本論文是探討半指派問題的敏感度分析。在實務上，公司內部的人力配置，常會有相似的工作或任務需求，因此，配置人力時就會有分組作業的情況產生。此時，傳統的一對一指派特性，就不適用於此情況。而半指派分配的模型為將每個人指派到各組，此模型適用於具有相同工作或任務需求的分配上。另外，由於半指派分配的高度退化特性，導致於傳統的敏感度分析方法，在要求最佳解基底不變下所求出的敏感度分析擾動範圍，並不符合實際狀況。
此論文所提出的半指派分派敏感度分析則考慮到退化解所造成的退化基底問題。為了克服此問題，我們在尋求敏感度分析範圍時，只須要求正值基底不變，而退化基解可以改變。如此一來，基底的退化解可以選擇退出，替代新的退化解進入，而不改變最佳指派的狀態。因此當遇到有退化解時，使用此方法，可以獲得較傳統敏感度分析的範圍更寬敞的結果。本論文中，我們提出了一演算法來以得各成本係數的敏感度分析範圍。我們也進一步使用了一個例子來解釋此演算法的流程。最後，亦提供數據分析的結果以顯示此演算法的效率。

關鍵字:半指派問題，敏感度分析，退化

This thesis concentrates on sensitivity analysis of the semi-assignment problem (AP). Since there are identical tasks or works to be assigned in a company, the semi-AP can be more practical as a planning tool then classic assignment problem. Due to the high degeneracy of the semi-AP, traditional sensitivity analysis, which decides the perturbed range where the current optimal basis remains optimal, is impractical.
Advanced sensitivity analysis of the semi-AP we proposed in this study is concerned with obtaining the perturbed range of cost coefficients that can be perturbed without the current positive variable set changing, but allowing the change of the degenerate basic variables or move to other extreme point when multiple optimal solution occurs. Concerning high degeneracy of the semi-AP, we can broaden the perturbed range by allowing that basis changing, as long as maintaining the same positive variable set of the current problem. In this thesis we propose an algorithm for determining the perturbed range of the assigned and unassigned cell. An illustrative example is presented in order to demonstrate the procedure of the proposed algorithm. Computational results will also provide to demonstrate the efficiency of the proposed algorithm.

Keywords:
Semi-assignment problem, sensitivity analysis, degeneracy.

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