Abstract
近年來, 多目標線性規劃問題的容忍度分析逐漸受到重視。但是關於這方面的論文, 均假設決策者能提供權重, 來明確的表達他的偏好結構。所以, 這些研究僅考慮一個非凌越端點的容忍度分析, 也就是決策者最偏好解的分析。然而, 除非決策者非常瞭解自己所面對的決策問題, 否則單一方案並不足以提供有效的決策資訊。所以, 為了提供更完整的資訊以做為決策的參考, 對對非凌越集做容忍度分析是有必要的。為了達成研究的目標, 我們對以下三種情況進行非凌越集的容忍度分析, 分別是 (1)變動成本係數,(2)變動資源限制,(3)同時變動成本係數和資源限制。 P.L.Yu和M.Zeleny提出了一個理論, 說明一個非凌越集可被分割成有限個非凌越面。以這個理論為基礎, 我們有系統的說明如何由非凌越端點的容忍區域,推得非凌越集的容忍區域。本文分為五章, 第一章介紹提要。第二章則作文獻回顧。在第三章中則探討前述三種變動的理論結果。在第四章中, 首先對這三種變動容忍度分析的方法作一探討, 次則提出對應之演算法。在最後一章中我們作一總結, 並且對未來可能接續之探討提出部份的論述。Tolerance analysis in multiple objective linear programmes hasbeen drawn much attention in recent years. All of these paperswere assumed that a decision maker can provide his/herpreference structure as a weight of importance explicitly, sothe sensitivity analysis was done on one nondominated extremepoint only. That is, the most preferred solution by the DM.However, DM may not realize his/her preference structure.Moreover, the final decision is not necessarily a nondominatedextreme point. Instead, it can be any nondominated point.Therefore, it is necessary to analyze the entire nondominatedset in order to provide more complete information for decisionmakings. To achieve our aim of study, three cases areconsidered in the tolerance analysis of a nondominated set: (1)when the cost coefficients are perturbed, (2) when the RHS isperturbed, (3) when both the cost coefficients and the RHS areperturbed simultaneously. P.L.Yu and M.Zeleny have presented atheory which shows that a nondominated set can be divided intoa group of nondominated faces. Based on the theory, we proposea method to obtain the tolerance region of a nondominated setfrom the tolerance regions of nondominated extreme pointssystematically.