，新设施的数量对最低临界 p 值的影响不同。随着新设施数量的增加，PMP 和 FPMP 的最低临界 p 值分别增加和减少。