本研究根據兩種不同的整數規劃演算法發展多維參數敏感度分析，此演算法分別為Bell和Shapiro(1975)提出的迭代對偶法以及分枝界限法，兩種演算法求解過程中不斷加入限制式至原問題中，因此我們可以利用求解過程中得到的資訊建立對偶問題，並進一步計算定理所需的閾值。根據本研究所提出的敏感度分析定理，在主問題與對偶問題強對偶成立的條件下，當目標係數的變化量不小於此閾值，則最佳解維持不變。最後，我們分別將提出的理論應用於多維參數目標係數變動問題的數值實驗中，並比較結果及計算效率。

This study develops multi-parametric cost coefficient sensitivity analysis theorems for integer programs from two different algorithms: the iterative dual method proposed by Bell and Shapiro (1975) and the branch and bound algorithm. We develop post-optimality analysis theorems, which indicate that the optimal solution remains optimal if the change of cost coefficients is not less than the thresholds. The theorem implies that with information as byproduct of these two algorithms, the thresholds can be computed. We carry out numerical experiments with multi-parametric cost perturbation problems using two proposed theorems separately and compare the results and computational tractability.

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