In practical integer optimization applications, perturbations of multiple cost coefficients often occur simultaneously. One important example is the perturbation of the probability distribution estimates for scenarios of a stochastic integer optimization cost function formulation. This study aims to develop multiple cost coefficients sensitivity theorems, which indicate that the optimal solution remains the same if the perturbation amount of cost coefficients is greater than or equal to the derived bounds. We developed two sensitivity theorems. One depends on the underlying algorithm, the iterative dual method proposed by Bell and Shapiro , and the other directly uses the optimal integer output that can be obtained by any algorithms. We carried out numerical experiments using the two proposed theorems separately to compare their effectiveness and computational tractability. These theorems are useful especially when dealing with the problems where the cost coefficients change frequently.

在实际的整数优化应用中，多个成本系数的扰动经常同时发生。一个重要的例子是随机整数优化成本函数公式场景的概率分布估计的扰动。本研究旨在开发多个成本系数敏感性定理，该定理表明，如果成本系数的扰动量大于或等于导出的界限，则最优解保持不变。我们提出了两个敏感性定理。一种依赖于底层算法，贝尔和夏皮罗提出的迭代对偶法，另一种直接使用任何算法都可以得到的最优整数输出。我们分别使用这两个提出的定理进行了数值实验，以比较它们的有效性和计算易处理性。这些定理在处理成本系数频繁变化的问题时特别有用。